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Notes: A partir de I'opérateur-densité d'un système quantique à n états, sont définies et calcultes des constantes du mouvement pour lesquelles est proposée I'appellation nouvelle de conjoncturelles. On établit qu'il en existe au maximum n - 1 linéairement indépendantes. A I'aide des sous-algèbres su(m) (m 〈 n ), on montre comment il est possible d'introduire, suivant la forme de I'hamiltonien, des constantes du mouvement conjoncturelles reliées aux composantes du vecteur de cohérence.

Notes: Our objective in this work is to gain insight into the contrasting carcinogenic activities of vinyl chloride (definitely carcinogenic) and trans-dichloroethylene (apparently inactive). The initial metabolic step for each molecule is believed to be epoxidation of the double bond, and there is evidence indicating that for vinyl chloride, this epoxide (chlorooxirane) is its ultimate (direct-acting) carcinogenic form. This article presents the findings of a computational study of the reactive properties of trans-dichlorooxirane (the epoxide of trans-dichloroethylene). An ab initio SCF-MO procedure was used to determine the energy requirements for stretching the C—O and C—Cl bonds (SN1 reactivity) and to study the epoxide's SN2 interactions with ammonia, taken as a model nucleophile. The starting points were the oxygen- and chlorine-protonated forms of the epoxide. The structure of the system was reoptimized at each step along the various reaction pathways. The results of this work are compared to an analogous earlier study of the reactive properties of chlorooxirane. The chlorineprotonated C—Cl bonds are found to have much lower energy barriers to stretching than do the oxygen-protonated C—O bonds. In the SN2 processes, intermediate complexes are formed with ammonia by both the oxygen- and the chlorine-protonated epoxides; the latter complexes are the more stable. Based on our results, we propose two mechanisms (one SN1 and the other SN2) whereby trans-dichlorooxirane can interact with N7 of guanine to produce an adduct analogous to one formed by chlorooxirane, which has been found to be the primary in vivo DNA alkylation product of vinyl chloride and to which has been attributed the carcinogenicity of the latter. Overall, trans-dichlorooxirane is found to be chemically more reactive than chlorooxirane; this may help to account for the much lesser carcinogenic and mutagenic activities of trans-dichloroethylene, since the epoxide may be reacting with other cellular nucleophiles before it reaches the key site(s) at which the carcinogenic or mutagenic interaction would occur. We also offer some speculations concerning other possible factors related to the differing carcinogenicities of vinyl chloride and trans-dichloroethylene, such as ease of epoxide formation and the likelihood of oxygen protonation.

Notes: A procedure is described for the efficient evaluation of the energy matrix elements necessary for atomic configuration-interaction calculations. With the orbital configurations of an N electron system in spin state S written as the irreducible representations [21/2N-S, 12S] of the permutation group S( N ), it is possible to evaluate readily the energy matrix elements of a spin-free Hamiltonian expressed in terms of the generators of the unitary group. We show how the use of angular momentum ladder operators permits the effective generation of a basis of eigenstates of L2, Lz as well as S2 and Sz, for which the energy matrix elements may be evaluated with ease.

Notes: The mechanism of unimolecular 1,1-elimination of H2 from carbocations has been investigated by the semiempirical MNDO method in view of its very good performances in the analogous elimination from H2CO. Contrary to previous suggestions, the critical configuration obtained at the MNDO level is characterized by a reduced symmetry with respect to the reacting molecule and by a very short H—H distance. RRKM computations of the rate constants and isotope effect employing MNDO results for the activation energies and vibrational frequencies indicate also that the present, nonsynchronous mechanism is compatible with all the available experimental data.

Notes: The semiclassical models considered here are composed by charge distributions coming from ab initio quantum-mechanical calculations on actual molecular systems. These charge distributions interact with one another according to the laws of classical electrostatics. This article describes some results of a systematic examination of the performances of this model in a variety of cases, with the aim of putting in evidence the usefulness and the limits of this inherently approximate representation of chemical interactions. Intermolecular interactions are examined first; the test cases are interactions of neutral molecules with H+, Li+, and C1-, and the formation of H-bonded complexes. Attention is paid mainly to the energetics of the processes; each interacting molecule is considered as a unique entity and classical molecular reactivity indexes (electrostatic potential V, polarization term P) are introduced to compute the interaction energy, to interpret the details of the interaction process, and then to elaborate on less expensive computational procedures. Intramolecular interactions are considered. Attention is paid to the question of defining chemical groups starting from SCF molecular wavefunctions. The transferability and conservation degree of groups derived from localized orbitals of actual molecules is examined in detail, taking as tests their ability to reproduce charge distribution, one-electron observables, and energy. The effect of classical fields on these groups is then examined, taking into consideration external fields originated either by a point charge or by a solvent, and internal fields deriving from substitution of chemical groups. The intergroup analysis is then extended to the case of bimolecular reaction acts by considering the whole system as a supermolecule. Approximate computational procedures able to reproduce the main features of these interactions are proposed and tested. All through the article the performances of the classical models are compared with ab initio SCF calculations (mainly of low or intermediate quality).

Notes: Some brief, general comments on the concept of molecular structure will be given. Some important points connected to the use of models in the interpretation of molecular structures will also be mentioned. The main theme in one part of the presentation will be the cooperative efforts made by experimentalists (mainly spectroscopists) and theoreticians (computational chemists) in order to measure, predict, and analyze the perturbations on the cyclopropane ring by different substituents. The aim is to demonstrate that ab initio calculations of a certain quality can constitute an important support for experimental studies in that they are able to discriminate between different models that otherwise are equally probable. The second part of the presentation will be concerned with a class of molecules that gives both experimental structural chemists and computational chemists a great challenge, namely, the metallocenes. A discussion of some of the grave discrepancies between theory and experiment regarding their geometry will be given.

Notes: In the framework of the SCF-RPA scheme and ppp approximation we studied the excitation spectrum of pyrene, coronene, ovalene, and hexabenzocoronene. The triplet stability matrix of the corresponding Hartree-Fock solution was also studied for each molecule. At variance with the case of long linear polyacenes [M. Baldo, G. Piccitto, R. Pucci, and P. Tomasello, Phys. Lett. 95A, 201 (1983)], all these molecules do not display Hartree-Fock triplet instability. Furthermore, the theoretical analysis indicates that the electronic structure of the molecular series can be characterized by a dimensionality intermediate between one and two, with a smooth transition between the two limits. The transition is essentially determined by the molecular shape. The analysis is supported by the fairly good agreement of the theoretical spectra with the available experimental data.

