ALBERT

Notizen: The hydrogen-bond geometry observed by neutron diffraction of 24 carbohydrate and 32 amino acid crystal structures is analyzed and compared. Of the 100 O—H———O bonds in the carbohydrate structures, 25 were three-centered (bifurcated). This bigamous behavior is rationalized in terms of the 25% greater number of acceptor oxygens than donor hydroxyls and the need to preserve the “cooperative effect.” The predominant hydrogen bonds in the amino acids are the zwitterion type , 64 out of a total of 145. Of these, 51 are three-centered. Again the rationale appears to be an equilization of donor and acceptor functions, since each carboxylate group generally accepts between four and six hydrogen bonds.

Notizen: The dicarbonyl methylglyoxal reacts with the lysine residues of proteins to give brown colored products with a small oxygen-dependent free radical content. Electron spin resonance (ESR) experiments employing ethylene diamine as a model for protein lysine residues are reported. The prevention of imine formation between methylglyoxal and the amine models either by pretreatment of methylglyoxal with glutathione or by methylation of the amine led to brightly colored reaction products and a much higher radical content. From an analysis of the ESR spectra it is clear that the reactions between methylglyoxal and the simple model amines developed far beyond those in the protein-methylglyoxal systems. It is proposed that this difference is accounted for by the enormous steric effects of the proteins. The relevance of the observations to the “browning” reaction in foods is briefly discussed.

Notizen: Steady-state conductivity and dielectric measurements in the range of 10-5 Hz to 33 GHz are reported for bovine serum albumin and lysozyme as a function of hydration and NaCl content. The electrical properties are understandable in terms of the existence of charge carriers whose hopping-type transport process is directly influenced by the nature of the protein-water interaction. These mobile charges are considered to be protons originating from ionizable carboxylic groups.

Notizen: It is outlined how the authors arrived at the existence problem of the intermediate states (IS) possibly appearing in bounded crystals with perfect bulk structure and of certain zig-zag states (ZZS) in almost periodic (even disordered) biopolymers. Earlier results are summarized and commented. An example is given for how to enhance the appearance probability of ISS. It is shown that within a narrow critical interval, the width of which is about the eighth of the average separation of the bulk states in the k space of the finite linear chains, any state becomes an his (almost IS), which is very similar to the IS and approaches it continuously. Estimating the effects of in-plane and in-terplane vibrations of stacked aromatic planar compounds on the delocalized π-electron structures, it is concluded that the valence modes have a strong effect on the in-plane π-electronic systems, but a very small one on the interplane π-electronic interactions. The longitudinal acoustical modes of finite polynucleotide DNA models and their root mean square amplitudes are estimated by the method of Peticolas. According to the results obtained, DNA-like and layered graphitelike systems seem to be the probable host systems of 1%. if they exist at all. The appropriateness of the recursion method is discussed to search for unusual electronic states and structures. Such studies are the first unsteady but exciting steps toward the construction of the molecular computers.

Notizen: Ab-initio molecular orbital (MO) calculations on the model peptide, N-methylacetamide (NMA), protonated N-methylacetamide (p-NMA), and two natural dipeptides, glyclyglycine (Gly-Gly) and alanylalanine (Ala-Ala), are reported. Calculations at the STO-3G. 3-21G. and 4-31 G levels account for the predominance of the trans conformation in globular proteins. By use of p-NMA as a model precursor, the formation of the peptide bond is studied by the methods of molecular quantum mechanics. These calculations lead to the conclusion that the trans conformation should predominate, in agreement with the crystal structural data on globular proteins. In order to reduce the amount of computer time required for what are evidently the first ab-initio MO calculations on natural dipeptides, force-field calculations have been employed to obtain the conformational potential energy maps.

Notizen: Ab-initio MODPOT/VRDDO/MERGE SCF calculations were carried out on 2,6-dimethyl-N-nitroso morpholine and on four isomers of α-hydroxy substituted derivatives. The NNO bond angle is found to be 1135°, in agreement with that observed in dimethyl nitrosamine. The two methyl groups are found to be most stable in the equatorial position. The axial position is found to be the most stable orientation for the α-hydroxy group in both the syn and the anti isomers. This is in agreement with the observed axial orientation of straight chain alkyl substituents at the α position in N-nitroso piperidine. An investigation was made on the effects of internal rotation in the parent compound. A 90° rotation about the N—N bond raises the energy ∼.0526 a.u. or ∼33 kcal/mol. In the 90° orientation, population analysis shows a decrease of ∼0.1 e in the gross atomic population (GAP) of the nitroso oxygen and in the total overlap population for the N—N bond. There is a corresponding increase of ∼0.05 e in the GAP on the amino nitrogen. The GAP on other heavy atoms and overlap in other bonds show little effect from internal rotation of the nitroso group. Electrostatic molecular potential energy contour maps indicate differences as a function of conformation.

Notizen: The FSGO molecular fragment technique has been employed to perform ab-initio SCF-MO calculations on morphine and naloxone in the free-base and N-protonated forms. Particular features of electronic structure which have been investigated are molecular-orbital (MO) density distributions, energies and ordering, as well as the correlation of specific orbitals between different molecular species. It has been found that high-energy occupied and low-energy unoccupied MOS are centered on the aromatic moiety of both drugs, enabling the ring to act either as an electron donor or as an acceptor in a charge-transfer interaction. Comparison of corresponding MOs in the free base and the acid cation of both morphine and naloxone demonstrates that the field of the cationic head causes a dramatic downward shift in orbital energies. Thus in the N-protonated drugs the acceptor capability of the benzene ring is greatly enhanced at the expense of its suitability as a donor. Furthermore, the allyl group of naloxone becomes highly activated as an electron acceptor through N-protonation. Investigation of the molecular electrostatic potential of the free-base species has revealed preferred avenues of approach for electrophilic and nucleophilic entities. However, the N-protonated species shows no regions of attraction for electrophiles. In both the free base and the acid cation, the vicinities of the nitrogen atom and the 3-hydroxy group are found to be favorably disposed for electrostatic interactions with receptor entities possessing the proper charge or polarity. Based on the findings with regard to electronic structure, a simple model has been suggested to explain the binding of morphine and naloxone at the opioid receptor.

Notizen: Hemoglobin-catalyzed hydroxylation of aniline may be taken as a model for similar reactions catalyzed by cytochrome P-450. Using ultraviolet-difference spectroscopy and 1H nuclear relaxation techniques, the binding of aniline to hemoglobin was examined. From the magnitude of paramagnetic effects of ferric iron on aniline protons, using the correlation time determined from the magnetic field dependence of water proton relaxation rates, aniline was found to bind to methemoglobins such that the aromatic protons are 8.5 ± 0.7 Å, away from the high-spin Fe3+. A mode of binding is proposed where the aniline molecule is hydrogen bonded to the distal histidine of hemoglobin.

