bluuebunny/crossref_metadata_2025 huggingface dataset:
Biogenese der Betalaine Biotransformation von Dopa und Tyrosin in den Betalaminsäureteil des Betanins. Vorläufige Mitteilung
Authors: Miller H. E. , Rösler H. , Wohlpart A. , Wyler H. , Wilcox M. E. , Frohofer H. , Mabry T. J. , Dreiding André S.
Published: December 2004

During studies on the biogenesis of betalains (I) in cactus fruits (Opuntia sp.). DL‐dopa‐1‐[14C] and ‐2‐[14C] were incorporated into betanin (III) which was obtained radiopure after crystallization. The specific activity remained constant after conversion to betanidin (IV) and to a neobetanidin derivative (IX). Reaction of radiobetanin with proline afforded indicaxanthin (V) carrying more than 90% of the radioactivity. Dopa (VI) is thus an efficient precursor for betalamic acid (VIII) but not for cyclodopa (VII). Decarboxylation of radiobetanidin and radioindicaxanthin showed that the carboxyl group of dopa remained a carboxyl group in the biotransformation to betalamic acid. It is concluded that the aromatic ring of dopa is cleaved and that re‐cyclization involving the nitrogen generates the dihydropyridine moiety. Under the same conditions mevalonic acid, aspartic acid and phenylalanine showed low incorporations. Studies with beet seedlings and DL‐dopa‐1‐[14C], ‐2‐[14C] and DL‐tyrosine‐1‐[14C] afforded similar results but with low incorporations.
Die Synthese von Cyclodopa (Leukodopachrom)
Authors: Wyler H. , Chiovini J.
Published: December 2004

The synthesis of the methylester of cyclodopa (5.6‐dihydroxy‐indoline‐2‐carboxylic acid) is achieved by oxidative conversion of dopa methyl ester to dopachrome methyl ester and its subsequent reduction at pH 8, using respectively potassium hexacyanoferrate(III) and sodium dithionite. The efficiency of the oxidation step was found to be dependent on the rather low concentration of the reactants and the very short reaction time involved. After its production cyclodopa methyl ester was stabilized by immediate protonation followed by acetylation leading in a high yield to O,O,N‐triacetyl cyclodopa methyl ester. By partial hydrolysis this derivative gives an O,N‐diacetyl cyclodopa methyl ester and further N‐acetyl cyclodopa methyl ester. Cyclodopa methyl ester and cyclodopa are obtained by prolonged anaerobic hydrolysis. Micro‐separation procedures, nmr‐, uv‐spectra and chiral‐optical properties of cyclodopa and its derivatives are reported and discussed. It is shown by nmr evidence that under acidic conditions the aromatic proton on C(7) of cyclodopa slowly exchanges with deuterium. When an alcoholic solution of cyclodopa methyl ester and semicarbazide is allowed to oxidize in the air, the semicarbazone of dopachrome methyl ester forms.
Über Pyrrolizidinchemie. 10. Mitteilung [1]. Synthese von (±)‐dehydroheliotridin
Authors: Viscontini M. , Gillhof‐Schaufelberger H.
Published: December 2004

Die Synthese von (±)‐Dehydroheliotridin, dem enzymatisch produzierten Hauptabbauprodukt der Alkaloide Lasiocarpin und Heliotrin, wird beschrieben. Als Edukt dient 1,6‐Dihydroxy‐2, 5‐dicyan‐hexatrien‐(1,3,5)‐dicarbonsäure‐(1,6)‐diäthylester, der mit β‐Alaninäthylester versetzt wird. Das erhaltene 1‐(2‐Äthoxycarbonyl‐äthyl)‐2‐äthoxycarbonyl‐3‐cyanpyrrol wird zu einer Tricarbonsäure hydrolysiert, dann verestert und schliesslich zu (±)‐1,6‐Diäthoxycarbonyl‐7‐oxo‐6, 7‐dihydro‐5H‐pyrrolizidin cyclisiert. Letzteres ergibt Dehydroheliotridin durch Verseifung, Decarboxylierung, Veresterung zu 1‐Methoxycarbonyl‐7‐oxo‐6, 7‐dihydro‐5K‐pyrrolizidin und anschliessende LiAH4‐Reduktion.
Physical and Chemical Characterization of Pig Kidney Particulate Aminopeptidase
Authors: Wacker Hans , Lehky Pavel , Fischer Edmond H. , Stein Eric A.
Published: December 2004

Pig kidney particulate aminopeptidase (EC 3.4.1.2) was purified by a modification of the procedure of Wachsmuth et al. [3] to a state of homogeneity according to criteria of ultracentrifugation and polyacrylamide gel electrophoresis, and some of its physical and chemical properties were determined.

The purified enzyme (specific activity 30 ± 3 μmoles leucine‐p‐nitroanilide hydrolyzed/min/mg) has a s20,w = 9.82 S at pH 8 and a molecular weight of about 280,000 as determined by high speed sedimentation equilibrium. Divergence between the number‐, weight‐ and z‐ average molecular weights, and a sharp decrease of these values at low protein concentration, suggest that one is dealing with an associating‐dissociating system.