Notes: The proteinoid model for the emergence of cellular life in a stepwise evolution has been extended. The properties of the resultant laboratory protocell have been further catalogued. These include syntheses of peptide and internucleotide bonds, which thus provide an explanation of locale for the emergence of the coded genetic mechanism. Other properties found include arrays of activities of the bioelectrical type, which suggest an investigatable component of consciousness. Throughout the sequence from amino acids to electrically active protocell, molecular selection is manifest an nonrandom reactions and interactions.

Notes: Enzymes are catalysts occurring in living cells. The aim of this paper is to describe some basic properties of enzymes and to understand on a physical basis how the intracellular milieu may control the kinetics of enzyme reactions. We shall therefore consider in succession some kinetic properties of enzymes in solution and the way cell surfaces and biological membranes control the dynamics of enzyme reactions. The choice of topics which have been selected in this paper is somewhat arbitrary and certainly reflects the tastes and the personal interests of the authors.

Notes: It is shown that in the framework of the π-electron approximation even polyenes can be unambiguously divided into 4L- and 4L +2- classes. The classification scheme is based upon the sign alternation of the bond-order between the first and the last atoms and upon the different information content of the bond-order distribution for 4L- and 4L +2- polyenes, respectively. The classification has been shown to hold for the four lowest-lying electronic states: the ground state 1Ag-, the spectroscopically permitted excited state 1Bu+, the spectroscopically forbidden state 1Ag-, and the lowest triplet state 3Bu+ at all levels of sophistication in the π-electron approximation, ranging from the simple Hückel Hamiltonian to the PPP-multi-CI approach. It is shown that the proposed classification is valid also for heteropolyenes and polyenelike/heteropolyenelike fragments from complex organic molecules. The classification has been shown to be useful for the theoretical interpretation of thermo- and photoelectrocyclic reactions. The sign of the bond order between the first and the last atoms (or the average information content) determines unambiguously the topology of the forming cyclic transition state and, thence, the course and the mechanism of these reactions. The results obtained indirectly support the hypothesis that the lowest excited states in butadiene and hexatriene are of the type 1Bu+.

Notes: There are two metabolisms in animal cells. The first is well known and produces ATP for processes like muscular contraction. The second, which has been overlooked until now, activates oxygen and combines it with the reducing power of our food, thus providing energy to maintain order in the cell and control its proliferation. The central catalysts of this “protometabolism” are methoxy derivatives of hydroquinone or benzoquinone. Methoxy-p-hydroquinone activates oxygen and oxidizes 2,6-dimethoxy-p-hydroquinone to 2,6-dimethyoxy-p-benzoquinone. This latter interacts with ascorbic acid and passes the oxidizing power on to the SH groups of the cell.

Notes: The principal theory about the origin of life holds that life is the evolutionary culmination of processes involving the production of complex organic molecules from simple precursors (chemical evolution) and through increasing complexity, the eventual evolution of “living” systems and subsequent biological evolution. The beginning of this chain of events was the production of the elemental precursors (C, H, N, O, along with P and S) in the stars of the universe. Just how they were formed and distributed and what role they played in early planetary history is fundamental to our concept of the origin of life and the subject of this article.

Notes: The generalized genetic code is applied to alternative codings recently derived from studies of mitochondrial protein synthesis. It is argued that mitochondrial protein synthesis is comprised of a class of biological contexts, rather than a single biological context, and that there exist, therefore, multiple mitochondrial genetic codes. The evolutionary implications of multiple mitochondrial genetic codes are discussed.

Notes: This article summarizes and extends our computational studies (ab initio, SCF-MO) of the reactive properties of halogenated hydrocarbon epoxides. For five such epoxides (ethylene oxide, propylene oxide, chlorooxirane, trans-dichlorooxirane, and epichlorohydrin), we analyze and compare first the energy requirements for stretching the C—O and C—Cl bonds, and second, the reactivities of the epoxide ring carbons toward a model nucleophile, ammonia. At each step along the various reaction pathways, the structure of the system was reoptimized. The epoxides were taken to be protonated, either on the oxygen or on the chlorine. Ring opening via monomolecular rupture of a C—O bond was found to occur significantly more readily when there is a —CH3 or —Cl substituent on the carbon. Epichlorohydrin is exceptional, in that stretching a C—O bond leads to a movement of the chlorine toward the carbon in question, forming a three- or four-membered ring. The stretching of protonated C—Cl bonds has remarkably low energy requirements, even when the carbon is not part of the epoxide ring. The interactions with ammonia produced intermediate complexes, which are particularly stable when there is a chlorine on the other ring carbon. The formation of the primary in vivo DNA alkylation product of vinyl chloride, suggested as being responsible for the carcinogenicity of the latter, is discussed. The most negative values of the electrostatic potentials near the oxygens of 21 different epoxides are listed and analyzed in terms of their relationship to the nature of the substituent on the epoxide ring. Also discussed are our earlier findings that epoxide carcinogenicity appears to be associated with a relatively strong negative potential near the oxygen, and that the abilities of epoxides to inhibit epoxide hydrase correlate well with this oxygen potential (modified by a parameter to take account of steric effects).

Notes: Various configurations of the system composed of benzene and acetylene are investigated in an effort to identify the most stable. The total interaction energy is computed as the sum of the dispersion energy ED and ΔESCF, the interaction energy calculated by ab initio molecular orbital methods. Pairwise summation schemes of both the atom-atom and bond-bond types are used to evaluate ED. The most stable structure is found to be that in which the acetylene approaches benzene from above and is oriented such that it lies directly along the C6 axis of benzene. Although the contribution of dispersion to the total interaction energy is dominant, the smaller electrostatic component plays a crucial role in controlling the relative orientations of the two molecules. Indeed, it is possible to select the most stable configuration solely on grounds of the most favorable quadrupole-quadrupole interaction. The likelihood of observation of this configuration is further confirmed by consideration of basis set extension and entropic effects.

Notes: It has been demonstrated that externally applied electric fields perturb the distribution of some of the molecular components of biological membranes. Various electrostatic, hydrodynamic, and structural forces that result from the application of the external field influence both the dynamics and equilibrium distribution of intermembranous molecules. From a model we have shown that the electrostatic force arising from the polarization of the counterion distribution will have a significant effect on the migration of charged membrane components. For small fields this effect on migration is independent of cell size and inversely related to temperature. In a similar model, alternating electric fields are shown to perturb the distribution of charged intermembraneous components in a manner that is not reversed in a single cycle, and while the induced dipole moment of the cell after several complete cycles is small, the induced quadrupole moment is much more significant. The effect of various physical parameters within these models will be shown.

Notes: The HeI photoelectron (PE) spectra of six 4-substitued 3-methyl-1-phenylpyrazolin-5-ones and the unsubstituted parent compound were measured. The interpretation of the low-energy region of these spectra is attempted on the basis of HAM/3 molecular orbital calculations, making allowance for different tautomeric forms of the compounds. The results indicate preference of the CH versus the NH and/ or OH tautomer of these compounds in the gas phase at the temperatures employed (100-150°C).