Notizen: The solution conformations of two DNA octanucleotides, (GGAATTCC)·(GGAATTCC) and (AAAGCTTT)·(AAAGCTTT), have been investigated by theoretical calculations of NMR shifts. The calculations of proton chemical shifts have been made, taking into consideration the ring current effects and the atomic magnetic anisotropies of the bases. The computed shielding constants for B-DNA, alternating B-DNA, the Levitt propeller-twisted model and the Dickerson propeller-twist model (based on crystallographic data) have been compared with experimentally available shifts. For the (AAAGCTTT)·(AAAGCTTT) double helix the experimental data are available only for the exchangeable protons HN1 and HN3; thus a complete and detailed evaluation is impossible for this system. For (GGAATTCC)·(GGAATTCC) the results indicate that the A·T pairs are propeller twisted à la Levitt and Dickerson.

Notizen: The exponential transformation of the molecular orbitals, that has been previously used to achieve a process with a convergence of quadratic quality in SCF closed-shell calculations [J. Chem. Phys. 72, 1452 (1980)] has been extended to UHF determinantal wave functions built from different orbitals for different spins. Explicit formulas are given for the first and second derivatives of the energy to be varied. The method is illustrated by UHF calculations for systems described as standard singlets (Li2 and F2) or triplets (NH) at the RHF approximation level, as well as for CH, CH2, CH3 molecular fragments in their valence states.

Notizen: The development of a flexible intra- and intermolecular empirical potential function is described, which is designed for investigating the geometric structure of large molecular systems. The intramolecular components in the potential consist of harmonic bond stretching and angle bending terms, out-of-plane deformation terms, and torsional terms; intermolecular components include nonbonding, hydrogen bonding, and electrostatic terms. Bond lengths, angles, and torsional angles are predicted to within 2% of experiment, with most cases being within 1%. The suitability of the intermolecular potential was tested by crystal packing calculations; in all cases the results obtained were in excellent agreement with experiment.

Notizen: In an attempt to account for the selectivity displayed by valinomycin with respect to the binding of alkali metal cations, theoretical computations were performed of the interaction energies of this macrocyclic carrier with Na+, K+, Rb+, and Cs+. Subtracting from these interaction energies the corresponding dehydration energies of the cations yields a set of values of the energy balance, the ordering of which follows the ordering of the binding constants measured experimentally in polar solvents. The possibility of extending the procedure to the alkaline-earth cations Mg2+ and Ca2+ is examined.

Notizen: Ascorbic acid enhances the free radical electron spin resonance signal obtained when methylamine interacts with methylglyoxal. Previous ab-initio calculations have shown that methylglyoxal and other ketoaldehydes may act as possible electron acceptors in Szent-Györgyi's theory of cancer. Ascorbic acid is also known to be involved in cancer.The ab-initio SCF method has been used to study the electronic structure of ascorbic acid and its metabolites. The bulk of the calculations involved the use of α-hydroxytetronic acid as a model for ascorbic acid, and related compounds as models for the ascorbyl radical and dehydroascorbic acid. Complete geometry optimizations by the force method were carried out for the model compounds, using an STO-3G basis set.To obtain an estimate of possible charge transfer involving these molecules, ab-initio “supermolecule” calculations were carried out using formamide and glyoxal. A large number of planar and stacked orientations were considered The anion acts as a substantial donor in many of the stacked conformations, but the charge transfer is rather small in all these systems.

Notizen: Aminoacyladenylates play a central part in both protein enzymatic and polypeptide prebiotic synthesis. Previous general studies on aminoacyladenylate conformations were extended to some aspects related to polypeptide prebiotic synthesis. Major conclusions drawn from these quantum mechanical PCILO calculations are: (1) In the presence of an ammonium group the glycylphosphate system forms a double seven-membered ring. This folded conformation possesses an important rigidity. This occurs in neutral or acidic solutions. It agrees with experimental observations showing that there is no polymerization in this case, in the absence of catalyst. Thus the catalytic part of montmorillonite clays, which can break the ring by compensation of the anionic and cationic charges, can be understood. (2) When the amine group remains in its neutral form (in basic solutions), numerous stereo structures are allowed for the glycylphosphate stem, among which a ring of weak stability. This is still in good agreement with the observation of polycondensation at high pH without catalyst. (3) The phosphate linking system is flexible enough to allow the extension of the polypeptide chain between the clay layers. This is in accordance with the mechanism proposed by Paecht-Horowitz in which the phosphate is locked on the edge of the montmorillonite sheet.

Notizen: Local coordinate systems are introduced into open sets of topological spaces, defined for the nuclear configuration space R of polyatomic nuclear systems. The open sets are directly related to common chemical concepts, such as chemical structure, reaction mechanism, and stability of reaction paths. A topological model of molecules and chemical reactions is a generalization of the geometrical model, and is particularly suitable to account for the nonrigid nature of chemical structures. The coordinate neighborhoods defined on R and on its submanifolds represent the extent and natural limits for partial analyses of multidimensional potential surfaces.

Notizen: The transfer of the central proton between the two NH3 units of (H3NHNH3)+ is studied using the 4-31 G basis set within the ab-initio Hartree-Fock formalism. Electron density difference maps are constructed which clearly indicate electronic redistributions which accompany the half-transfer of the proton from its equilibrium position (NH—N) to the midpoint of the hydrogen bond (N—H—N). The overall loss of electronic charge from the proton-accepting molecule originates in three distinct regions of space, while a density buildup of smaller magnitude is observed in a characteristic region centered about the N nucleus. Similar regions are noted for the proton-donating molecule, although the changes are reversed in sign. A partitioning of the total density changes into contributions from the various molecular orbitals demonstrates that the a1 orbitals are associated with density shifts along the H-bond axis. Changes in the N lone pairs are attributed chiefly to the (5a1,6a1) pair and are somewhat attenuated by opposite shifts involving the (3a1. 4a1) pair. Orbitals of e symmetry lead to polarizations of the NH bonds and density shifts perpendicular to the H-bond axis.

