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Notes: The almost exclusive association of the molecular geometry dependence of the relativistic correction with the valence orbital contribution to the mass-velocity and Darwin terms is investigated using SCF and MCSCF wavefunctions. The requirement of orthogonality of the valence orbitals to the core orbitals is confirmed to be the mechanism responsible for the increase in (the absolute value of) relativistic energy upon decrease of the internuclear distance. Certain “fingerprint”-type features of the valence relativistic correction, revealing the identity of the particular core orbital giving rise to it, are identified.

Notes: General formulas are derived for molecular integrals which arise in the linear-response theory when it is applied to the van der Waals interactions between molecules. These integrals are essentially the matrix elements of the Fourier transformed double Coulomb operator between any Cartesian Gaussians. The computational aspects of these formulas are also discussed.

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: The concepts underlying the definition of bond energies in terms of potentials at the nuclei are outlined. The theory is rooted, first, in a definition of the energy, Ei, of “atom” i in the molecule in terms of the potential energy, V(i, mol), of nucleus Zi in the field of all the electrons and nuclei of the molecule: Ei = Kimol V(i, mol). The Kimol parameter, which is not required to be a constant in the derivation of the energy expression describing the contribution of an ij bond, turns out to be virtually constant for each atomic species - a situation which is exploited in numerical applications. Second, the Hellmann - Feynman theorem is applied in the calculation of the derivative, δΔEa*/δZi, of the atomization energy, ΔEa*, using (i) the exact quantum-chemical definition of ΔEa* and (ii) the view that ΔEa* is the sum of bond energy contributions, εij, plus a small interaction between nonbonded atoms. The individual bond energies derived in this manner necessarily depend on local charges at the bond-forming atoms. Numerical applications illustrate how this new bond-energy formula provides a simple link between typical saturated, olefinic, acetylenic, and aromatic hydrocarbons.

Notes: The adsorption of metals on ionic surfaces takes place on preferential sites and is affected by the presence of defects. In order to provide some theoretical indication concerning electronic energy changes connected with these effects, we have extended previous work [A. Julg and M. Bourg, J. Phys. Lett. 43, L243 (1982)] where Lin clusters embedded in a matrix simulated by point charges had been studied by STO-6G (G-70) calculations. We have treated an Li2 molecule in the presence of an fcc lattice of positive and negative point charges placed at the distances characteristic of an LiF crystal: The perfect surface as well as steps and point defects have been thus simulated. In this article we briefly describe the results obtained.

Notes: The phenomenon of biological specificity is described, and a history of discoveries related to the phenomenon is presented. Aspects of biological specificity described include the mechanism of the immune system, chemotherapy, enzyme-substrate specificity, neurotransmitters, autoassembly of viruses, autoassembly of subcellular organelles, differentiation, and cellular recognition. A model for biological specificity involving both steric and electrostatic complementarity is presented and the role of structured water and hydrophobic forces is also discussed.

Notes: The structure-activity relationship of sweet molecules is chosen as an example to illustrate a mechanistic approach of soft agonist-receptor interactions. It is shown that an essentially geometric model of the receptor site can explain the activity of most sweet molecules, both rigid and flexible. The relevant conformations of flexible molecules in solution are extracted from a combination of NMR data and of energy calculations. A possible experimental simulation of the receptor environment in solution is illustrated by the complex of a dipeptide sweetener with a crown-ether.

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: The problem of code origin is presented in the context of increasingly complex events in the origin of life. The likely sequence of events appears to progress from abiotic synthesis of biological monomers to polymers to formation of protocells, which would be capable of competition and further evolution. We propose that rate of polymer formation was a critical controlling parameter of rate of protocell propagation. This would lead to selection of autocatalytic and mutually catalytic reactions of polymer formation. Primitive proteins would catalyze polynucleotide formation, and polynucleotides could be used as anvils of noncoded polypeptide synthesis. Proteins that could catalyze this latter reaction (assignment catalysts) would play an important role in subsequent evolution of a genetic code. Competing populations of assignment catalysts would possess very nonlinear dynamics of production of the catalysts themselves. An analysis of this dynamics shows that it has a rich family of bifurications which would provide a pathway for gradual approach to a genetic code. The selection criterion in this process would be efficiency of utilization of monomers and energy for the production of assignment catalysts.