Amino acid analysis revealed the presence of considerable quantities of carbohydrates in the enzyme. Colorimetric, gas chromatographic and enzymatic analyses demonstrated the presence of glucosamine, galactose, mannose, fucose and sialic acid residues in the ratio of 1:0.89:0.75: 0.13: 0.13, amounting to ca. 400 residues or 20% (56,000 daltons) of the molecular weight. With the exception of sialic acid, the carbohydrate content was remarkably constant from preparation to preparation.

Analyses by both atomic absorption spectrometry and the dithizone method showed that zinc–the only metal found in significant amount–was always present in the ratio of 2 atoms per molecule. It is therefore proposed that pig kidney particulate aminopeptidase is a Zn‐containing glycoportein.
Dünnschichtchromatographie als Hilfsmittel in der radiochemie. 6. Mitteilung. 1. Trennung von Sn, 125Sb und 125mTe. ‐ 2. Trennung von As, Sb und Sn
Authors: Seiler H.
Published: December 2004

1. Thin‐layer chromatography is applied to the separation of the nuclids of the decay‐chain: 125Sn → 125mTe. Different factors influencing the separation are investigated. The method can be used for the carrier‐free separation of 125mTe. 2. As, Sb and Sn have been separated by thin‐layer chromatography.
Etude par spectrométrie de masse du cyclopentanediol‐trans‐1,2
Authors: Singy G. A. , Buchs A.
Published: December 2004

The electron impact induced fragmentation of trans cyclopentane‐1, 2‐diol has been investigated using derivatives specifically labelled with deuterium and high‐resolution mass spectral data. The elimination of the elements of water from the molecular ion involves at least three mechanisms whose relative importance has been evaluated. A fragmentation scheme based upon metastable peaks and labelling is presented.
Kinetik und Mechanismus einer Dis‐Azokupplung. 22. Mitteilung zur kenntnis der azokupplungsreaktion
Authors: Gloor B. , Zollinger H.
Published: December 2004

The kinetics of the second step in the formation of a dis‐azocompound from 4,4′‐bis‐diazobiphenyl (bisdiazotized benzidine) with 2‐naphthol‐3,6‐disulfonic acid have been investigated at 25°C, ionic strength I = 0.01 in aqueous buffers (pH 6.78 to 7.71). As expected the reaction is first order with respect to the naphtholdisulfonate (triple) anion, but astonishingly it has only an apparent order n = 0.65 with respect to the electrophilic reagent. This order is due to an aggregation equilibrium in which dimeric and oligomeric aggregates are formed whose electrophilicity is at least 50 times lower than that of the monomeric diazonium ion.
Substituted 9‐Oxabicyclo[4.2.1]‐ and 9‐Oxabicyclo[3.3.1]nonanes (Part II)
Authors: Ganter C. , Duthaler R. O. , Zwahlen W.
Published: December 2004

The preparation, isolation, structure determination, and some reactions of the two stereoisomers of 2‐iodo‐9‐oxabicyclo[4.2.1]nonane (9 and 10) and of 2‐iodo‐9‐oxabicyclo[3.3.1]‐nonane (11 and 12), respectively, are described.

Iodine cleavage of the [4.2.1]‐iodomercuri compound 3 yielded the iodides 9, 10, and 11, and iododemercuration of the [3.3.1]‐iodomercuri compound 6 afforded the iodo compounds 9, 11, and 12, respectively. Direct treatment of 4‐cycloocten‐1‐ol (1) with iodine in chloroform resulted in the exclusive formation of the two endo‐iodides 9 and 11.

Raney nickel treatment as well as lithium aluminium hydride reduction of each índividual iodo compound 9, 10, 11, and 12 gave the corresponding unsubstituted 9‐oxabicyclononane (4 or 8, respectively) with the unaltered skeleton. No rearrangement products could be observed.

An oxonium ion is involved as an intermediate in the reaction of the endo‐iodides 9 and 11 with silver acetate leading to an identical mixture of the two acetates 15 and 16 as well as in the isomerization of 9 to 11.
Mechanismus der Bildung und des Zerfalls von Amidkomplexen, II. Ni2+ und N, N′‐Diglycyl‐äthylendiamin bzw. N, N′‐Diglycyl‐1,3‐diaminopropan
Authors: Kaden Th.
Published: December 2004

The kinetics of a two proton transfer between a blue octahedral and a yellow square planar nickel(II) complex with N, N′‐diglycylethylenediamine (I, n = 1) resp. N, N′‐diglycyl‐1, 3‐diaminopropane (I, n = 2) have been studied by spectrophotometry and pH‐stat technique. The structure of these complexes and the mechanism of their interconversion are discussed and their reactions are compared with the analogous reactions of the copper(II)‐N, N′‐diglycyl‐1, 3‐diamino‐propane complexes [1].
Sulfidkontraktion via alkylative Kupplung: Eine methode zur darstellung von β‐dicarbonylderivaten. Über synthetische methoden, 1. Mitteilung
Authors: Roth M. , Dubs P. , Götschi E. , Eschenmoser A.
Published: December 2004