Notes: Potential derived (PD) point charges and segmental multipole moments are calculated for water, uracil, thymine, and cytosine using STO-3G quality wave functions. The PD point charges are used to estimate the electrostatic interaction energies for a series of complexes of water with these nucleic acid bases. It is shown here that the results obtained using simple PD charge model is very similar to those obtained from more elaborate segmental multipole moment analysis.

Notes: The internal energies of hydration of the Ala dipeptide in the C7, C5, αR, and PII conformations were computed with the Monte Carlo method. The results indicate that both the αR and PII conformations are preferentially stabilized by hydration in general accord with the results of recent experiments described by Madison and Kopple. The major contributing factor for the stability of internal energy of hydration for these conformations can be traced to the hydration of the carbonyl group.

Notes: A second-quantization formalism is used to derive closed formulas for one- and two-center matrix elements of two harmonic oscillators with different force constants. The method is based on a linear transformation between the creation and annihilation operators of the two harmonic oscillators, the use of the Baker-Campbell-Hausdorff theorem, and Cauchy's integral formula. As presented, the proposed procedure is considerably simpler than the ones hitherto employed.

Notes: In earlier studies continuous deformations (homotopies) of reaction paths on potential-energy hypersurfaces and families of homotopically equivalent reaction paths have been used to investigate a group of fundamental reaction mechanisms intrinsic to the hypersurface. Using some of the above results, in this work we shall demonstrate that the catchment region topology (within which chemical species are represented by open domains of the potential surface) admits a unique algebraic structure of reaction paths. This algebraic structure (a groupoid and its subgroups) establishes a link between two earlier representations, and gives some insight into the relations between various reaction mechanisms.

Notes: Dissociation reactions of NaCl into the ionic and the neutral atomic states and the interactions Na+-Na+ and Cl--Cl- of the like ions are investigated quantum mechanically at the configuration interaction level of approximation. Data including the calculated total equilibrium energies, dissociation energies, and bond distances are reported together with the tabulated interaction energies at a wide range of nuclear separations.

Notes: Møller-Plesset perturbation theory has been applied to investigate the influence of electron correlation on the mechanical and optical properties of infinite periodic polyethylene (PE) and on the optical properties of polydiacetylenes (PDAs). The microscopic Young's modulus and deviations from Hooke's law have been calculated for PE using both restricted and unrestricted Hartree-Fock (RHF, UHF) zeroth-order wave functions. These deviations become really important in the region of 30-40% elongation ∊ and they lead to a maximum of the retractive force of f = 0.814 mdyn at ∊ = 0.38 and of f = 0.631 mdyn at ∊ = 0.31 in the case of RHF and UHF reference functions, respectively. The best theoretical value of the longitudinal elastic modulus of PE (comparing different atomic basis function sets) is 334 GPa at the HF level and 276 GPa including electron correlation. The charge transfer exciton spectrum of PE and of PDA models has been calculated with the help of a Green's-function approach using quasiparticle states of the electron polaron method. The first singlet excitations occur at 8.67 eV in PE and at 1.7-2.1 eV in PDAs, in good agreement with experiments.

Notes: Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.

Notes: We propose a variant of the coupled-cluster (CC) method in which spin orbitals of the reference Slater determinant are optimized in a self-consistent way. This approach is a reformulation of the Brueckner-Hartree-Fock (BHF) method used in nuclear physics and known also as the exact SCF method. We discuss the use of the reference-state determinants built of HF, natural, and Brueckner spin orbitals, with relations among them investigated in terms of the many-body perturbation theory (MBPT). It is shown that the Brueckner spin orbitals emerge as a convenient basis set in the coupled-cluster method and equations that determine these spin orbitals are found. The Brueckner spin orbitals can be calculated as eigenvectors of a certain Hermitian one-electron operator which has a form of the Hartree-Fock operator plus a “correlation potential” depending linearly on two- and three- electron cluster amplitudes. The usual decoupling scheme in the coupled-cluster method leads to a hierarchy of approximations; in the first nontrivial one the three-electron cluster amplitudes are neglected, and the two-electron ones are determined by solving Čižek's CPMET equations. We also analyze the problem of spatial, spin, and time-reversal symmertry in the CC and BHF methods. If (and only if) the reference-state determinant belongs to a one-dimensional representation of a certain symmetry subgroup of the system, the CC operator and the BHF one-electron operator are invariant with respect to this subgroup. Thus the restricted (entirely symmetry-adapted) version of the BHF method can be formulated only for the closed-shell systems. This is done for the above-mentioned approximate BHF method. We discuss also the usefulness of the BHF method in application to extended metallic systems.

Notes: If a set of orbital functions φi(r) is an approximate solution to the self-consistent field equations for an atom, the scaled orbital functions ψi(r) = λi3/2φi(λir) will be a better solution if the scale parameters λi are properly chosen. The best choice of the scale parameters is determined by the variational principle. Two applications of this idea are made in this paper: one is an improved iteration scheme for solving the self-consistent field equations; the other is the calculation of the effects of relaxation when an electron is moved from one shell of an atom to another or is removed from the atom. In the first application the number of iterations required to converge the self-consistent field process is reduced by about two-thirds over the usual methods. In the second application, a sample calculation for argon shows the relaxation energies on ionization being calculated to within 0.5 eV.

Notes: An ab initio TDHF calculation of the derivatives of the dynamic polarizability of methane with respect to the non-totally-symmetric normal coordinates is performed. The derivative with respect to S4 shows within a frequency range well out of resonance a remarkable change, even a change of sign. The resulting scattering activity is enhanced by a factor of 50 as compared to the static case.

Notes: External magnetic field effects upon photochemical reactions in solutions are interpreted in terms of the magnetic field dependence of singlet-triplet conversion of radical pairs. The importance of the relaxation mechanism is shown for the hydrogen abstraction reaction of benzophenone in the excited triplet state in a micelle solution.

Notes: We present results on the energetics of the hydrogen bridges for the Guanine-Cytosine pair obtained in a DNA fragment consisting of three stacked base pairs in the B-DNA conformation. The wave function computations on the 87 atom system are all-electron ab initio SCF-MO computations obtained with a basis set of 1032 primitive gaussian functions contracted to 315. Even if the results are only preliminary, one can tentatively advance conclusions relative to the molecular field effect of stacked base-pairs on the potential energy surface for a hydrogen bond. These computations have been performed with a modified version of our molecular program, which uses an IBM 4341 host and six to ten attached array processors (FPS-164) in parallel. The strategy to convert the program from sequential to parallel is briefly outlined and comparisons with our parallel system are made with a present-day “vector” super-computer. From these studies, we conclude that if one adopts the “parallel” approach presented and tested here, much larger chemical systems than previously are now amenable to all-electron ab initio computations.