Notes: After a brief review of empirical and nonempirical schemes used in the study of molecular properties, the difficulties associated with structure-activity correlations are outlined. Part of the difficulty originates with the lack of precise definition of a structure. An analogy is made with similarly vague concepts of structural chemistry - the notion of aromaticity. This follows with the description of a characterization of structures by selected graph invariants. In particular we consider the count of weighted paths derived from suitable weighting of the individual bonds in a structure. We adopted the weighting factors (mn)-1/2 introduced originally for the definition of the connectivity index. The approach thus combines some features of the very successful connectivity index with features of path sequences, found very useful in comparative studies of related compounds. As an illustration of the combined approach we consider a set of some 40 therapeutically active substances, studied previously by others, and derive their clustering (classification) which is solely based on the count of weighted paths and is devoid of any empirical parametrization.

Notes: The transport of deuterium ions in α-cyclodextrin has been monitored using a mass spectrometer to show how the protonic conductivity varies with the extent of water-based hydrogen bond networks in the cyclodextrin hydrate. By means of mass-spectrometric and microprobe analysis measurements it has been possible to distinguish between ionic and protonic conductivity in hydrated lysozyme, and further details have been obtained concerning the physical origins of the low frequency dielectric dispersions (the so-called α and Ω dispersions) exhibited by hydrated protein powders.

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: Ab initio crystal orbital calculations with extended basis sets and model potentials are performed for one-dimensional periodic systems. The results of restricted Hartree-Fock-type calculation for all-trans polyacetylene (CH)n and linear and bent hydrogen-bonded poly(hydrogen fluoride) (HF)n are mainly reported. The results, in particular total energies per unit cell, are shown to be much more dependent upon the basis sets than on the method of lattice-sum truncation, number of k points, or order of neighbor interactions.

Notes: The Rayleigh-Schrödinger perturbation theory for a localized nonorthogonal basis of three-center bonding and antibonding orbitals is examined up to fourth order. Results are reported utilizing the Hückel and Pariser-Parr-Pople model Hamiltonians and compared with those determined from the two-center bonding model and with exact results when they are known. The three-center bond model is found to be especially useful in the treatment of delocalized systems in which the slow convergence of the two-center bonding schemes leads to ambiguities in the relative energies of identical conformations as well as incorrect geometry predictions.

Notes: Binary electron impact ionization or (e, 2e) spectroscopy has recently been employed to measure molecular orbital momentum distributions in a variety of molecules. Interpretation of the momentum distributions ρ(q) has been facilitated by the use of the wave-function autocorrelation function B(r). In some cases differences in the autocorrelation function of two orbitals may be semiquantitatively interpreted in terms of contour plots of the average and difference of their position-space orbital amplitudes. The σg and σu orbitals of a homonuclear diatomic provide a simple illustration of this point. Calculated and experimental spherically averaged ρ(q) for the predominantly N 2p lone-pair HOMOs of NH3 and CH3NH2 are shown using a ΔB(r) analysis to indicate significant participation of the CH3 hydrogens in the lone-pair orbital of CH3NH2. Although the difference in ρ(q) between the lone pairs of NH3 and CH3NH2 is adequately reproduced by split valence (SV) level ab initio SCFMO calculations the experimental ρ(q) have their maxima at considerably smaller absolute values of q then that obtained from either SV or near Hartree-Fock SCFMO calculations. Experimental and calculated momentum distributions are also presented for the 2t2g HOMO of Cr(CO)6. A ΔB(r) analysis of ρ(q) for this orbital confirms that it has mixed Cr 3d and CO 2π character.

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: The generator coordinate approximation is applied to the hydrogen molecular opn. A series of numerical experiments, using different quality electron states, is presented. The results of these nonadiabatic calculations are compared with theoretical predictions.

Notes: The magnetic susceptibility of the BH molecule and the screening constants of its nuclei have been calculated by the finite perturbation SCF method, using London field-dependent atomic orbitals. Several sets of contracted Gaussian functions have been used. The split valence triple-zeta basis set augmented with bond functions and lone-pair functions gave good results with regard to accuracy and computer time. The calculated quantities are close to those obtained by other authors using very large field-independent basis sets.

Notes: We have carried out a series of calculations of the interaction energy between two hydrogen atoms in their ground states, using three kinds of exchange perturbation theory. One objective was to test the accuracy that could be achieved with these perturbation methods. A second was to see if the results were consistent with those for H2+. The perturbation equations were solved within the configuration interaction approximation, using 226 partially symmetry-contracted, two-electron basis functions. The set of Slater-type basis orbitals was chosen so that we could approximate within two percent the most accurate calculated interaction energies. We report here our second-order energies at a series of nuclear separations and compare them to the best values that have been published. Some of the published values are inaccurate. We also present the percent errors in the interaction energies approximated by summing through second and third orders. We discuss some general implications of our results.