The experiments described in reaction schemes 1–12 indicate that sulfide contraction via alkylative coupling (see scheme p. 729) is a potentially general method for the synthesis of secondary vinylogous amides and enolizable β‐dicarbonyl compounds.
Photochemische Umwandlungen, 42 [1] Photoisomerisierungen im 5‐Isopropyliden‐tetracyclo‐[4.3.0.02,4.03,7]non‐8‐en‐System. Vorläufige mitteilung
Authors: Prinzbach H. , Auge W. , Basbudak M.
Published: December 2004

Direct photochemical excitation of the tetracyclo[4.3.0.0.2,4.03,7]non‐8‐enes 7a–d leads to a mixture of the isomers 8a–d and 10a–d, with the former being the main products. On sensitization by acetone the formation of 10a–d is clearly favored. The cis‐bishomobenzenes 9a–d are the postulated intermediates. Spectral data and some thermal reactions are described.
A note on the theory of interatomic long‐range forces
Authors: Fukui Kenichi , Yamabe Tokio
Published: December 2004

A comment is made on the multipolar expansion formula of the long‐range force between hydrogen atoms previously obtained. The second‐order perturbation energy neglecting exchange in the framework of the Unsöld approximation is evaluated exactly. An extension is made to helium atoms, and to other s‐electron interactions. An approximate method is suggested to estimate the interatomic force between two atoms in general.
Scaled AMO calculations on the hydrogen molecule. III. The 1s2s3∑ state
Authors: Brändas Erkki
Published: December 2004

The potential energy curve for the 1s2s 3∑ state of the hydrogen molecule is calculated in a scaled version of the AMO approximation. Deviations from a simple potential curve occur. The agreement with experimental data is found to be better for the present state than for the 1sσ2pσ 1∑ state studied in a previous paper.
Upper and lower bounds and the generalized variation‐perturbation approach of many‐electron theory
Authors: Goscinski Osvaldo , Sinanoǧlu Oktay
Published: December 2004

The theory of upper and lower bounds is used in conjunction with the “varied‐portions approach” (VPA) of the “many‐electron theory of atoms and molecules” (MET). Upper and lower bounds equations are derived. It is recognized that if a very natural portion of the full variational expression is made stationary, according to (VPA), a for of Löwdin's lower bound wave equation results. By using the bracketing theorem it is also possible to give lower bounds to the quantities arising from the (VPA) of (MET). This will be useful to study in the future the (MET) pair correlations and to supplement the computational methods currently available with lower bound estimates as well.
Application of the extended method of calculation for atoms and ions having the electronic configurations 1s22s22pN
Authors: Jucys A. P. , Kaminskas V. A. , Kaveckis V. J.
Published: December 2004

The atoms and ions in the electronic configurations 1s22s22pN (N = 2, 3, 4, 5, 6) are examined. N hydrogen‐like radial orbitals for 2p electrons were used. The calculated energies of the 2p shell are compared with those of the ordinary method and with experimental results. The intermultiplet separation ratios are considered as well.
The calculation of atomic associations using LISP
Authors: Schnupp P.
Published: December 2004

Preuss's approximation formula for energy surfaces of multicentered molecules uses the “atomic associations” of the molecule to calculate certain constants. A LISP program was developed which calculates all atomic associations of a given molecule taking into consideration possible permutation degeneracy. As an example the atomic associations of methyl alcohol are listed. The largest molecule under study so far is ethyl alcohol. Its 289 different atomic associations were obtained in 3 min including compilation time. Not using the permutation degeneracy one would have had to consider 21147 atomic associations for this molecule, a task unfeasible from memory space and computing time limitations.
Long‐range coherence and energy storage in biological systems
Authors: Fröhlich H.
Published: December 2004

Biological systems are expected to have a branch of longitudinal electric modes in a frequency region between 1011 and 1012 sec−1. They are based on the dipolar properties of cell membranes; of certain bonds recurring in giant molecules (such as H bonds) and possibly on pockets of non‐localized electrons. In Section 2 it is shown quit generally that if energy is supplied above a certain mean rate to such a branch, then a steady state will be reached in which a single mode of this branch is very strongly excited. The supplied energy is thus not completely thermalized but stored in a highly ordered fashion. This order expresses itself in long‐range phase correlations; the phenomenon has considerable similarity with the low‐temperature condensation of a Bose gas. General consequences and proposals of experiments are discussed in section 3.
Das SCF–MO–P(LCGO)‐Verfahren und seine Varianten
Authors: Preuss H.
Published: December 2004

A modification of the SCF–MO–LCGO method is proposed in the form of a qualitative ab initio method. Naphthalene is treated as a test case; good agreement between calculated and experiemental results is obtained. The capabilities of the method for quantum‐chemical calculations are discussed.
Free‐electron model for hyperpolarizability of the π‐electron system in benzene
Authors: Sen Purnendranath , Basu Sadhan
Published: December 2004