Notes: The cross section for ionization of Ne Rydberg atoms (17 ≲ n ≲ 40) by Si(CH3)4 is measured to be (7.0 ± 3.0) × 10-14 cm2, whereas that by C(CH3)4 is less than 1.2 × 10-15 cm2. This remarkable difference is explained by a mechanism of vibrational deexcitation of the target molecule. The observed cross sections are reproduced by a calculation using the dipole-moment derivatives for the lowest infrared-active modes, v17-v19, measured by far-infrared spectroscopy.

Notes: A rich body of quantitative data is available from experiments at MIT on the devolatilization of coal at various temperatures and residence times in argon and at Brookhaven on flash pyrolysis of coal at various temperatures, residence times, and pressures in several nonreactive and reactive gases. We here attempt to develop a realistic representative molecular model of coal which is compatible with proximate and ultimate analysis of coal, x-ray diffraction and other analyses of coal structures, the MIT devolatilization data, and the Brookhaven pyrolysis data. The last set gives yields of the various gases methane, ethane, and ethylene; the light liquids benzene, toluene, and xylene; and of heavy liquids or tars. We propose molecular models and a reasonable kinetics which give encouraging results in realtion to these data. Our results suggest that further developments via quantum chemistry might provide a pathway to the understanding of coal pyrolysis and combustion.

Notes: The price-performance relationship in main frames of the 1970s and those of the present is examined and it is found that Grosch's Rule is no longer valid. It is shown that the price-performance relationship not only depends on the CPU power but on the whole computer configuration and the organization of data processing. In this context, the price-performance relationships of centralized and more decentralized forms of organization are examined. The price-performance relationship in main frames and in microcomputers is compared. It is predicted that, after a period of advantages in using microcomputers, a reverse tendency may be expected.

Notes: The authors describe the generation by a CONVERT based microcomputer program of Hamiltonian matrix elements between spin-adapted basis functions suitable for configuration interaction calculations. The input consists of Dirac brackets formed from the proper linear combinations of Slater determinants expressed in second-quantized notation; the output is the symbolic value, in Mulliken's notation, of the matrix elements in terms of one- and two-electron integrals.

Notes: The line strengths of 2-2 and 3-3 transitions (2s22p53s-2s22p53p-2s22p53d, 2s2s2p63s-2s2p63p-2s2p63d, 2s22p53l-2s2p63l) have been calculated for the Ne isoelectronic sequence (Z = 14 ÷ 100). The calculation has been carried out in intermediate coupling. Relativistic corrections have been included through the Breit operator. Perturbation theory in 1/Z has been used to account for electronic interactions.

Notes: The eigenstates of the matrix representation of the Dirac operator for c → ∞ do not approach their nonrelativistic counterparts in the same basis. This wrong “Schrödinger limit” is shown to be the main reason for the phenomenon known as “variational collapse.” After a short review of existing proposals to overcome the “variational collapse,” a systematic study of the possible ways to avoid it is given. All discussed approaches are analyzed in terms of various criteria that one wants to fulfill. The most promising approach consists of a free-particle Foldy-Wouthuysen (FW) transformation on operator level and a back transformation on matrix level (approaches C2 and C3). This implies a modification of the free-electron part of the matrix representation of the Dirac operator and leads to the correct Schrödinger limit (and if one wishes even the correct Pauli limit) in the same basis (and to the exact results for a complete basis). The potential energy is unchanged, which makes the application to n -electron systems straightforward. Projection of the Dirac operator to positive energy states does not remove the variational collapse unless this is done in a very special way.

Notes: The electronic spectra of PdCl42- and PtCl42- are studied by quantum-chemical methods with the ultimate object being to understand the differences in reactivity for Pt(II) and Pd(II) complexes. Nonrelativistic ab initio UHF, DV - Xα, and MSXα methods give very similar assignments of the spectra for PdCl42-. The d-d spectrum for PtCl42-, which is very different from the d-d spectrum of PdCl42-, agrees qualitatively with the spectra obtained using the relativistic extended-Hückel (REX) and Dirac-Slater (DS) methods. Although the latter two methods disagree somewhat in the interpretation of the high intensity bands in PtCl42-, it appears reasonable to interpret at least one of the lines as a 5d → 6p transition.

Notes: Relativistically parameterized extended-Hückel (REX) calculations concerning species and exchange reactions in the system I or I* + I2 are reported, where I = 2P3/2 and I* = 2P1/2. From their experimental data for related halogen systems X + YZ XY + Z, E. B. Gordon, A. I. Nadkhin, S. A. Sotnichenko, and I. A. Boriev [(Chem. Phys. Lett. 86, 209 (1982)] have proposed a conservation rule for the spin-orbit state (X* → Z*, X → Z). The results of REX calculations, double-group symmetry analysis, and schematic state correlation diagrams reported here are consistent with the proposed conservation rule. Two of the transition states are linear and the third nearly so, but no Γ1/2-Γ3/2 crossings leading to spin-orbit conversion are found.

Notes: The autoionization widths of levels 1s 2s 2pjJ, 1s2s2 2S1/2, and 1s2pj2pj′ J have been calculated for ions with Z = 6-30. The calculation has been carried out in intermediate coupling. The decay amplitudes have been calculated in a relativistic approximation.

Notes: Various approximations which are possible for the theoretical description of colliding ion-atom systems are reviewed. With the emphasis on relativistic influences, a few comparisons of experimental results with relativistic calculations are made.

Notes: A one-component approach to molecular electronic structure is discussed that includes the dominant relativistic effects on valence electrons and yet allows the use of the traditional quantum-chemistry techniques. The approach starts with one-component Cowan-Griffin relativistic orbitals that successfully incorporate the effects of the mass-velocity and Darwin terms present in more complicated wave functions such as the Dirac-Hartree-Fock. The approach then constructs “relativistic” effective core potentials (RECPS) from these orbitals, and uses these to bring the relativistic effects into the molecular electronic calculations. The use of effective one-electron spin-orbit operators in conjunction with these one-component wave functions to include the effects of spin-orbit coupling is discussed. Applications to molecular systems involving heavy atoms and comparisons with available spectroscopic data on molecular geometries and excitation energies are presented. Finally, a new approach to the construction of RECPS encompassing the Hamiltonian and shapeconsistent approach is presented together with a novel analysis of the long-range behavior of the RECPS.