Notes: Ab initio spin-orbit matrix elements 〈3P2|Hso|3P2〉 and 〈3P1|Hso|1P1〉 have been computed for Mg, Ca, and Sr by using large Slater basis sets and the microscopic spin-orbit Hamiltonian. Results obtained at the valence, core-valence, and singles-plus-doubles configuration interaction level demonstrate the importance of including core-valence correlation. Oscillator strengths for the dipoleallowed 1P1-1S0 transition computed at the core-valence level are also in excellent agreement with experiment. Combining these results leads to radiative lifetimes for the 3P1 metastable states of 4.16 ms for Mg, 0.34 ms for Ca, and 21.2 μs for Sr. These are in good accord with experiment if the class of longer lifetimes is selected for Mg and the class of shorter lifetimes is selected for Ca. The present theoretical study establishes the following two points. First, that deviations from the Landé interval rule are an accurate reflection of the 〈3P1|Hso|1P1〉 matrix element for the heavier alkaline earths (Sr and Ba), but not for Mg, where spin-spin effects are comparable. Second, that the inclusion of direct relativistic effects is not necessary for quantitative agreement with the observed 3P1 lifetimes. Thus it appears that one is justified in using the Breit interaction as a first-order perturbation to describe radiative transitions occurring through off-diagonal mixing with intermediate states.

Notes: The differences between the anisotropic momentum densities of the isoelectronic molecules N2, CO, and BF are examined by the partial-wave decomposition technique. It is shown that in momentum space a qualitative manifestation of the different bonding situations in these diatomics occurs in the leading anisotropic component of the partial-wave expansion of the momentum density, and a quantitative manifestation in the anisotropy of the kinetic energy tensor. It is found that the isotropic momentum density is monotonically decreasing in these three molecules.

Notes: The experimental data on a series of 11,11-disubstituted methane-[10]annulenes and 11,11-disubstituted tricyclo[4,4,1,01,6]undeca-2,4,7,9-tetraenes allow the estimation of the molecular geometry along the ring closure reaction path for the parent hydrocarbon. Ab initio calculations of the energy as a function of the reaction coordinate indicate the existence of two minima corresponding to the open and closed structures.

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 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: 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 concept of the equalization of atomic electronegativities accompanving molecule formation is applied to a study of the electronic structure of polyhedral clusters of main-group atoms such as Ge, Sn, Pb, Tl, and Bi. Emphasis is placed upon charged clusters such as Sn9-x Pbx4-(x = 0 → 9), Sn9-xGex4-, Sn8-xPbx Tl5-, Sn2Bi22-, SnTe44-, etc. The role of the relativistic spin-orbit splitting of an np shell into np1/2 and np3/2 subshells in modifying atomic and hence molecular electronegativities is discussed. Correlations are made between calculated charge distributions and observed199 Sn NMR chemical shifts for clusters of a given size and charge. It is concluded that a useful picture of charge distributions in these clusters may be obtained from electronegativity equalization considerations.

Notes: This paper examines the numerical performance of the BFGS variable-metric algorithm and compares this performance with that of the DFP, SR1, and OC algorithms. Numerical results indicate that the BFGS algorithm is far superior to the DFP and SR1 algorithms and comparable to the OC algorithm. Although the BFGS algorithm offers a viable method for the direct determination of localized molecular orbital coefficients, the method is not yet competitive with the more traditional methods.

Notes: Essential defects of present-day semiempirical methods (CNDO/2, CNDO/S, MINDO/3, MNDO) can be identified on two levels. First, the formalism shared by nearly all these methods treats parametric expressions, supposed to refer to Löwdin orthogonalized orbitals, as transferable. At best, this idea is approximately valid for the β functions for strong bonds. Second, the expressions used for these approximately transferable functions are based on inadequate arguments. As a result, the errors in many terms of the energy expression amount to several electron volts. The mechanism of error compensation through the parametrization is investigated in detail and shown to be surprisingly flexible, at least for some combinations of errors. Some cases of systematic absence of compensation are identified, and for weak interactions, e.g., those responsible for the water dimer, the semiemperical expressions appear to be so irrelevant that a detailed analysis of the causes of their failure is no longer possible. Minimal requirements for a correct semiempirical approach are given in the MORBIT rules. The two-center one-electron integral β is to be replaced by a function introduced by Mulliken; an efficient approximation for this expression is proposed.