Notizen: To study the arrangement of substrates at the active site of creatine kinase, we have measured the paramagnetic effects of CrADP, an exchange-incrt paramagnetic analog of MgADP, on the nuclear spin lattice relaxation rates 1 /T1 of the protons of water and the protons and phosphorus nucleus of P-creatine in the presence and absence of rabbit muscle creatine kinase. Relaxivity titrations measuring the paramagnetic effect of CrADP on 1/T1 of water protons at several concentrations of the enzyme in the presence of P-creatine were used to study the binding of CrADP to the enzyme·P-creatine complex. The existence of a ternary enzyme·CrADP-P-creatine complex was confirmed by observing the paramagnetic effects of enzyme-bound CrADP on the 1 /T1 of the 31P nucleus and protons of P-creatine. From the magnitude of paramagnetic effects arising within the enzyme·CrADP·P-creatine complex, using the electron spin relaxation time estimated from the magnetic field dependence of 1 /T1 of fast exchanging water protons, a Cr3+-phosphorus distance of 6.0 Å, and Cr3+-proton distances of 11 and 12 Å, were obtained. These results imply the absence of a direct coordination of the phosphoryl group of P-creatine by the nucleotide-bound metal on creatine kinase but indicate proximity of enzyme-bound substrates and are consistent with van der Waals contact between a phosphoryl oxygen of P-creatine and the hydration sphere of the nucleotide-bound metal. Since the metal ion is coordinated to the γ-phosphoryl group of ATP on the enzyme, the overall migration of the phosphoryl group during phosphoryl transfer is ∼3 Å, toward the nucleotide-bound metal.Creatine kinase failed to catalyze phosphoryl transfer from P-creatine to CrADP as monitored by the disappearance of the 31P NMR signal of P-creatine in a solution containing CrADP, P-creatine and creatine kinase. The ability of an isomer of β,γ-bidentate CrATP to act as a partial substrate and our observation of the absence of phosphoryl transfer from P-creatine to CrADP indicate that metal ion coordination of the transferable phosphoryl group precedes phosphoryl transfer and is a requirement of the creatine kinase reaction.

Notizen: The energy of muscle contraction is generated by interactions between the proteins actin and myosin, acting together to hydrolyze a metaphosphate bond of ATP in the presence of Mg++, using the oxygen of a specific water molecule. The molecular setting for these events is described. A key feature is identified to be an attack by the water oxygen on one of the P—O—P bonds. The resulting hydrolysis liberates a phosphate group which is forcefully repelled from its original setting, perturbing metal ions and electron orbitals in the vicinity. The hypothesis is advanced that the accompanying perturbations excite an electron cloud to a hgher energy level, leading to a forceful expansion of the electron cloud. A model is presented representing the S-l head of myosin as being tilted with reference to the coordinates of the actin filament by the expansion of this cloud. This tilt represents a leverlike movement of the S-1 myosin head which is capable of powering the work of muscle contraction. Since the most important molecular participants in muscle contraction are present in all cells, the issues raised here are of very general biological significance.

Notizen: Molecular connectivities of submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)] corresponding to Kekulé structures of nine nonalternate hydrocarbons and four nonbenzenoid hydrocarbons containing four-membered rings are correlated with their Kekulé indices. In the latter class of compounds it was observed that the corresponding submolecules contain cut vertices and bridges in contrast to submolecules of benzenoid hydrocarbons which are devoid of such bridges. It was observed, furthermore, that the branching index goes up with the number of bridges in the submolecule. The results present an application to the abstract relation [D. Cvetković, I. Gutman, and N. Trinajstić, J. Chem. Phys. 61, 2700 (1974)] between resonance and MO theories.

Notizen: It is well known that the CNDO and INDO methods fail in the field of theoretical conformational analysis of conjugated compounds. The NDDO approximation, however, can be applied very successfully to this problem. In this paper, a comparative analysis of these three approximations is performed to clarify the reasons for the failure of the former two methods. It is shown that the defects are inherent in their formalisms, and there is no reasonable possibility to compensate them (e.g., by reparametrization) at the level of the CNDO and INDO approximations. The central inadequacy is the oversimplified treatment of the two-center exchange interaction. In the case of molecules containing heteroatoms with lone-pair electrons the known defects concerning the description of Coulombic interactions of anisotropic charge distributions can additionally influence the results. To overcome these shortcomings, at least an extension of the formalism to the level of the NDDO method is necessary.

Notizen: To calculate atom-atom interactions at high temperatures, one needs the electron densities of the interacting atoms. The present paper outlines an approach by which the temperature-dependent electron densities of compressed atoms may be obtained. The approach suggested makes use of the temperature-dependent Thomas-Fermi (TF) equation, and a variational principle by which this equation may be solved approximately.

Notizen: The performance of a recently proposed scaled one-electron Hamiltonian (SOEH) model is tested against parallel sets of restricted open-shell calculations by the method of Roothaan. It is found that the energy calculated by SOEH model, in general, lies slightly higher than the energy computed by the restricted open-shell method of Roothaan lending credibility to the application of variational argument to the scaled pseudoenergy functional (Eav) for deriving the SOEH model. The numerical stability of the converged SOEH energy with respect to changes in trial vectors indicates the reliability of the method. The SOEH model is shown to perform well in the calculation of geometries of radicals and ions. The convergence behavior of the SOEH model is compared with that of the restricted open-shell method of Roothaan.

Notizen: Operator Ω and reaction operator T of Löwdin are studied with a slightly different approach, which leads to a clearer understanding of their nature and brings out the relevance of the conditions for the invertibility of K studied in the preceding work in this series.

Notizen: The roles of kinetic and potential energy operators in the formation of a chemical bond are investigated using the virial and electrostatic theorems. It is shown that an integrated form of the virial theorem throws a new light on a paradox involving changes in the mean kinetic energy on bond formation. Detailed calculations on the ground state of H2+ lead to a surprisingly simple electrostatic approximation to the bond. The entire potential curve is given to good accuracy (ca. 80% bond energy) by the electrostatic forces between the two protons and a single, nodeless, spherically symmetric charge cloud representing the electron, provided that, if the bond is stretched beyond about 3.6 a.u. the charge cloud switches suddenly from a central location to a position near one proton.

Notizen: It is shown that the utilization of an average occupation number for open shell orbitals, having different occupation numbers in a degenerate wave function, tantamounts to disregard first order contributions in a CI-type expansion of the wave function. These contributions are taken into account in a SCF process that derives the differently occupied open shell orbitals as eigenfunctions of different Fock-type operators and accounts for the total symmetry.

Notizen: The singlet instabilities of the RHF ground state in infinite polyenes have been studied in the framework of a semiempirical PPP Hamiltonian, accounting for long-range Coulomb interactions until convergence of the ground-state energy per electron value. The symmetry-adapted RHF solution (SAS) has been shown to be unstable to the formation of bond-order alternation waves (BAW's) and charge-density waves (CDW's). The CDW solutions have been shown to be higher in energy than the corresponding BAW solutions and to represent saddle points of the energy hypersurface, unstable to the formation of BAW's for physically realistic range of variation of the semiempirical parameters. Analytical formulas for the SAS ground-state energy per electron have been derived in case of a Coulomb law and a Mataga-Nishimoto formula for the two-center Coulomb integrals.

Notizen: Calculations with pseudopotentials of double-zeta quality have been performed on ethylene, acetylene, and water molecules. A description of the carbon-carbon double and triple bonds is presented in the framework of the pseudo-FSGO method. A possible model of the oxygen lone pairs has been established and its functioning has been proved by calculations on the water molecule.

Notizen: A generalization of the Hartree-Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring-opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion-radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward-Hoffmann and Hughes-Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.