The hyperpolarizabilities of benzene have been calculated using a free‐electron model for the π‐electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γzzzz; γxxxx; γyyyy; γzzxx; γzzyy; γxxyy are non‐zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π‐electron system also shows similer dispersion.
Derivation of the Clebsch–Gordan coefficients by means of projection operators
Authors: Calais Jean‐Louis
Published: December 2004

The Clebsch–Gordan coefficients for the coupling of two angular momenta are derived by using the projection operator technique, developed by Löwdin. The derivation is done in two steps; first for the so‐called principal case, i.e. k = m, then for the general case with an arbitrary m. Two different derivations are given for the principal case, a direct one and one based on a recursion procedure. The general case is obtained from the principal case with a step‐down operator.
A variation principle for energy differences between states of two different Hamiltonians
Authors: Marron Michael T. , Weare Johan H.
Published: December 2004

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ℋ︁] = 〈X0| ℋ︁x – Wx|X1〉 – 〈Y0|ℋ︁y – Wy|y1〉 + 〈X0| Δ ℋ︁|Y0〉 · 〈X0| Y0〉−1. Δ ℋ︁ = ℋ︁y – ℋ︁x, |X0〉 and |Y0〉 are the wave functions for the X and Y states and |X1〉 and |Y1〉 are functions defined in the text. The principle is applied to a few simple examples.
Comment on a perturbation treatment of the ground state of two‐electron atoms using the coordinates r< and r>
Authors: White Ronald J. , Ramaker D. E. , Schrader David M.
Published: December 2004

A perturbation variation treatment of two‐electron atoms using exp (–αr< – βr>) as the zeroth order wave function is presented. The parameters α and β are variationally determined and the results are compared with the “physical” choice α = Z, β = Z – 1, and with Z−1 theory. The energy is given through fifth order in the perturbation.
A minimum principle for molecular systems allowing the use of discontinuous wave functions
Authors: Hall G. G. , Hyslop J. , Rees D.
Published: December 2004

In this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh‐Ritz method is also preserved.

The theory is applied to the H ion, potential energy curves are obtained for various “cut‐off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut‐off” region so that the upper bound is minimized is also discussed.
A multi‐configuration LCAO–MO study for complex unsaturated molecules. I. General theory and its application to the benzene anion
Authors: Nakayama M. , I'Haya Y. J.
Published: December 2004

A multi‐configuration LCAO–MO approach using a π‐bond order–bond length linear relation is introduced to predict the geometrical structures for the electronic ground and excited states of unsaturated hydrocarbons. The procedure is designed to include configuration interaction in each iterative computation where the π‐electron approximation is employed under the Pariser–Parr type semi‐empirical treatment.

The π‐bond order–bond length relation is determined as rpq = 1.523 – 0.193Ppq, when the bond lengths of ethylene, benzene and naphthalene are used and the groundstate functions including the singly and doubly excited configurations are taken into account to obtain the bond orders Ppq.

The iterative calculation is applied to the ground state and the two lowest excited states of the benzene anion in both D6h and D2h molecular geometries. The geometrical structures and the π‐electron energies are computed for the ground and excited states of the anion; for the latter, two types of configuration species are used. It is found that the first lowest excited state is not subjected to the Jahn–Teller effect and the calculated excited state energies do not agree with the observed values (c. 1.0 ∼ 2.5 eV higher than the observed values). The latter point is discussed in detail. It is also found that the resultant ground state energy depression due to configuration mixing is not very large and the two types of configuration species used give different CI effects on the energy levels of the two lowest excited states of the anion.

Finally, the stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the anion.
Hartree–Fock MO–LCAO equations with charge‐dependent atomic integrals
Authors: Karlsson Göran
Published: December 2004

The Hartree–Fock equations are derived in the MO‐LCAO approximation for the case when the integrals (except overlap integrals) over the atomic orbitals are charge‐dependent. It is shown that inclusion of the overlap matrix in the iterative procedure gives equations which are too complicated for the simple model under consideration. The approach is applied to the VESCF method in the PPP scheme.
Inter‐level differences in iron group atomic systems in the extended method of calculation
Authors: Jucys A. P. , Stasiukaitis V. J.
Published: December 2004

The extended method of calculation has been applied to calculate the inter‐level differences of the shell of 3d‐electrons in the iron group atomic system. The hydrogen‐like radial orbitals have been used. The results are compared with those obtained by ordinary methods of calculation as well as with experimental data.
Theoretical calculations on σ‐systems, part 1: Ethers and chloro‐substituted ethers
Authors: Ghosh Kunal , Bhattacharyya Subirnath , Sen Purnendranath
Published: December 2004

The charge on each atom of some ethers and chloro‐substituted ethers, their dipole moments and the quadrupole coupling constants of the chloroethers have been calculated with the method suggested by Del Re. There appears to be an intimate connection between the charge density on the oxygen atoms and the capacity of forming hydrogen bond.
Molecular formation and electron correlation in HeH+
Authors: Banyard K. E. , Baker C. C.
Published: December 2004