Notes: We have carried out a computational study of the reactive properties of chlorooxirane, the metabolically produced epoxide of vinyl chloride that is believed to be a direct-acting carcinogenic form of this molecule. An ab initio SCF-MO procedure (GAUSSIAN 70) was used to compute the energy requirements for stretching the C—Cl and both C—O bonds (SN1 reactivity) and to determine the course of the epoxide's possible SN2 reactions with ammonia, taken as a model for nucleophilic sites on DNA. The epoxide was assumed to be protonated; both the oxygen- and chloro-protonated forms were considered. At each step along the various reaction pathways, the structure of the system was reoptimized. For the oxygen-protonated epoxide, the C1—O bond has a significantly lower energy barrier to stretching than does the C2—O. (The carbon bearing the chlorine is designated C1.) However, both are very much higher than that of the C—Cl bond in the chloro-protonated form, confirming our earlier finding of the relative weakness of this bond. In the SN2 processes involving ammonia, intermediate complexes are formed with both carbons of the oxygen-protonated epoxide, the C2-complex being the more stable. However, the most stable ammonia complex occurs at C1 of the chloro-protonated epoxide. Our calculated results, both the energies and also the geometry changes, allow us to propose two possible mechanisms for the formation of the 7-N-(2-oxoethyl) derivative of guanine that has been observed to be the major in vivo DNA alkylation product of vinyl chloride and has been suggested as possibly being responsible for its carcinogenicity. One of these mechanisms is SN1 and starts with the chloro-protonated epoxide; the other is SN2 and involves the oxygen-protonated form.

Notes: Ab initio SCF as well as pseudopotential calculations were performed for determining equilibrium structures and relative stabilities of several disilyne isomers. For the singlet state there are only two structures, the bridged and the silavinylidene carbene, which correspond to minima on the energy hypersurface. The most stable of the six isomeric structures investigated is the bridged conformer in the 1A1 electronic state, followed by the silavinylidene carbene in the 1A1 and 3A2 electronic states. Inclusion of electron correlation by MRD-CI calculations has no qualitative influence on the relative stabilities found in the SCF calculations.

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: Regularities observed in the variations of calculated energy components, for example, those of electronic and nuclear repulsion energies in the analysis of conformational changes and in studies of the propagation of basis set errors in ab initio calculations, are found to be related to the variational principle and to the boundedness of energy expectation value functionals. These relations are analogous to the le Chatelier principle of equilibrium thermodynamics, and may be formulated as a general “compensation principle” for two sets of general parameters of the molecular total energy functional.

Notes: The aim of this study has been to determine how the hydrogen bond between formaldehyde and ammonia is affected by the ring-opening interaction of protonated ethylene oxide with the ammonia nitrogen. Our purpose is to gain insight into the possible effect of carcinogenic epoxides upon the hydrogen bonding within DNA base pairs; it is known that such epoxides react with nucleophilic sites in DNA, including amine nitrogens that are involved in hydrogen bonds to carbonyl groups. We have used an ab initio self-consistent-field molecular orbital procedure to compute optimized structures, interaction energies, and other properties of interest. The H2CO·HNH2 system and the protonated epoxide were found to form two stable complexes, with syn and anti orientations. Their formation is accompanied by a significant overall strengthening of the H2CO·HNH2 hydrogen bond, as indicated by both calculated force constants and bond lengths. An analysis of these and other properties, such as atomic charges, suggests that the interaction is leading to the formation of N-protonated ethanolamine, which is linked to the formaldehyde through the proton on the nitrogen. If carcinogenic epoxides have a similar strengthening effect upon some of the hydrogen bonds in DNA, it could interfere in the replication and transcription processes.

Notes: The leading term in the asymptotic expansions of the three-center contributions to the exchange matrix elements for a system of three hydrogen atoms is derived. The approximations are used to estimate the importance of three center interactions in “spin-aligned hydrogen”.

Notes: The singularities of the quantum-mechanical electron current density induced in a molecule by an external magnetic field are analyzed via the theory of the real autonomous systems of differential equations. Group-theoretical techniques, based on the idea of color symmetry, are developed, which predict the occurrence of singularities about molecular symmetry elements. Plots of induced electron current density have been obtained for the ethylene molecule through accurate coupled SCF calculations. The theoretical magnetic properties of ethylene obtained through this investigation are the most accurate reported so far.