Notizen: The nonplanarity of a peptide unit has been studied by the ab initio method (GAUSSIAN 76) considering both the pyramidal structure of nitrogen and the variation of the ω angle for the N-methyl-acetamide and N-ethyl-acetamide in their cis and trans conformations. Several semiempirical methods have also been used for the sake of completeness of this work. All methods except CNDO and PCILO support a nonpyramidal structure for the nitrogen. The distortions of the planarity of the peptide unit show for both cis and trans conformations of the model compounds a significant asymmetric shift of the minimum on the energy curve for the ω rotation.

Notizen: The calculations of long-range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σk = 1n CkR-k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.

Notizen: Euler transformation for accelerating convergence of a series is considered in the context of handling divergent (asymptotically convergent) perturbation series. A generalized (parametrized) version of this transformation is developed, based on the conjecture of Dalgarno and Stewart, which works better. Viewed from this standpoint, the Padé approximants follow as a special case of the parametrized Euler transformation (PET), as is the case with the μ transformation procedure of Feenberg in a perturbative context. The PET is shown to serve as a more general method of handling a divergent series and is able to appreciate the construction and convergence behavior of specific sequences of Padé approximants. The role of parametrization in the context of the Z-1 perturbation theory of atoms is also noted and the workability of the adopted strategy is demonstrated by choosing some specific test cases.

Notizen: A method is formulated for enumerating and constructing isomerization reactions of molecules exhibiting large amplitude nonrigid motions. This method not only enumerates the isomers of nonrigid molecules and the corresponding rigid molecules but also the symmetry species spanned by the equivalent structures whose representative is an isomer. Consequently, using the method of correlating the symmetry species of a group to the symmetry species of its subgroup the splitting patterns of isomers of nonrigid molecule to those of rigid molecule are obtained. This provides an elegant method for both enumerating and constructing reaction graphs. The method is illustrated with examples.

Notizen: Enzymes are large aperiodic structures and this hinders both ab initio molecular orbital and Bloch-type band theory of calculations. A frontier orbital perturbation theory of catalysis is applied to enzymes. Reasons are given for proposing that the induced-fit conformational changes, essential to enzymatic catalysis, leads to an increase in the electronic eigenvalue density at the active site, enhancing the necessary catalytic orbital perturbation.

Notizen: The hypothesis that an electrostatic effect of the buried aspartate side chain may contribute considerably to the extreme catalytic power of serine proteinases is presented. This statement is based on an analysis of environmental effects, due to amino acid residues in the vicinity of the Ser-221…His-64 couple and to hydration in subtilisin BPN'.

Notizen: The influence of a small deformation of CĈO angle in phenol (tilt), into the rotational far-infrared (FIR) spectrum is analyzed using several approaches. In all of them, the CNDO/2 method is used to determine the potential energy functions. In a first step, the C—O bond and the rotation axis are both supposed to coincide with the C2 symmetry axis of the phenyl group. With this assumption the torsional frequencies are calculated in both the symmetric and asymmetric rotor approximations. In a second step, the tilt of the C—OH bond is determined theoretically and found to be -3°, measured from the C2 symmetry axis, the C—OH bond crossing this axis, Using this second geometry, and taking as the rotation axis the C2 axis, the torsional frequencies are again determined in both approximations. An improvement of the calculated transition energies is encountered at each stage of the calculation, when compared with experimental data. Finally the importance of the introduction of a tilt into the FIR torsional frequency calculations is discussed.

Notizen: The considerations of Walsh rules are extended to rationalize the loss of planarity in the 1,3nπ* states of simple carbonyl and thiocarbonyl molecules. The role of Fermi correlation in shaping the differences between conformations in the singlet and the triplet state is emphasized. The role played by the π* orbital is also considered.

Notizen: In presence of external electric and magnetic fields, the Schrödinger equation for many-electron systems is transformed into a continuity equation and an Euler-type equation of motion in configuration space. Then, using the natural-orbital Hamiltonian, as defined by Adams, the two fluid-dynamical equations are derived in the three-dimensional space. This generates a “classical” view of such quantum systems, corresponding to an MCSCF wave function: The many-electron Schrödinger fluid consists of individual fluid components, each corresponding to a natural orbital and having its own charge density and current density. The local observables, viz., the net charge density and net current density, are obtained by merely summing over the natural orbitals, with the occupation numbers as weight factors; but, the net velocity field cannot be so obtained. Further, although each fluid component moves irrotationally in the absence of a magnetic field, the net velocity field is not irrotaional. The irrotational character of each velocity component is destroyed by rotation of the nuclear framework of the system while electron spin introduces an additional term, the spin magnetization moment, into each component current density. The physical significance of the fluid-dynamical equations as well as their advantages and disadvantages are discussed.

Notizen: A diabatic representation is introduced to describe electronic states around adiabatic pseudocrossings, as an alternative to presently available representations. A transformation from the adiabatic to the new diabatic representation is chosen to assure well behaved diabatic potentials for arbitrary momentum coupling strengths. Parameters of the transformation are determined by minimizing momentum couplings in the pseudocrossing region. The problem of two electronic states in one relative position variable is treated in detail and is studied with a numerical model. A comparison of results of our procedure and of other available ones is given. The present developments also provide a criterion for neglecting momentum couplings based on their strength and on the range of collision energies.

Notizen: The magnitude of reorganization energies in the photoelectron (PE) spectra of various transition metal compounds with Mn, Fe, and Ni as 3d center is studied by means of a variable INDO Hamiltonian. The Koopmans defects are analyzed as a function of the one-electron resonance integral βμνAB and as function of the one- and two-center electron-electron interaction integrals. βμνAB has the property of an inverse coupling constant; reorganization effects are enlarged with reduced βμνAB values. In the limit of very small resonance integrals a reduction of the calculated Koopmans defects due to modified localization properties of the orbital wave function is encountered. The two-center electron-electron interaction integrals γμνAB have been calculated via an exponential formula with a variable range parameter. In the limit of long-range potentials with flattened γ;μνAB gradients a significant reduction of relaxation and correlation is diagnozed; large defects are predicted in the short-range limit with steep gradients in the repulsion potential. The one-center Coulomb and exchange integrals (γμνAA, KμνAA) have been modified by a multiplicative factor. With enlarged one-center integrals enhanced Koopmans defects are encountered. The reorganization energies are determined by means of a Green's function approach with a renormalized approximation for the self-energy part.

Notizen: Using the optimal wave functions obtained by means of the superposition of correlated configurations method, elaborated previously, static and dynamic polarizabilities and rigorous lower bounds to them have been calculated for the ground states of three-electron atoms in the lithium isoelectronic sequence (Li I-C IV). The results can be treated with considerable confidence, especially for higher members of the sequence. Furthermore, the calculated rigorous lower bounds for static polarizabilities enable us to rule out several theoretical and experimental values obtained previously. The results obtained by us are then employed to evaluate the leading unknown terms in the Z-1-type expansion for the polarizability, extending thereby our treatment to much higher members of the isoelectronic sequence.