A one‐centre CI wave function for HeH+ reported by Stuart and Matsen for 0.1 ⩽ R ⩽ 5.0 has been analysed in detail from the viewpoint of molecular formation. Further, by means of a natural orbital analysis, it was possible to obtain some measure of the electron correlation contained within such wave functions for various R values. These effects were illustrated by means of a series of difference maps for the electron density. One‐ and two‐particle expectation values were obtained as a function of R. Thus, it was possible to study several aspects of the influence of the proton on the electron charge cloud as we pass from He through to the united atom Li+. The occupation numbers within the natural expansions were compared with those which arise from a similar analysis of a two‐centre wave function for HeH+. The “character” of such wave functions for HeH+, and also for He and Li+, were analysed and compared.
A new SCF procedure and its applications to ab initio calculations of the states of the fluorosulphate radical
Authors: Hillier I. H. , Saunders V. R.
Published: December 2004

Ab initio calculations using a small Gaussian basis set, including 3d orbitals on the sulphur atom, have been performed on the fluorosulphate radical and the related ions SO3F+ and SO3F−. A new SCF procedure is described and applied to the open shell cases discussed here. The results are compared with recent CNDO calculations and with the experimental transition energies of the radical.
Wellenmechanische Behandlung der Protonisierung von F‐ und CH3‐monosubstituierten Äthylenen
Authors: Fratev F. , Janoschek R. , Preuss H.
Published: December 2004

The systems C2H4F+ and C2H4CH have been investigated by the SCF–MO‐P (LCGO) method. It will be shown that the results agree with the empirical rule of Markownikoff. An explanation of the rule of Markownikoff is given by means of the computed results.
Molecular modelling with spherical Gaussians
Authors: Ford B. , Hall G. G. , Packer J. C.
Published: December 2004

A mathematical model of a molecule is proposed. The electronic structure is described using a molecular orbital wave function constructed from a small number of spherical Gaussians with optimized parameters. The models exhibit the desirable properties of numerical stability, objectivity and transferability. Results are given for CH4, C2H6, cyclo‐propane, H2O, CH2O and C2H4. They can be given a chemical interpretation in terms of chemical bonds, lone pairs and atomic cusps.
Note on the space part of anti‐symmetric wave functions in the many‐electron problem
Authors: Slater John C.
Published: December 2004

It is pointed out that if a many‐electron antisymmetric wave function is expanded as a sum of spin‐product functions, each multiplied by a function of coordinates, the resulting functions of coordinates have many of the same useful features found with the symmetric and antisymmetric functions representing singlet and triplet states in a two‐electron system. For finding the energy, or any function of coordinates only, in the approximation in which spin‐orbit interaction is neglected, one such function of coordinates can be used, the spins being disregarded. Simple procedures allow one to find matrix components of such operators as S2 and L . S from the functions of coordinates. These procedures are much easier to visualize than the use of projection operators, the permutation group, or other methods in current use. The general procedures are illustrated by application to the three‐electron problem of the lithium atom, as treated by Lunell, Kaldor, and Harris, and their application to the contact hyperfine structure is pointed out.
Time‐dependent Hartree–Fock calculations in the Pariser–Parr–Pople model. Applications to aniline, azulene and pyridine
Authors: Jørgensen Poul , Linderberg Jan
Published: December 2004

Propagator or Green's function methods are used to analyze the time‐dependent Hartree–Fock model. The non‐hermitian matrix problem for the time‐dependent Hartree–Fock solution is reduced to a problem related only to hermitian matrices. Particular attention is given to the calculation of oscillator strength in different approximations. The connection between the stability of the Hartree–Fock solution and the solution of the time‐dependent Hartree–Fock problem is demonstrated. The results of numerical calculations are given for aniline, azulene and pyridine.
Time–dependent quantum theory I. An absorber in an intense radiation field
Authors: Schurr J. M.
Published: December 2004

A function analogue of the formal operator theory of Goldberger and Watson for the decay of prepared states is developed with a modification that permits treatment of degenerate, interacting intermediate states. The theory is applied to the problem of absorption of radiation by an absorber in a very intense monochromatic beam. In particular, a simple two‐level absorber in a resonant monochromatic beam of sufficient intensity to induce transitions from the ground state at a rate exceeding the spontaneous emission rate from the excited state, but still lying well below the optical frequency characterizing the transition, is investigated with the conclusion that the absorption cross‐section falls off with the one‐half power of the incident intensity. Conditions for the possible experimental verification of this result are presented.
Computation of LCAO wave functions for ground states of polymers and solids
Authors: Andre J. M. , Delhalle J. , Fripiat J. G. , Leroy G.
Published: December 2004

The LCAO form of the Hartree–Fock method is discussed in its application to crystals. General formulae are given for obtaining Fourier coefficient of electronic density (in direct space) as well as of the band structure (in momentum space). Finally, it is shown that in its LCAO form, Slater–Hartree–Fock equations are very simple and that this method is of interest for numerical applications. Special integrals occurring in this formalism are evaluated for a Gaussian basis in the last part of this paper.
Perturbational calculation of the exchange forces in the two lowest states of the hydrogen molecule
Authors: Piela Lucjan
Published: December 2004