Notes: The gap equations for different Fukutome classes are derived in the formalism of second quantization. Compact orbital forms are given for the gap and related to energy difference of the new LUMO and HOMO, ∊LU-∊HO, obtained from the old RHF molecular orbitals. Approximate expressions are obtained by maximizing the average electron-electron repulsion energy. The simplifications obtained and possible applications to molecular systems are discussed and compared with the instability analysis of an RHF state.

Notes: Closed-shell RHF one-electron properties are calculated for H2S using a total of 41 different s, p basis sets and two polarized basis sets (6-31G* and 6-31G**). Total energies and geometries alone are not a comprehensive criteria for selecting the best basis sets. It is shown here that the comparison of a number of one-electron properties can serve as an excellent criteria for testing basis sets. The quality or reliability of a basis set is taken as being its agreement with a large uncontracted s, p basis set (s, p limit).

Notes: The Rayleigh-Schrödinger perturbation treatment can be applied in the quantum mechanical study of long-range interactions between molecules, when we can assume that the molecular charge distributions do not overlap. In these cases the multipole expansion is a good approximation of real interaction potential and can be treated as a perturbation. In this paper we obtain closed expressions for the anisotropic long-range interaction energy between two molecules in all orders of the perturbation, using spherical tensor formalism. Then we show how spherical multipoles and polarizabilities of the isolated molecules can be inserted into general formulas for interaction energy.

Notes: The hydrogen-bonding interaction of protein with the adenine-uracil base pair was investigated by the ab initio MO method (STO-3G level). We found that the stability of the base pair was greatly affected by the hydrogen-bonding interaction of several residues of protein in different ways, depending on whether the interacting species is charged or neutral, whether the interaction is made from the major groove or minor groove side, and which of the two, adenine or uracil, is hydrogen bonded. These results were interpreted as the cooperative interaction between the base pair hydrogen bonds and external ones. The implications of the present results to biological functions were also discussed.

Notes: Solvent effects on different transmission mechanisms of spin-spin coupling constants are analyzed from a theoretical viewpoint. Medium effects are introduced using the solvaton model, and the decomposition of coupling constants in σ- and π-electron transmitted components is accomplished with the PRMO method. Trends thus obtained are in fairly good agreement with experimental findings reported in the literature. In all types of couplings studied in this work, σ and π components show opposite behavior when increasing the polarity of the solvent.

Notes: Monte Carlo simulations were carried out on clusters consisting of one hydrogen peroxide molecule and n water molecules, n being 100 and 250. Quantum-chemical potentials were used for the interactions between the species. The torsional angle was allowed to change in the simulation and its equilibrium value was found to change from ∼115° in the dilute vapor phase to ∼80° in the aqueous surrounding. At the same time the cis barrier became smaller than the trans barrier, as opposed to in the isolated molecule. A continuum model using the reaction field technique was investigated parallel with the simulations; with a reasonable size of the spherical cavity, containing the H2O2 molecule, it was found possible to qualitatively reproduce the Monte Carlo results.

Notes: A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn-Sham quasiparticle concept and the Levy-Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.

Notes: The influence of vibronic coupling between two harmonic CBO potentials with equal minima positions on the electronic absorption and emission spectra is investigated in the framework of our model using the variational procedure. The numerical results, being identical with those obtained through the vibronic coupling model of Fulton, Gouterman, and Brickmann, are discussed with regard to the longest-wavelength electronically forbidden transition, its vibrational structure, and the Stokes loss.

Notes: Conformational properties of 3-deazapurine nucleosides (namely, 3-deazaadenosine and 3-deazaguanosine) have been investigated by the PCILO method. Both C(2′)-endo and C(3′)-endo sugar puckers have been considered and the results indicate that the conformational preferences of these nucleoside analogs are quite different from those of their parent nucleosides adenosine and guanosine, respectively. This result has been correlated in terms of the biological inactivity of these nucleoside analogs.

Notes: A recently proposed orbital optimization technique based on the use of the inverse of the level-shifted Fock operator is successfully applied to a large number of pathologically divergent cases. The possibility of eliminating convergence problems by adopting a similar modification in the operation of the orthogonal gradient method is also successfully tested.

Notes: The band structure of porphyrinatonickel(II) (2) has been studied by means of crystal orbital calculations that are based on the tight-binding approximation; the computational framework is a recently developed INDO model for transition metal compounds of the 3d series. The porphyrinato polymer has been studied in an eclipsed arrangement (2a) and in a staggered conformation (2b) where neighboring layers are rotated by 41°. The total energy of the metallomacrocycle has been decomposed into one- and two-center contributions; the latter interaction parameters have been fragmented into physically feasible resonance, exchange, and classical electrostatic (electron-electron, electron-core, core-core) interactions. It is shown that individual two-center potentials between atoms in neighboring layers are prevailingly determined by the electrostatic interaction energy. The NiNi coupling in the chain is highly repulsive; important stabilizing interactions are predicted between the 3d center of one cell and the electronegative N atoms in the neighboring layers. Stabilizing and destabilizing electrostatic interaction potentials largely compensate each other; the net stabilization in the polymer comes from the accumulation of resonance and exchange increments. The unoxidized Ni(II) porphyrinato polymer is an insulator. Several ligand bands (π, σ, and lone-pair) are predicted on top of bands with significant Ni 3d admixtures; the conduction band of the unoxidized strand is of ligand π* character. The dense manifold of ligand states in the vicinity of the Ni 3d states (3dz2, 3dx2-y2, 3dxz/3dyz) prevents the formation of bands in the polymer that are strongly localized at the 3d center. Ni 3dz2 and 3dx2-y2 interact strongly with ligand lone-pair and σ states. Avoided crossings between ∊(k) curves in k space lead to compositions in the various bands that differ significantly at the bottom and the top. The INDO crystal orbital formalism predicts a partial oxidation of ligand bands in derivatives of 2 that contain oxidants (e.g., halides). The theoretical findings derived for 2 are compared with available experimental data on highly conducting porphyrinatonicke(II) polymers (tetrabenzo and octamethyltetrabenzo derivatives of 2).

Notes: A general expression for the Fourier transform of the basis functions of exponential class has been derived. Particular cases of Slater functions, hydrogen-like functions, Shull and Löwdin functions, Shavitt, Filter, and Steinborn functions have been considered. In many particular cases the Fourier transforms have been shown to reveal some important special properties (reduction to four-dimensional harmonics, quadratic transformations, etc.) which considerably simplify the mathematical treatment of these functions and lead to new possibilities in the development of calculation methods for multicenter integrals.

Notes: The CNDO/BW modification of the CNDO/2 approximation was used within the PCILO framework. It was shown on some significant examples that all the good results of the original PCILO-CNDO/2 method can be reproduced by the modified version PCILO-CNDO/BW at least. Thus, preserving the quality of its results a computer-expense-reduced PCILO method is proposed for calculations on large molecular systems.