Notizen: Two small groups (E, σν) and (E, C2) are proposed to describe the orbital symmmetry of the whole reaction paths with respect to suprafacial and antarafacial sigmatropic rearrangements. Furthermore, the symmetries of the two small groups are extended to the systems as a many body treatment performed by Matsen.

Notizen: There is considerable evidence indicating that the carcinogenic action of vinyl chloride involves metabolic conversion to the epoxide (chlorooxirane) as the initial step. In order to learn more about its subsequent behavior, we have computed structures, energies and other properties for two different protonated forms of the epoxide, and also for two possible rearrangement products, chloroacetaldehyde and acetyl chloride. An ab initio SCF-MO procedure (GAUSSIAN 70) was used. Oxygen protonation is found to weaken both C—O bonds, the effect being greater for the bond involving the carbon bearing the chlorine. Chlorine protonation leads to a marked weakening of the C—Cl bond; this suggests a possible loss of HCl, leaving behind a carbonium ion (and possible alkylating agent or rearrangement precursor). Thus, while C—O bond breaking is doubtless an important reaction pathway for chlorooxirane, our results indicate that attention should also be focused upon the C—Cl bond; its rupture may conceivably be a key step in the biological action of vinyl chloride.

Notizen: A method has been developed to analyzed the bond and current correlation structures of a molecular many-electron wave function. It is shown that the second order density matrix contains information about the bond and current correlations in its off-diagonal components with respect to the indices of orbital basis functions. We break down the off-diagonal correlation functions into five kinds: charge, spin scalar, spin quadrupole, charge spin, and spin polar correlation functions. For a real wave function, the four correlation functions, except for the spin polar one, have only symmetric-symmetric and antisymmetric-antisymmetric components. The former components give site-bond and bond-bond correlations of charges and spins, while the latter components give current-current correlations of charges and spins. The spin polar correlation function has only symmetric-antisymmetric components that give site-current and bond-current correlations of spins. The five off-diagonal correlation functions are expressed in terms of the off-diagonal components of the second order density matrix. The linked off-diagonal correlation functions are defined in that they give dynamical bond and current correlations. The method is applied to the analyses of the bond and current correlations in the low lying exact eigenstates of the PPP Hamiltonian of benzene.

Notizen: This work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch-Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch-Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU(2) ⊃ U(1). The Clebsch-Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch-Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU(2) ⊃ G through the resolving of a system of nonlinear equations.

Notizen: The nature of the correlation function G(1,2) appearing in the definition of the reduced first order density operator γ′(1,2) = ρ(1)1/2ρ(2)1/2G(1,2) is analyzed. It is shown that when G(1,2) is expanded in terms of plane waves in the context of a single-determinant approximation to the wave function, the correction to the Weizsacker term in the kinetic energy density expression is the Thomas-Fermi term.

Notizen: In the framework of our theoretical approach of the structure and reactivity of chemical intermediates we have been led to reexamine the concept of stability which is widely used by the experimentalists often without specifying its true meaning. In this work we propose a more general definition of the concept of stabilization energy, namely, \documentclass{article}\pagestyle{empty}\begin{document}$$ SE = \Delta H_a - \Sigma N_{AB} E_{AB} $$\end{document} where ΔHa is the heat of atomization of the species under consideration and the EAB's are standard bond energy terms derived from the heats of atomization of reference compounds. Using experimental heats of formation or semiempirical ones deduced from theoretical heats of reaction of appropriate isodesmic processes, we have calculated the stabilization energies of various types of chemical species: saturated, unsaturated and conjugated molecules, free radicals, carbocations, and carbanions. The results obtained can be rationalized in terms of steric hindrance, angular strain, polar interactions, electron delocalization, and substituent effects. Moreover, we have shown that heats of hydrogenation and bond dissociation energies do not provide accurate information on the thermodynamic stabilization of unsaturated compounds and free radicals, respectively. Among other applications the concept of stabilization energy allowed us to propose a detailed classification of free radicals and to rationalize their reactivity. Considering the particular case of radical recombination reactions we have been able to deduce interesting equations showing the relations between the concept of stabilization energy and other quantities commonly used in chemical physics, namely, the bond cleavage enthalpy [BDE(C—C) if one considers alkane thermolysis], the thermodynamic stability measured by the free enthalpy change of a given reaction, and the kinetic stabilization related to the activation energy of a chosen chemical process \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {{\rm BDE}(R - R) = E(R - R) - 2{\rm SE(R}^ \cdot {\rm)} + {\rm SE(R} - R{\rm),}} \\ {\Delta G^0_r 2{\rm SE(}R^ \cdot {\rm)} - {\rm SE(R} - R{\rm)} - E(R - R) - T\Delta S^0,} \\ {E_a (r) = \alpha [ - {\rm BDE(}R - R{\rm)}] + \beta ({\hbox{Evans - Polanyi relation}}),}\\ {E_a (r) = a[2{\rm SE(R}^ \cdot )} - {\rm SE(}R - R{\rm)] + }b{\rm .} \end{array} $$\end{document} This analysis allowed us to give a new interpretation of the adjectives transient, persistent, and stable introduced by Griller and Ingold and to show that the persistence of a radical may be due to other factors than steric ones. In conclusion, the concept of stabilization energy appears to be a good tool for rationalizing the static and dynamic properties of chemical species.

Notizen: Two-dimensional fully numerical solutions of the Hartree-Fock problem are reported for the singlet ground states of H-, He, H2, and HeH+. The H2 energy at R = 1.4 a.u. is -1.13362957 a.u.

Notizen: In this paper, some operator endomorphisms which give rise to conditions for N representability of pth order density matrices are presented.

Notizen: A simple analysis of the bonding between the d orbitals in binuclear complexes of chromium indicate that the usual multiple bond picture used to describe these systems is incomplete. This analysis is fairly general and depends only on the symmetry of these complexes and the rather weak coupling between the 3d orbitals on the two metal centers. A series of INDO calculations on Cr2Cl8-4 and Cr2(CH3)8-4 are reported, and suggest that the dominant description of the bonding is one of two Cr atoms antiferromagnetically coupled. Although this description properly accounts for the eclipsed versus staggered conformations found for these systems, the calculated bond length is too long. An analysis of the components of the wave function suggests that the role of multiple bonded structures (configurations) may be small but is important in its influence in shifting the very flat potential energy surfaces to shorter Cr—Cr distances.

Notizen: The interaction energies of proton with ethylene and substituted ethylenes in a positive bridged ion have been calculated by ab initio MO method with STO-3G basis set, and the energies were further decomposed according to decomposition scheme proposed by Kitaura and Morokuma [Int. J. Quantum Chem. 10, 325 (1976)].