The interaction energies in the ground (X1Σ) and the first excited (b3Σ)states of the hydrogen molecule were calculated using the modified Jansen and Byers Brown perturbation method. Calculations were performed for nine values of the internuclear distance R in the range 5 a.u. ≦ R ≦ 9 a.u. The present results were compared with the interaction energies calculated by four other perturbation methods as the expectation values of the H – E0 operator with the function accurate up to the first order. The results show that the method can give satisfactory values of the interaction energies.
On the theory of electron correlation in atoms and molecules: Relation between cluster expansion theory and the correlated wave functions method
Authors: Roby Keith R.
Published: December 2004

A relation between the cluster expansion theory of many electron wave functions and the correlated wave functions method is established. In this way, the theoretical basis of the method is elucidated and the approximations involved in its application become apparent. General forms of the correlated wave function, differing in certain important respects from that form usually assumed, are derived.
Time‐Dependent quantum theory. IV. Effect of lattice relaxation on the optical spectra
Authors: Schurr J. Michael
Published: December 2004

The absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line‐width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue‐shift of the absorption spectrum and a red‐shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over‐all shape, of the emission line calculated here with those observed in the Vegard–Kaplan band of N2 dissolved in rare gas crystals is discussed.
Laplace transform method in two‐photon spectroscopy theory
Authors: Makhanek A. G. , Korolkov V. S. , Fedorov A. F.
Published: December 2004

This paper formulates a number of problems of the two‐photon spectral theory and characterizes the analytical methods of solving them as worked out by the authors. The efficiency and wide application of the Laplace transform method is demonstrated by the most typical examples of the cross section analytical calculations of two‐photon processes, dynamical polarizability, and bremsstrahlung at the scattering.
Spin‐Free quantum chemistry. XX. The alternancy quantum number
Authors: Matsen F. A. , Welsher T. L.
Published: December 2004

The assignment of the alternancy quantum number to the N‐electron states of neutral alternant hydrocarbons is discussed within the spin‐free unitary group formulation. Alternancy is defined with respect to both molecular graphs and molecular orbital eigenvalues. The properties of the molecular orbitals of alternant hydrocarbons result from requiring the assignments in terms of atomic orbital and molecular orbital Gel'fand states to be consistent. State correlation arguments are used to remove the arbitrary phase factor present in previous treatments.
A variational treatment of the potential of impurity ions in semiconductors with spatially variable dielectric constants
Authors: Csavinszky P.
Published: December 2004

The primary purpose of the present paper consists in obtaining a correction to Dingle's potential for a (point) impurity ion (embedded) in Si or Ge. This goal is accomplished by making use of a variational principle in taking into account the effect of the spatial variation of the dielectric constant in the respective medium. It is found that the resulting impurity‐ion potential can be represented as the product of Dingle's potential and a factor which, with increasing distance from the charged impurity, approaches unity. The secondary purpose of the present paper consists in suggesting a way for the modification of an impurity‐ion potential that has been obtained previously with a boundary condition, that, in retrospect, is open to criticism. It is shown that the modified impurity‐ion potential can be represented as the product of the author's previous potential and a factor which, with increasing distance from the charged impurity, approaches unity.
Evaluation of some trigonometric series occurring in infinite chain polymer calculations
Authors: Delhalle J. , Delhalle S. , Harris F. E.
Published: December 2004

Closed formulas are presented for a number of trigonometric series whose summands contain inverse powers of one or two quadratic forms. It is shown how to arrange the formulas to remove apparent numerical instabilities, and useful numerical approximations are identified together with the range of their validity.
Representability
Authors: Erdahl R. M.
Published: December 2004

We survey the present status of the representability problem. We introduce in the last section a new class of representability conditions.
Application of the two‐body density matrix of the ground state for calculations of some excited states
Authors: Rosina M.
Published: December 2004

It is pointed out that the density matrices of the ground state contain valuable information concerning the calculation of particle‐hole excited states. As an illustration, results on the nuclei 16O, 20Ne, and 28Si are presented, using small model spaces.
Density matrix methods in orbital optimization for MCSCF calculations
Authors: Garrod Claude
Published: December 2004

The problem considered is that of selecting the finite orbital basis which will minimize the energy in a given size CI calculation. (1) A one‐body operator is defined which has as eigenfunctions the desired optimal basis. The operator is defined in terms of the basis which leads to a self‐consistency problem of Hartree‐Fock type. (2) A method of successive orbital rotations is defined which is shown to have desirable convergence properties.
Incompletely symmetric non‐bloch electron states in perfect cubic crystals. I. Eigenproblem and its solution
Authors: Kunert A.
Published: December 2004

In the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s‐type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.
Incompletely symmetric non‐bloch electron states in perfect cubic crystals. II. Density of states in the FCC lattice
Authors: Kunert A. , Olszewski S. , Wierzbicki A.
Published: December 2004