Notes: A treatment for a strong crystal field of cubic symmetry is given using the unitary group approach. Projection operator techniques are utilized to achieve results equivalent to those given recently by Wen Zhenyi.

Notes: The energetic behavior of one-dimensional (HF)n and (H2O)n chains with added or inserted H2O or HF was studied by means of the PCILOPSI method presented in Part I. The results were compared with the ones by the original PCILO method. The stabilization energies are in good qualitative agreement; energy differences due to impurity effects even quantitatively agree. The results show that the PCILOPSI method is well suited for the study of perturbed periodic molecular systems.

Notes: A general formalism will be outlined, which uses steady-state wave functions for the study of nonlinear phenomena occurring in molecular systems interacting with intense electromagnetic fields. The steady-state approach has the advantage of being free from the secular divergencies and normalization terms which appear in a perturbation expansion of the time-dependent wave function. A physical interpretation of the steady states will be given by considering the interaction between the molecule and the quantized electromagnetic field. The steady states appear as states of the combined system molecule plus electromagnetic field, with eigenvalues corresponding to the energy levels of the combined system in a semiclassical approximation. Evolution operators will be introduced and used to derive formulas for n-photon transition probabilities between molecular states both in the ordinary configuration Hilbert space and in the composite Hilbert space spanned by the steadystate wave functions.

Notes: Ab initio calculations (self-consistent-field Hartree-Fock) using 6-31G and STO-4G basis sets are used to investigate the interaction between guanidinium and methylguanidinium ion with the carboxylate group of formate. Binding energies and optimum geometries are obtained and compared with reported results using a smaller basis set (STO-3G). The importance of this interaction in proteinsubstrate binding is discussed.

Notes: The electronic intracule density, a three-dimensional contraction of the spinless electron pair density, is the probability density function for an interelectronic vector. A computationally efficient algorithm for the evaluation of the basic two-electron intracule integral for GTOs is presented. In order to provide an initial understanding of the topography of intracule distributions, anisotropic intracule densities for the X1Σg+ ground states of the H2 and N2 molecules are reported and analyzed.

Notes: Clusters formed by the OH- ion and carbon dioxide are investigated using ab initio Hartree-Fock calculations, with 6-31 G and 6-31 G* basis sets. Geometries and binding energies are determined.

Notes: A general theory for response properties is presented which is applicable to perturbations affecting the molecular basis set, notably nuclear derivatives. A perturbation-independent Fock space is introduced, and the necessary reorthonormalization of a truncated basis set after a perturbation is explicitly incorporated in the Hamiltonian. Explicit formulas for MCSCF first- and second-order properties are presented, and some computational aspects are briefly discussed. A brief comparison with previous results is given.

Notes: The operator technique with a minimum of commutator algebra is employed to calculate matrix elements of any number of operators between distorted, displaced harmonic oscillator wavefunctions. The results are valid for multidimensional integrals, and regardless of the extent of the Duschinsky effect. General recursion relations useful in machine calculations are given. The formalism is illustrated for the well-known one-dimensional Franck-Condon integrals.

Notes: The multiple bond description supplied by localized molecular orbitals obtained within the ZDO approximation is analyzed. In particular, conditions for the appearance of σ-π separation and of continuous degeneracy of the localization sum against σ-π mixing are given for two current ZDO energy- and density-localization methods. Likewise, a convenient modification of the latter is presented together with some illustrative examples.

Notes: SCF calculations using a split-valence basis set were carried out for N3, P3, N4, and P4 showing that there are substantial structural differences between the clusters of these elements, nitrogen and phosphorus. An analysis of the nonadditive three- and four-body contributions to the binding energies of these systems is carried out and shown to be quite close to the values predicted from qualitative considerations by Murrell [Chem. Phys. Lett. 55, 1 (1978)].

Notes: In this survey paper the different possible theoretical ways of treating the SN2 reaction are explained. It is shown that, in the future, experience and theory will very likely complement each other.

Notes: The concept of the chemical bond is very old. Many interpretations have been proposed. Nevertheless, the problem is far from being solved. At the present time, the chemist has the choice between two models: the Lewis model (electron pairs) and the quantum model. In spite of a current opinion, both models are not logically equivalent. The localization of molecular orbitals is only a mathematical operation which does not involve any physic localization of the electrons. The loge theory is not more satisfying owing to the fact that loges with minimal fluctuation do not exist in all molecules. The theory of orbital domains seems to bring a solution. Nevertheless, its interpretation can be obtained only outside the strict framework of quantum mechanics.

Notes: Some mathematical implications of the extended nature of model chains are reviewed to call attention to their importance in electronic structure calculations at the restricted Hartree-Fock Roothaan level.

Notes: Most of the work of theoretical physical chemists and chemical physicists relates at least indirectly to the mechanisms of physicochemical processes. Therefore it is important to examine the meaning and the scope of that notion in the context of recent developments in computational studies. After a brief mention of the meaning of the expression “elementary” physicochemical processes (EPCP), the authors adopt as a definition of mechanism a cause - effect description of an EPCP based on metastable and transient states corresponding to minima and saddle points of the potential energy surface; these states transform into one another according to appropriate selection rules. The so-called reaction-path Hamiltonian can be seen as the starting point for a quantum interpretation of the mechanism concept. On this basis the reaction coordinate, the mechanism profile, and the transition state can be fitted into the same framework. Selection rules are illustrated on the symmetry rules, with a few recent examples of applications which also show their limitations. “Propensity” rules allowing surmises on the nature of a transition state from a static picture of the initial state are also considered and their connection with “reactivity indices” emphasized. Processes involving excitation of electronic states as well as environmental effects are briefly examined. Finally, a specific example taken from surface studies is described in some detail to provide the grounds for further reflection.

Notes: In spite of tremendous advances in computational quantum chemistry during recent years, there remains the problem of how to deal with molecules so large that calculations of electronic structure and properties require the use of simplified models. This review contains (i) an appraisal of some currently available theoretical models together with proposals for further development, and (ii) a discussion of the use of such models (via variation-perturbation theory) in the interpretation and prediction of electronic properties. The great majority of electronic properties can be discussed in terms of three distribution functions: the electron density, the spin density, and the current density. The electron density is “observed” in x-ray scattering and the spin density in (spin-polarized) neutron scattering, while the current density (present whenever a magnetic field is applied) gives rise to effects observed typically in ESR and NMR experiments. The aim of model calculations should be to obtain a realistic picture of the distribution functions, sufficient for semiquantitative property calculations. For this purpose, as history suggests, it may not always be essential to proceed to the limits of computational feasibility.