Notizen: Correlation corrections to coupled Hartree-Fock (CHF) static dipole polarizabilities and dipole moment of the HF molecule are calculated using third-order Rayleigh-Schrödinger perturbation theory with Møller-Plesset partitioning (RSMP) in a finite-field procedure. Computations are also made for the dipole moment and polarizability derivatives at the equilibrium internuclear separation. Three different basis sets using contracted Gaussian orbitals augmented by field-induced diffuse polarization functions have been employed to investigate the nature of variation of the properties under study, and the importance of field-induced diffuse polarization functions is discussed. [2/1] Padé approximants are used to accelerate the convergence of the properties. The correlated dipole moment and polarizability values are in excellent agreement with the existing theoretical and experimental values. The dipole moment derivative is in perfect agreement with the existing correlated value. However, the polarizability derivatives at SCF and correlated levels differ appreciably from the existing SCF values and represent as improvement.

Notizen: The observed proton hyperfine coupling constants of radicals from resorcinol and 2-carboxylic, 5-carboxylic, and 5-methyl resorcinols in acidic and alkaline solution were reproduced by means of the INDO (intermediate neglect of differential overlap) with molecular geometry adjusting method. The bond lengths of C—O were longer in acidic solution than in alkaline solution and the total energies were lower in acidic solution than in alkaline solution. The assignments of the coupling constants of the radicals from resorcinols were |A2| 〉 |A5| in alkaline oxidation and |A2| 〈 |A5| in acidic oxidation.

Notizen: In the present work, the problem of the determination of the potential energy surface for nonrigid molecules is examined in the case of the double rotation of the methyl groups in acetone. From the symmetry adapted functional form for the potential, the minimum number of configurations to be calculated is deduced in order to have a reliable surface. With this consideration in mind, the potential energy surface of acetone is determined in some Hartree-Fock semiempirical (CNDO/2) and ab initio procedures with different standard basis sets. In addition, ab initio calculations are performed using different sets of floating Gaussian functions in order to introduce some polarization effects in the wave function. Finally, the influence of the electronic correlation effects in the barrier height, and the role of the possible relaxation of the structure during the rotation is discussed.

Notizen: Cross sections for energy transfer into many-body systems can be expressed in terms of time-correlation functions (TCFS) of transition operators. A semiclassical version is presented by treating internal motions as quantized and relative motions as classical. The time evolution of internal motions can be calculated in the Heisenberg picture and avoids expansions in target states. The decoupling of fast and slow internal motions is treated and applied to vibrational-rotational decoupling in polyatomic molecules. Results are presented for Li+-CO2 collisions.

Notizen: Water chain intervention in the hydrolysis of methyl fluoride and in some tautomeric 1,3 proton transfer reactions has been studied. The results show that in solution the process are neither unimolecular nor bimolecular as in the gas phase, but are multimolecular, where the geometric parameters of the solvent intervene in the reaction coordinate.

Notizen: The computational considerations involved in calculating ordinary and rotatory intensities and electronic excitation energies in the random phase approximation (RPA) are examined. We employ a localized orbital formulation in order to analyze the results in terms of local and charge-transfer excitations. Occupied orbitals are localized by the Foster-Boys procedure. The virtual space is transformed into a localized “valence” set that maximizes dipole strengths with the occupied counterparts, and a delocalized remainder. The two-electron integral transformation is performed with an efficient algorithm, based on Diercksen's, that generates only the particle-hole-type integrals required in the RPA. The lowest solutions of the RPA equations are obtained iteratively using a modification of the Davidson-Liu simultaneous vector expansion method. This allows the inclusion of the entire set of particle-hole states supported by a basis set of up to 102 orbitals. Calculations at this level give better excitation energies and intensities than SDCI methods, at substantial savings in computational effort. Comparative timings, computed results and analysis in terms of localized orbitals are given for planar and distorted ethylene using extended atomic orbital bases including diffuse functions. The results for planar ethylene are in excellent agreement with experiment.

Notizen: Nonlinear equations are important for the description of dissipative processes and soliton-related phenomena. One of the principal aims of the theory of symmetry breaking in quantum mechanics is to provide a systematic method for introducing interactions which reduce the symmetry of a system. Such a method is applied here to compute the general form of the symmetry-breaking interaction F(x,t, Ψ, Ψ*) for the time-dependent Schrödinger equation in one spatial dimension \documentclass{article}\pagestyle{empty}\begin{document}$$ \left[{\partial _{xx} + 2i\partial_t - 2g_2(t)x^2 - 2g_1(t)x - 2g_0 (t)} \right]\psi (x,t) = F(x,t,\psi,\psi *). $$\end{document} For F = 0, it has been shown that the Lie algebra of space-time invariances of this equation is S1 = s1 (2,IR)□w1, the Schrödinger algebra. Following the method of Boyer, Sharp, and Winternitz, all conjugacy classes of subalgebras of S1 are given. For each subalgebra, the most general form of the interaction term F(x,t, Ψ, ψ*) is constructed. The potential F then reduces the symmetry from S1 to the considered subalgebra. Furthermore, the one-dimensional subalgebras of S1 obtained above partition S1 into orbits of operators. To each orbit there corresponds a coordinate system in which the above equation separates variables. A partial resolution of the solutions of the above equation has been obtained by exploiting this relation. The algebraic approach to symmetry breaking yields a rich variety of interaction terms F, which appear to generalize the nonlinear Schrödinger-Langevin-Kostin equation for nonconservative systems and the so-called nonlinear Schrödinger equation. A criterion in terms of the existence or nonexistence of Bäcklund transformations is conjectured in order to distinguish between dissipative and soliton equations.

Notizen: Calculating the electrostatic potential around the Ser-His-Asp catalytic triad in serine proteinases the very important substituent effect of the buried aspartate is revealed. It is found that the strong Coulomb field of this distant but charged side chain considerably enhances the nucleophilicity of the active serine hydroxyl group. The interpretation of the vital importance of aspartate may replace the “charge-relay” hypothesis which seems to be disproved in the light of recent experiments.

Notizen: Effective solutions for two difficulties which may be present in MCSCF calculation are discussed: (i) We show how the large configuration state function state expansion case may be handled simply and effectively without the introduction of extraneous projection operators or Lagrange multipliers; (ii) we present a simplified two-electron integral transformation procedure which significantly reduces the operation count (and hence computational efficiency is increased) for second order and particularly for third order MCSCF procedures. The procedures we introduce use some freedom available in the orthogonal complement Cl space and the virtual orbital space to simplify MCSCF calculations.

Notizen: A modified scheme for SCF interaction energy decomposition has been proposed where the nonphysical basis set superposition error (BSSE) has been corrected by means of the counterpoise method. A new procedure to separate the exchange and induction energy terms free of nonphysical BSSE has been tested in the case of the H2O dimer. The first order BSSE appears to be non-negligible for strong hydrogen bonded complexes. In addition the scheme allows separation of the long-controversial charge-transfer contribution within the induction term, which has been considerably overestimated in previous studies.

Notizen: The carbene reaction 1CH2 + C2H6 was studied with the semiempirical method SINDO 1. The pertinent transition states and products were obtained by geometry optimization on a CI surface. We find the insertion reaction forming C3H8 greatly favored compared to the double insertion leading to CH4 + C2H4. The result is qualitatively the same for the reaction of the two possible intermediate radicals CH3 and C2H5. The geometries and energies of all transition states are presented.