Notes: The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H2+ momentum distribution, it is shown that an infinite sequence of nodes does exist along the pz axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the pz axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the pz axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J(q) are discussed.

Notes: Hyperspherical coordinates are used to construct a matrix representation of a general N-particle Hamiltonian in the case where the interaction is electrostatic. The Yukawa interaction can be treated similarly, as is shown in an appendix. The basis functions used to construct the matrix representation of H are mononomials inthe 3N coordinates of the particles, multiplied by functions of the hyperradius. Methods for transforming from this representation to a symmetry-adapted representation are also discussed.

Notes: Coupled Hartree-Fock perturbation theory, within the framework of an accurate calculation, has been employed to visualize the electronic current density vector field induced by an external uniform magnetic field in the acetylene molecule. The current regime in a plane containing the molecular axis is rather different from those usually accounted for, evidencing the presence of a toroidal vortex in the C—H bond. The maps are useful in rationalizing the experimentally observed proton and carbon NMR chemical shifts.

Notes: We give an example of multidimensional numerical solutions in momentum space, for the Hartree-Fock equations of the simplest molecule with more than two electrons and two nuclei.

Notes: Analytic expressions have been derived for tensor convolutions of basis functions of exponential class (the reduced Bessel functions, the Slater, and the hydrogen-like functions). For reduced Bessel functions, in particular, the method suggested in the paper is a more clear and compact alternative to the laborious proof of the important Filter and Steinborn convolution theorem.

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: Valence bond (VB) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, φp, per site. Hubbard and Pariser-Parr-Pople (PPP) models illustrate ionic problems, with zero, one, or two electrons in each φp, while isotropic Heisenberg models illustrate spin problems, with only purely covalent VB diagrams. The difficulty of nonorthogonal VB diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-½ Heisenberg rings and chains of N ≤ 20 spins, or 2N spin functions, are solved in C2 symmetry as illustrative examples. The lowest S = 1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations corresponding to polyacetylene. VB diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.

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: 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: 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: 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: Density functional theory provides a natural and rigorous definition of an atom in a molecule in its ground state: The molecular electron density is the sum of atomic densities, the atoms have the same chemical potential as does the molecule, and the atoms are minimally promoted from their ground states. These atoms in general are not spherical, and in general they bear nonintegral charges. Charge transfer on molecule formation is thereby uniquely defined. Calculations by Palke and by Guse are reviewed, in which the hydrogen atom is identified in the hydrogen molecule.

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: The inelastic scattering of a light atom (helium) from a metallic surface with creation or annihilation of electron-hole pairs is studied. Diagonal and off-diagonal matrix elements of the atom-metal interaction are discussed. The nonadiabatic contributions to the scattering are analyzed in terms of a statistical potential. Explicit calculations are performed for a jellium model at electron densities corresponding to Al and Na. The electron-hole pair excitation probabilities turn out to be of the order of 10-5-10-3.

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: The questions considered are (1) How can “order” and entropy S(t) of a biological organism increase together during the growth process, in view of the common notion that entropy is a measure of disorder? The question is answered by an attempt to decouple entropy and disorder. The generalized point of view leads to the above “common notion” only if the number of possible states of the system n(t) is independent of time. However, in any given case one needs to know how S and n depend on time. (2) There are overwhelmingly more states of the matter of a living object which correspond to the absence of life than there are for the presence of life. This leads to the idea that spontaneous generation and replication of organisms are statistically unlikely. This is explained by presenting in a unified manner quantum mechanical considerations which go back twenty years or so. They resolve the “paradox” of the existence of life. They also show precisely what one needs to know about the statistical assumptions which one can reasonably make concerning the (uncertain) conditions which give rise to organisms and to replication.

Notes: In contemporary cells biological information is largely stored in nucleic acids. Therefore, a prerequisite in many theories on the origin of cellular life is the pre-existence of self-replicating polynucleotides that had to be formed by abiotic processes on the prebiotic Earth. It is usually assumed that the spontaneous synthesis of a self-replicating polynucleotide could take place readily. However, serious stereochemical obstacles exist which make such a synthesis extremely improbable. Amino acids, on the other hand, which are abundantly formed in prebiotic simulation experiments, are relatively easily polymerized to macromolecules (protoproteins) that share with modern proteins many properties: e.g., definable nonrandom structure, selected amino acid sequences, enzymelike activities, and self-assembly into supramolecular structures. Prebiotic polyamino acids are therefore regarded as the first informational macromolecules. The origin of this information is the chemical reactivity of the various prebiotic amino acids and their chemical response to their environment. The first informational polynucleotides were likely formed by a polynucleotide polymerase activity of prebiotic protoproteins. A comtemporary model for this process is seen, e.g., in the activity of template-free QB-replicase.