Notes: A summary is given of our recently developed semiempirical pseudopotentials and their applications, and new results are presented on the K2 molecule.

Notes: Charge transfer in adsorbate-substrate systems has been studied in the limiting case of an unperturbed substrate extending the Anderson-Newns treatment to two- and three-dimensional substrates. This allows comparison of different chemisorption sites within an essentially analytic treatment. Important changes of the local densities of states with respect to the usual one-dimensional model are obtained. The resulting charge transfers are of the same order of magnitude as those obtained by adding correlation effects to the one-dimensional Anderson-Newns model.

Notes: A proof is given for the triangle inequality of distance function d in the reduced nuclear configuration space M, used in the differentiable manifold model of potential-energy hypersurfaces [P. G. Mezey, Int. J. Quantum Chem. Quantum Chem. Symp. 17, 137 (1983)]. This result completes the proof that M is indeed a metric space with metric d.

Notes: We discuss the solution of the integral equation \documentclass{article}\pagestyle{empty}\begin{document}$$ W(x,x') = \upsilon (x,x') + \int {W(x,x''} )P(x'',x''')\upsilon (x''',x')dx''dx''' $$\end{document} over complex domains of integration, such as the constant energy volume in solids and numerically tabulated functions, in the biquadratic limit. This will come in handy in the consistent inclusion of correlation effects in solid-state computations.

Notes: It is suggested that the extreme efficiency and specificity observed for chemical reactions in biological systems (compared to chemical reactions occurring under common chemical conditions) is mainly due to special features of these reactions. A key position is ascribed to the role of weak intermolecular interactions (also called noncovalent or van der Waals); in addition, the important role of the entropy and of cyclic or cavitylike shapes of numerous reaction sites, together with the influence of strong local electric fields on transport phenomena and reactivity are discussed. The greatest attention is paid to the applicability of computational methods for evaluation of weak intermolecular interactions, ranging from beyond Hartree - Fock methods to empirical potentials.

Notes: The arrangement of membrane-bound pigments, proteins, and lipids in the thylakoids of higher plants is described, and the role of the membrane in preventing the back-reaction is discussed. The photosynthetic bacterium halobacterium halobium is also described. A simplified quantum-mechanical picture of the primary process in photosynthesis is presented, and the mechanism of electron-hole separation in this picture is compared with the corresponding mechanism in a silicon solar cell. An appendix discusses the application of Frenkel exciton theory to the antenna effect.

Notes: A brief review is given of the three main known biochemical mechanisms of human oncogene activation. The underlying possible physical and chemical mechanisms (both short- and long-range) caused by chemical carcinogens are also briefly discussed. The probable role in carcinogenesis of conformational solitons generated after the release of carcinogens previously bound to nucleotide bases is pointed out. For such a soliton the Hamiltonian is written down and the solution of classical equations of motion is outlined.

Notes: An improved Monte Carlo procedure is described for the evaluation of molecular integrals, which is particularly suitable for multicenter and/or two-electron calculations. The method is almost independent of the complexity of the atomic orbitals involved, and the results can be obtained with an uncertainty which is fairly adequate for most applications and with very moderate waste of computer resources. In the version presented here there is only a restriction concerned with the positive value of some functions involved, as described in the text, but this possibility does not arise in much of the practical work. An example with a two-dimensional exchange integral is worked out in detail.

Notes: In my life as a scientist I have come upon two major problems which, though rooted in science, though they would occur in this form only to a scientist, project beyond science, and are I think ultimately insoluble as science. That is hardly to be wondered at, since one involves consciousness, the other cosmology. The consciousness problem was hardly avoidable by one who has spent most of his life studying mechanisms of vision. We have learned a lot, we hope to learn much more; but none of it touches or even points, however tentatively, in the direction of what it means to see. Our observations in human eyes and nervous systems and in those of frogs are basically much alike. I know that I see; but does a frog see? It reacts to light; so do cameras, garage doors, any number of photoelectric devices. But does it see? Is it aware that it is reacting? There is nothing I can do as a scientist to answer that question - no way that I can identify either the presence or absence of consciousness. I believe that to be a permanent condition that involves all sensation and perception. Consciousness seems to me to be wholly impervious to science. It does not lie as an indigestible element within science, but just the opposite: Science is the highly digestible element within consciousness, which includes science as a limited but beautifully definable territory within the much wider reality of whose existence we are conscious. The second problem involves the special properties of our Universe. Life seems increasingly to be part of the order of nature. We have good reason to believe that we find ourselves in a Universe permeated with life, in which life arises inevitably - given enough time - wherever the conditions exist that make it possible. Yet were any one of a number of the physical properties of our Universe otherwise - some of them basic, others seeming trivial, almost accidental - that life, which seems now to be so prevalent, would become impossible, here or anywhere. It takes no great imagination to conceive of other possible universes, each stable and workable in itself, yet lifeless. How is it that, with so many other apparent options, we are in a Universe that possesses just that peculiar nexus of properties that breeds life? It has occurred to me lately - I must confess with some shock at first to my scientific sensibilities - that both questions might be brought into some degree of congruence. This is with the assumption that mind, rather than emerging as a late outgrowth in the evolution of life, has existed always, as the matrix, the source and condition of physical reality - that the stuff of which physical reality is composed is mind-stuff. It is mind that has composed a physical Universe that breeds life, and so eventually evolves creatures that know and create: science-, art-, and technology-making animals. In them the universe begins to know itself. Also such creatures develop societies and cultures - institutions that present all the essential conditions for evolution by natural selection [variation, inheritance (mainly Lamarckian), competition for survival] so introducing an evolution of consciousness parallel with though independent of anatomical and physiological evolution.

Notes: Experimental studies on 5-hydroxytryptamine (5-HT) and its congeners have shown these compounds to interact with the same receptors in peripheral tissues and in brain. To evaluate the importance of the relative position of the 5-HT-like recognition elements at these receptors, we studied two compounds structurally related to 5-HT in which the structural elements involved in receptor recognition are positioned differently from 5-HT: 5-hydroxyaminotetrahydrobenzindole (FHATHBIN) in which the position of the side chain is fixed with respect to the indole, and 4(β-aminoethyl)-5-hydroxyindole (FAEFHI) in which the side chain is flexible, and connected to the indole at the C4 position (rather than at C3 as in 5-HT). Ab initio molecular orbital calculations of the molecules and model fragments were performed with STO-3G and 3-21G basis sets, using structural optimization procedures. The results show that both structures possess the reactivity elements required for the interaction with the 5-HT receptor, but that FAEFHI cannot be recognized at the 5-HT receptor because the side chain is held in the wrong conformation with respect to the indole portion by a strong hydrogen bond between the side chain amine group and the hydroxyl at C5. We report results from competition experiments for binding at high affinity 5-HT binding sites in brain membranes which support this conclusion by showing that FAEFHI has low affinity for these sites.