Notizen: Exact computer-generated formulas can be produced for each term of an infinite series that gives the value of three-center Coulomb integrals over Slater-type orbitals of the s-type with equal screening constants. As a specific example, the Coulomb energy of an equilateral triangular arrangement of all 1s orbitals is calculated using seven terms of an infinite expansion to obtain an answer comparable to earlier work in elliptic coordinates. Generalization to all three-center cases of this implementation of the Löwdin α-function method is straightforward.

Notizen: Hartree-Bogoliubov-Valatin (HBV) theory may be implemented with Lipkin Hamiltonians to obtain self-consistent BCS wave functions which describe bond formation and dissociation. These wave functions are in turn vacuua for Nambu's representation of Feynman-Dyson-Goldstone diagrammatic perturbation theory, and hence provide suitable references for the many-body treatment of correlation. Exact SCF solutions of the HBV equations are equivalent to special even-replacement MC-SCF solutions. The latter are similar to generalized valence bond theory, and require one Fock operator for each one-particle shell. The commutative coupling case of HBV theory is realized when the number-conserving renormalized one-body and number-nonconserving pairing operators commute. In this case, a set of orbital equations which involves a single Fock operator may be solved. Since this could prove to be a significant simplification for large systems, the commutative coupling and exact solutions are compared here for the fragmentation of H2 and F2. Results suggest that commutative coupling orbitals will be useful for the aforementioned many-body theory.

Notizen: A MNDO study of molecular geometries, enthalpies, formation, atomization, bond separation, and hydrogenation of a series of unsaturated boron-nitrogen compounds, linear with two and three members and cyclic with three, four, five, and six members are presented. For all these molecules, MNDO calculations are in excellent agreement with available ab initio calculations or experimental data. The high rotational barrier in aminoborane H2BNH2, 30.6 kcal/mol, and the length of bond in iminoborane HBNH, 1.183 Å, imply strong double and triple BN bond character in these two molecules. In the odd membered heterocycles, examination of the molecular geometries and energies of equilibrium states shows that in all cases, the stability of the compounds grows with the number of boron atoms and decreases with that of the nitrogen atoms. Moreover, compared study of the two BN-fulvenes with their homologous hydrocarbon shows that only BN (BB)-fulvene has a polyenic structure similar to that of fulvene.

Notizen: The linear, quadratic, and cubic response of a multiconfigurational Hartree-Fock state to a time independent one-electron perturbation has been derived. A comparison between the exact response functions as obtained from Rayleigh-Schrödinger perturbation theory and the multiconfigurational Hartree-Fock response functions allows a identification of matrix elements of the perturbation operator between the ground and excited states and between excited states. We discuss some ambiguities which result from such an identification.

Notizen: Monte Carlo simulations in the isothermal-isobaric ensemble for the α phase of solid N2 have been carried out with two different pair potentials obtained from ab initio quantum chemical calculations. Comparison is made with data obtained from empirical potentials as well as with experimental data, and in general, the agreement with experiment is found to be good. It is also found that the differences between experiment and theory can largely be attributed to correlation effects, not considered in the quantum mechanical calculations of the pair potential.

Notizen: The AGP wave function is used to describe the ground state potential energy curves of Li2 and CH+. Moderate size basis sets are used. The computational aspects of the AGP optimization are discussed and the nature of the AGP wave function versus internuclear separation is examined.

Notizen: Doped semiconductors with shallow impurities provide an ideal situation to study a collection of hydrogenlike atoms under controllable experimental conditions. We present the results of recent cluster calculation on the electronic properties of such systems.

Notizen: Experimental base stacking and hydrogen bonding enthalpies, as determined from double stranded DNA melting studies, are compared with theoretical calculations of interactions between the respective DNA interconstituent components. Comparisons are made in relation to the differences in magnitudes, sequence dependent spreads, and trends. It is shown that the use of an effective dielectric constant reconciles the differences between the experimental and theoretical values. Suggestions are made for calibration of potential functions suitable for nucleic acid conformational analysis.

Notizen: An overview is given here of band structure calculations on the fourth and fifth group transition metal monocarbides, mononitrides, and monoxides, published since the review article by Calais [J.-L. Calais, Adv. Phys. 26, 847 (1977)]. Furthermore, the relations of three categories of experimental properties, which allow insight into the electronic structure of the above mentioned compounds, and the results of band structure calculations are discussed. Theoretical predictions are compared with experimental findings. The considered experimental properties are valence band photoemission spectra, valence band x-ray emission spectra, and optical properties.

Notizen: Conformational energy calculations at the PCILO level of approximation were performed on β(1 → 3) linked disaccharide consisting of N-acetylgalactosamine and galactose of the Forssman antigen to examine the side group conformations and their influence on the mutual orientations of the two pyranosyl rings. Two low energy regions for the glycosidic bond conformation have been located in the grid search using classical potential functions. The PCILO energy minimizations were then carried out in each of these regions. The preferred orientations of the nonreducing pyranosyl ring relative to the reducing ring were found to be in agreement with the available x-ray results. Moreover, the orientations of groups attached to the anomeric carbons were in good accordance with the requirements of the exo-anomeric effect.

Notizen: The molecular electrostatic potential of the triple helix poly(dT)·tpoly(dA)·poly(dT) is calculated, and the results are examined in relation to those obtained for its component double and single helical parts. For the double helix presenting the standard Watson-Crick hydrogen bonds, the deepest potentials are formed on the side of the major groove, a situation similar to that observed in the A-DNA duplex. For the double helix presenting Hoogsteen-type hydrogen bonds the deepest potentials lie in the major groove, on the side of the pyrimidine strand. In the triple helix the deepest potentials are located in the major groove in a narrow zone over the thymine bases of the Watson-Crick pair.

Notizen: Interacting stereo-irregular chains of hydrogen atoms, which simulate the topological structure of many conducting polymers, are generated by a computer and solved numerically with the unrestricted Hartree-Fock method with a modified spin polarized potential. The electron localization is investigated, and a mechanism for the interchain tunneling is discovered. Local antiferromagnetic ordering is derived which may explain the AF behavior observed in some conducting polymers.

Notizen: The glycan moiety of the bacterial peptidoglycan consists of alternatingly β(1 → 4) linked disaccharides of N-acetylglucosamine (NAG) and its 3-O-D lactic derivative, N-acetyl β-D-muramic acid (NAM). PCILO conformational energy calculations have been carried out for NAG-NAM and NAM-NAG disaccharides to see whether or not the glycan strands possess a chitinlike structure as suggested by earlier workers. In agrement with recent experimental findings, the present results also suggest that the chitinlike structure is energetically disallowed. Furthermore, the bulky N-acetyl substituents at C2 positions of the two sugar molecules are found to be relatively less important in stabilizing mutual orientations of the two pyranosyl rings.