The electron density of both the perturbed and unperturbed crystal can be made up of individual terms described by the basis functions of irreducible representations of the crystal point group. For the perfect FCC lattice, a detailed comparison was made between the density of states, calculated in terms of the LCAO wave functions classified according to representations of the crystal point group, and the density of states, provided by the Bloch theory.
Determination of the charge distribution in nonmetallic crystals. I. Theory and application to tetrahedrally coordinated solids
Authors: Julg André , Marinelli Francis , Pellégatti Alain
Published: December 2004

A SCF method using localized molecular orbitals which are built up on hybrid atomic orbitals is proposed to obtain the charges in infinite crystals. Hybrid orbitals are built up on a minimal STO basis set. The formalism has been adapted in order to take into account the periodicity of the system and its infinite size by introducing the Madelung constant. The total energy is given by an infinite sum of terms each corresponding to the energy of a bond in the crystal field. Minimizing this bond energy with respect to eigenvectors it is straightforward to obtain the electronic charges, whence the polarity, i.e., the ionicity, of bonds. In this first paper, we study and discuss the polarity of bonds in zincblende and wurtzite‐type compounds built up on first and second row elements. Our values are coherent between themselves and in agreement with other authors' results. The connection with electronegativity and polarizability is discussed.
Regularity and asymptotic properties of the discrete spectrum of electronic hamiltonians
Authors: Combes J. M. , Seiler R.
Published: December 2004

We analyze the electronic part of diatomic molecular Hamiltonians as a function of the internuclear distance, x. We prove analyticity outside x ≠ 0 of eigenvalues in the discrete spectrum and differentiability up to second order for the associated projection operators. Furthermore, it is shown that for large internuclear distances they converge to eigenvalues and eignprojectors of the separated atoms.
Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1s2 ground state of H−, He, Li+, and Be++
Authors: Roothaan C. J. Clemens , Soukup George A.
Published: December 2004

New techniques have been developed for atomic self‐consistent‐field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five‐point generalization of the Numerov formula is used; the error term is of the order h10. While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10–11.
Isoscalar factors for tetragonal, orthorhombic, monoclinic and triclinic shubnikov point groups
Authors: Kotzev J. N. , Aroyo M. I. , Angelova M. N.
Published: December 2004

The relations between isoscalar factors for corepresentations of antiunitary magnetic point groups are discussed in the case of associated corepresentations. The tables of the isoscalar factors for the single‐ and double‐valued corepresentations of all tetragonal, orthorhombic, monoclinic, and triclinic Shubnikov point groups are given. Some peculiarities of the calculation method of the isoscalar factors for corepresentations are considered.
Warped linear analytic tetrahedral scheme for brillouin zone integrations
Authors: Oriade Joseph
Published: December 2004

We provide an alternative to the biquadratic analytic scheme BIQ published earlier. This form, AMPLIN, is similar to the older linear analytic scheme, LIN. This scheme is much faster than BIQ.
The tautomers of uracil: A local correlation treatment
Authors: Boughton James W. , Pulay Peter
Published: December 2004

The relative energies of all six uracil tautomers have been determined at the MP4(SDQ)/6‐31G** level, using both conventional correlation theory and the Local Correlation method. Geometries were optimized at the SCF/6‐31G* level with offset forces. Comparison of our energies with energies from structures optimized at the SCF level supports the conclusion that offset forces are an advantageous alternative to correlated geometry optimization. The Local Correlation method compares very well with conventional Møller–Plesset theory, recovering at least 98.4% of the conventional correlated energy in all cases. More importantly, the relative energies also show good agreement with the conventional results, even for these delocalized systems. CPU timings show a substantial computational savings for the Local Correlation method over the conventional method. The results of the local method using Boys localization are compared with those using Pipek–Mezey localization. The dioxo tautomer (1) is predicted to be the most stable. The (1)–(3) and (1)–(4) energy differences are found to be within the bounds estimated from experimental work. © 1993 John Wiley & Sons, Inc.
Gaussian expansions from STOs by the distance between subspaces
Authors: De La Vega J. M. Garcia , Miguel B.
Published: December 2004

Expansions of STO orbitals with GTOs for the first‐row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least‐squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first‐row atoms are included: energies and expectation values of ri and pi for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.
Coupled cluster Green's function method: Working equations and applications
Authors: Nooijen Marcel , Snijders Jaap G.
Published: December 2004

Detailed working equations are derived for the ionization part of the single‐particle Green's function within the coupled cluster Green's function (CCGF) framework. The CCGF method is applied to the calculation of vertical ionization potentials (IPs) of a number of small molecules, notably, HF, N2, CO, F2, CS, C2H4, H2O, and H2CO. The results for the outer‐valence IPs, with an average error of 0.12 eV, compare favorably to third‐order equation‐of‐motion calculations within the same basis set (average error 0.28 eV) and outer‐valence GF (OVGF) values taken from the literature (average error 0.17 eV). Ground‐state properties that derive from the CCGF are compared to expectation values obtained in the related normal coupled cluster methods (NCCM) approximation from a formal point of view. Correlation energies obtained in CCGF are compared to CCSD results for the above series of molecules and, in addition, the so‐called true correlation energy density as obtained from the CCGF is compared to the result from an accurate MR–CI calculation for a highly correlated system: the HF molecule at large internuclear separation. © 1993 John Wiley & Sons, Inc.
Electronic structures of high‐Tc superconductors LnBa2Cu3O7 (Ln  Pr, Nd, Gd, Dy)
Authors: Li Ming
Published: December 2004