Notes: The Slater-Koster resolvent formalism of exciton theory, as proposed originally by Takeuti, has been applied to calculate charge transfer exciton states and to investigate hypochromism in polynucleotides. As a first step, spatially well localized ab initio Wannier functions (WFS) are calculated at the Hartree-Fock level using a two-phase (inter- and intramolecular) localization procedure for the Fourier transformation of the Bloch functions. The single particle energies, entering the Green's function of the polymer, are corrected for electron correlation effects with the help of second order Møller-Plesset (MP) perturbation theory. The interelectronic matrix elements, used in the MP calculation as well as in solving the resolvent problem for the excitons, are calculated in terms of the WFS. Singlet- and triplet-excitonic dispersions, oscillator strengths, the possible affects of ions, hydration, and aperiodicity on the exciton spectrum are discussed.

Notes: The extent of reactivity of a guanine in B-DNA toward aflatoxin B1 depends on the base sequence surrounding that purine in the double helix. In order to account for this variability, we have computed the ASIF (accessible surface integrated field) index for the N7 atom (at which the reaction occurs) of guanine in a G—C pair surrounded on both sides by different types of base pairs in a model oligohelix. When the conformation of the helix is maintained in the B-DNA form, the correlation ASIF reactivity is limited. A study is performed showing the influence on the ASIF index of different departures from the regular B-DNA conformation, likely to occur in a double helix. It is shown that the correlation ASIF reactivity can be strongly improved by allowing some local departures from this regular arrangement.

Notes: We discuss in this paper the various objections to the Kubo formalism initiated by van Kampen. We motivate the need to embed the system of interest in a larger reservoir to resolve these objections using the van Hove limit. In particular, in the context of spin magnetic systems, we show that it is precisely the spin-lattice coupling together with the above limit which is responsible for the validity of the linearization ansatz.

Notes: As a first step toward a solution of the general Hartree-Fock equations for a one-dimensional Coulomb system we construct charge current waves by pairing restricted Hartree-Fock orbitals with functions from their orthogonal complement. The degree of pairing is determined by the solution of the corresponding gap equation. Special attention is paid to the screening problem.

Notes: We present a method for the computation of cohesive and structural properties of solids. The method is based on a local orbital description of the wave functions, an ab initio pseudopotential construction for the ion-core potential, and a local density treatment of exchange and correlation energies. Key elements of the method include the direct computation in real space of all the matrix elements, a noniterative evaluation of the total energy, and the transferability of the total electronic potential. The combination of these elements allows an accurate, yet less complex, treatment of a wide variety of systems. We shall illustrate the method by considering several prototypical systems: the diamond crystal, the diamond (111) surface, the silicon crystal, and the molybdenum crystal. With respect to the bulk crystalline properties, i.e., the cohesive energy, the lattice constant, the bulk modulus, etc., we obtain state of the art agreement with experiment. With respect to the diamond surface, we have considered several models for the reconstructed 2 × 1 surface. Of the models considered, we find only the undimerized π-bonded chain reconstruction has a total energy lower than the relaxed 1 × 1 surface.

Notes: Aspects of recent local density (LD) studies on transition-metal clusters, surface complexes, and oxide defect structures are presented. The evolution of the LD theory as a reliable means of predicting spectroscopic and structural properties of transition-metal systems is explored. As specific examples we consider the magnetic impurity problem, the chemisorption of simple molecules, and the effect of oxide vacancies on x-ray absorption cross sections.

Notes: Problems which arise in the application of closed-shell coupled-cluster approaches to quasidegenerate or almost degenerate situations are discussed and the basic classification of quasidegeneracy types is outlined. Recent coupled-cluster results obtained for the cyclic polyene model, particularly in the strongly correlated limit, are briefly discussed and the unexpected features of approximate and localized coupled-pair approaches are pointed out.

Notes: Recent progress in the mathematical physics and quantum chemistry of Coulomb Green's functions is summarized. Analogy with the defining relation for the Green's function has led to a finite model for the Fermi contact interaction which avoids spurious divergences in second-order perturbation calculations. The Hamilton-Jacobi mechanics of the Coulomb problem is reviewed. A compact parametrization for Hamilton's principal and characteristic functions provides a key element in further developments. These include a semiclassical representation for the Coulomb propagator in Feynman's formalism and a new propagator in the domain of Coulomb Sturmian eigenstates. In projected applications, approximate many-electron Green's functions constructed from combinations of one-particle Coulomb propagators provide a basis for computation of atomic and molecular eigenvalue spectra.

Notes: Techniques for applying hyperspherical coordinates to the quantum-mechanical many-body problem are reviewed. An improved method is presented for evaluating matrix elements of the Hamiltonian of a system of particles. This method involves a rotation in the many-dimensional coordinate space of the system, and it can be applied not only to Coulomb potentials, but also to potentials of other types, such as, for example, the Lennard-Jones potential. It is shown that symmetry-adapted hyperspherical harmonics in the m = 3N-dimensional coordinate space of an N-particle system form a convenient basis set for the solution of the hyperangular part of the many-particle Schrödinger equation. Methods are presented for constructing hyperspherical harmonics of a type which are simultaneous eigenfunctions of Λ2, L2, and Lz, as well as being basis functions for the group of permutations of identical particles. The method presented here for coupling angular momenta by harmonic projection (without the use of Clebsch-Gordan coefficients) has broad applicability.

Notes: Results of self-consistent field-local spin density-scattered-wave calcualtions are reported for small cluster (13-14 atoms) containing nickel and copper atoms in various proportions and for these clusters interacting with a CO molecule adsorbed on a top or a hollow site. The effect of alloying on the magnetism of the clusters in similiar to that found in the bulk case, namely (i) the Ni magnetic moments decrease with Cu content and (ii) the spin polarization on the copper atoms is very small. The effect of Cu is mainly limited to the fist nearest-neighbot Ni atoms. In agreement with experiment, adsorption of CO on pure Ni clusters causes a decerese in the magnetic moments of nearby Ni atoms, and we have recently proposed a detailed mechanism which explains this effect. The influence of Co on Ni magnetism for Ni—Cu + CO clusters is investigated and is shown to be the same as in the pure Ni case as long as no Cu atoms are present in the first coordination shell of the Ni atom(s) involved in the bond. If Cu atoms are present in the first coordination shell, the stabilization of the Ni potential by CO chemisorption leads to increased Ni—Cu covalent interactions. For the cases we have examined, this modified Ni—Cu binding leads to a small increase rather than the usual decrease of the Ni moment for the atom directly involved in the chemisorption.