Notizen: The MO theory of structural polyhedrons is one of the basic subjects closely related to the bonding theory of complex compounds and clusters. A series of valuable papers on this subject have been contributed by Hoffman, Wade, King, and Lauher et al. A method called “group overlap method” for constructing the symmetry orbitals and for calculating the group overlap integrals is proposed. It is hoped that the group overlap method may be used for the qualitative and quantitative MO study of structural polyhedrons.

Notizen: Quantum chemical ab initio MODPOT/VRDDO calculations have been carried out on the following aminonitrobenzenes for which crystal structures had been determined experimentally: 4-nitroaniline; N,N-dimethyl-p-nitroaniline; 2,4,6-trinitroaniline; 1,3-diamino-2,4,6-trinitrobenzene (DATB - Form I); 1,3,5-triamino-2,4,6-trinitrobenzene (TATB); 2,3,4,6-tetranitroaniline; N-methyl-N,2,4,6-tetranitroaniline (Tetryl); and N-(β,β,β-trifluoroethyl)-N,2,4,6-tetranitroaniline. These quantum chemical calculations were performed on the molecules in their conformations as found in their crystal structures. The calculations were carried out with our own ab initio programs which also incorporate as options several desirable features for calculations on large molecules: ab initio effective core model potentials (MODPOT) which enable calculations of valence electrons only explicitly, yet accurately, and a charge conserving integral prescreening evaluation (which we named VRDDO-variable retention of diatomic differential overlap) especially effective for spatially extended molecules. Aminonitrobenzenes are especially interesting since there are inherent intramolecular ring distortions and deviations from planarity and intramolecular hydrogen bonds as well as intermolecular hydrogen bonds causing further deviations from planarity. The theoretical indices resulting from the quantum chemical calculations are relevant to a number of properties and behavioral characteristics of these molecules, both intramolecular and intermolecular. The charges on the atoms [from the gross atomic populations (GAP's)] are needed for calculation of the atomic multipole-atomic multipole electrostatic contributions (a dominant factor) to the intermolecular interaction energies. These electrostatic interaction energies are part of the input necessary for calculations on the crystal packing and densities of these molecules. These GAP's are also of value in interpreting the experimental photoelectron and ESCA spectra of these molecules. The total overlap populations (TOP's) between atoms are related to the inherent bond strengths and can serve as a quantitative replacement for the old empirical bond length-bond order-bond energy relationship still used by explosives chemists to identify the “target bonds” (the weakest bonds). The TOP's are of considerable value in predicting and tracing initiation and subsequent steps of explosive phenomena. The molecular orbital energies of the lowest unoccupied orbitals are of interest since nitroexplosives have been implicated in testicular toxicity and the initial metabolic activation appears to proceed through a one-electron reduction of the nitroexplosive.

Notizen: An analysis of the leading effects of a propagator approach to the calculation of resonance energies is presented. By comparison with ΔSCF results, a simple approximation formula has been developed which contains the main features of the VN-1 potential option and the diagonal Tamm-Dancoff approximation. This result is expected to be a useful guide for further refinements of the many-body aspects of the theory.

Notizen: The electron density and the molecular electrostatic potential of the β-carbolines are studied using ab initio STO-3G wave functions. The analysis was done from the point of view of a previous model built with monoamine oxidase substrates and irreversible inhibitors. The results confirm the usefulness of the model and make it possible to propose new precision to the molecular electrostatic potential patterns needed to have monoamine oxidase inhibitory activity.

Notizen: The transition energy and geometry of the lowest excited (nπ*) singlet and triplet states of CO, CS, HNO, H2CO, HFCO, and F2CO molecules are calculated by CNDO/S and CNDO/2-VN-1 potential methods, and the results are compared with those of experimental and ab initio theoretical studies, wherever available. In the calculation of the vertical transition energy, the performance of the CNDO/S method is seen to be generally more satisfactory than that of the CNDO/2-VN-1 potential method, while the reverse is true for the excited-state geometry. The CNDO/S method as such fails to describe the geometry of the excited state, but a combined version (CNDO/S-2) of CNDO/S and CNDO/2, as well as the CNDO/2-VN-1 potential method is fairly successful in this regard.

Notizen: On the basis of a high-quality LCAO MO SCF calculation, covalency versus ionicity of a Co-F bond in the CoF6(n-) complexes, where n = 4, 3, and 2, is discussed. The overlap and gross atomic populations, delocalization of certain MOS, and the charge densities in the bond region as well as around F's all indicate that the covalency increases as n decreases or the valency of Co increases in these complexes.

Notizen: In an n level quantum system there is a relation between each density operator and an element of su (n) Lie algebra. This relation is also established between Cartan's subalgebras and the complete sets of compatible observables. A scalar product is then defined in this algebra in order to introduce orthonormal bases and to simplify many calculations about expectation values of observables. Therefore simple general rules were established which show how to determine (completely or partly), from linearly independent observables, the density operator of the system.

Notizen: The elastic forward scattering of high-energy electrons from molecules has been studied in the second Born approximation. An integral transformation has been adopted to evaluate the second Born integrals analytically without explicit use of molecular wave functions. In the high-energy limit, the differential cross section for the forward scattering is expressed in terms of electric dipole and quadrupole moments, the second moment of charge distribution with respect to the molecular center, and transition dipole moments. All these quantities are shown to be computable from molecular electron densities in the ground state.

Notizen: We examine the short-range behavior of the spherically averaged Hartree-Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the Xαβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.

Notizen: By the means of gauge invariance of the continuity equation Fick's law of diffusion can be extended to also comprehend the chemical reaction. In the case of first-order reactions a complete set of eigenfunctions is obtained. These solutions provide a tool for pattern recognition in biochemical and biological problems (e.g., formation of chromosome banding). The transport equation, including reactions of second order, exhibits soliton solutions describing the propagation of a kinetic process in a medium (molecular chain, fluids, etc.). A relationship to the soliton solutions of the nonlinear Schrödinger equation and Korteweg-de Vries equation of hydrodynamics is also indicated. The propagation of a reactive process (transition state) occurs in many problems of molecular biology. The Brownian motion of ions undergoing a reaction of first order in a constant magnetic field is also exactly solved.

Notizen: In the study of the ground-state binding energy of atoms, relatively more attention has been paid to the gradient expansion of the kinetic energy term of the Thomas-Fermi-Dirac model than to the gradient expansion of the exchange term of this model. Recently Shih and Shih, Murphy, and Wang have focused on this problem and calculated the first gradient expansion correction to the Dirac exchange term by making use of electron densities constructed from Hartree-Fock wave functions. In previous work, aimed to introduce the shell structure of atoms via a variational procedure using the energy density functional formalism, electron densities have been obtained for the Na atom within the Thomas-Fermi-Dirac model with and without the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. In this paper we make use of the respective electron densities and calculate the first gradient expansion corrections to the Dirac exchange term. The results show that, for the Na atom, the magnitude of this correction is about 1% of the magnitude of the total binding energy.