In the present paper, the electronic energy‐band structures of the LnBa2Cu3O7 (Ln = Pr, Nd, Gd, and Dy) were investigated employing the EHMO approach based on the tight‐binding method. The results show that the substitution of Nd, Gd, and Dy for Y in YBa2Cu3O7 complicates the shape of the Fermi surface and results in an increase in the number of energy bands crossing the Fermi level, Ef. Compared with those of YBa2Cu3O7, the electronic densities of states at Ef, N(Ef), for NdBa2Cu3O7, GdBa2Cu3O7, and DyBa2Cu3O7 increase greatly, whereas those of PrBa2Cu3O7 are very small. The results given by the present calculations explain why the substitution of Nd, Gd, and Dy for Y in YBa2Cu3O7 can still maintain the high transition temperature Tc, while PrBa2Cu3O7 is a semiconductor rather than a superconductor. © 1993 John Wiley & Sons, Inc.
Molecular surface electrostatic potentials and local ionization energies of Group V–VII hydrides and their anions: Relationships for aqueous and gas‐phase acidities
Authors: Brinck Tore , Murray Jane S. , Politzer Peter
Published: December 2004

We have computed ab initio HF/6‐31+G* electrostatic potentials and average local ionization energies on the molecular surfaces of the Group V–VII hydrides and corresponding anions of the first three rows of the periodic table. The surfaces were defined to be specified contours (0.002 or 0.001 au) of the molecular electronic density. The most negative potentials, VS,min, and lowest ionization energies ĪS,min, were located and determined. Their magnitudes separately satisfy limited correlations with gas‐phase protonation enthalpies and aqueous pKa values. Our results indicate that VS,min, and ĪS,min are complementary, the former reflecting electrostatic factors and the latter being related to charge transfer/polarization. More general relationships for protonation enthalpies are obtained when both VS,min and ĪS,min are explicitly included. Solution‐phase and gas‐phase acidities are shown to correlate very well if electrostatic effects are explicitly taken into account. © 1993 John Wiley & Sons, Inc.
Early stages of LiX, BeH2X, and BH3X pyrolysis (X stands for NH3 or OH2): A theoretical study of weak dative complex stability
Authors: Sana Michel , Leroy Georges
Published: December 2004

In this work, we study theoretically the thermal decomposition of weak dative complexes (namely, the complexes between BH3, BeH2, or LiH and ammonia or water). The most accurate calculations have been carried out at the MP4sdtq/6‐311++G(3df,2p) level on MP2full/6‐31G** fully optimized geometries. The transition structures for hydrogen evolution are described. The rate constants were obtained using conventional transition‐state theory. Stability conditions for the complexes were considered. Water complexes are less stable than are the corresponding ammonia derivatives. Lithium complexes seem to be very unstable. It seems that beryllium compounds could be synthesized. Borane derivatives are known experimentally. We find, as observed, that the first hydrogen evolution occurs only above room temperature. Iminoborane seems not to be easily accessible under pyrolysis conditions. Other reactions require less activation energy. Finally, the early stages of the ammonia–borane pyrolysis and paths to open‐chain polymers as well as to cyclic structures are described. © 1993 John Wiley & Sons, Inc.
On the Car–Parrinello computational scheme: Rigorous treatment
Authors: Kryachko Eugene S.
Published: December 2004

Given a manifold of parameters associated with a trial many‐electron wave function to evolve in a fictitious time, the Lagrangian of the corresponding classical system of the parameters' degrees of freedom is constructed explicitly for the case of the closed‐shell Hartree–Fock approximation. The relevant equations of motion of a non‐Newtonian type are derived. The formulae for the masses of the parameters' degrees of freedom are obtained in the limit of small velocities. The Newtonian dynamics described by the Car–Parrinello Lagrangian is discussed. © 1993 John Wiley & Sons, Inc.
Band structures of al‐doped superconductors YBa2Cu3–xALxO7 + δ
Authors: Ming Li
Published: December 2004

Based on the EHMO approach, an approximate treatment of electronic energy‐band structures is suggested. By employing this treatment, computations of the band structures for the Al‐doped superconductors YBa2Cu3–xAlxO7 + δ were carried out. It is shown by analysis of the band structures and the density of states that the 2D Cu–O planes in the YBa–CuO superconducting system play a dominant role in superconductivity, whereas the 1D CuO ribbons have indirectly an influence on superconductivity through the connection of the O(4) atoms to two CuO planes. © 1994 John Wiley & Sons, Inc.