Notes: Activation of amino acids appears to have played a crucial role in prebiotic peptide bond formation. As a model of this process in living systems, phosphates have been used as amino acid activators. The possible role of clay and other minerals has also been investigated. We are presently using ab initio methods to investigate the activation of amino acids by these agents, as an initial step in peptide bond formation. A model of this activation process is described by the reaction: The first step in such an investigation, reported here, was to determine the lowest energy structures of a suitable set of reactants. As initial models of amino acids, Z was chosen to be H and NH2, corresponding to acetic acid and glycine, respectively. XO4Hn+1 = H3PO4 represents a phosphate group, while Si(OH)4 describes an edge tetrahedral site of a clay mineral. Al(OH)4- was also included to represent a tetrahedral edge site where the silicon is replaced by an aluminum. Finally, to complete the series XO4Hn+1, H2SO4 was added to the set of reactants. All species were optimized using the STO-3G and STO-3G* basis sets. For H3PO4 and Al(OH)4-, STO-3G* full optimizations were not possible. In these cases, certain torsional angles were optimized separately, then held at the optimized value, while the rest of the bond lengths and angles were optimized. All structures were compared to other calculations and to experimental geometries when available.

Notes: Based on previous research from these laboratories various structural analogs of 3-hydroxyflavone were tested for inhibition of glyoxalse I (S-lactoyl-glutathione methylglyoxal lyase, isomerizing; EC 4.4.1.5). The substrate of glyoxalse I (Glo I), methylglyoxal, has growth inhibitory properties. Glo I was purified 7000-fold from human red blood cells, and the concentration of various flavones was determined for 50% inhibition (I50) of enzyme activity. These compounds resemble the transition state of the methylglyoxal hemimercaptal as previously reported [Int. J. Quantum Chem. Quantum Biol. Symp., 10, 357 (1983)]. The I50 in μM varies from 5 to 330 for the flavones tested, with the parent compound 3-hydroxyflavone having an I50 of 10 μM. The most inhibitory compound in vitro was myricetin (5 μM), which has a 3′,4′,5′-trihydroxyphenolic ring at the 2 position of the pyrone ring.

Notes: The proton hyperfine coupling constants for the family of methoxyl-substituted semiquinones in aqueous solution have been determined by electron spin resonance (ESR) spectroscopy. These data and the electrochemical midpoint potentials for the corresponding series of substituted quinone/hydroquinone couples are discussed. Neither the additivity principle describing quinoidal hyperfine coupling constants nor the Hammett substituent relationship predicting electrochemical behavior are obeyed by these methoxyl-substituted quinones. It is shown, however, that the experimental data can be rationalized in terms of neighboring group interactions that occur between adjacent methoxyl substituents. Such perturbations apparently lead to a breakdown of hyperconjugation between the electronic bonding structure of the quinone ring and the methyl group of the methoxyl moiety. It is pointed out that ubiquinone is a dimethoxyl compound whose properties are determined by such neighboring group interactions. This observation may have important consquences for the fabrication of ubiquinone analogs and quinone-based drugs.

Notes: Ab initio calculations have been carried out on the reaction of NO+ with amines, using a 4-21G basis set. The influence of solvation was investigated using one to three molecules of H2O. Geometry optimizations were carried out on reactants, products, and intermediates. The results show that loss of CH3+ is energetically favorable and this fact has implications with respect to the mechanism of carcinogenesis by dimethylnitrosamine.

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: Living cells produce natural ac fields. This is shown by several experimental approaches. These are (1) the direct instrumental detection, as on yeast cells [1,2] and on the alga, Netrium Digitus [2]; (2) cellular spin resonance of lone cells [3-5]; and (3) dielectrophoresis, wherein the accumulation by the cells of tiny particles (ca. 2 μm diam) of either high or low permittivity is compared [4,6-8]. The oscillations are evident in a wide spectrum of cell types ranging from primitive bacteria to man's. In one species where cell morphology links readily to phases in the life cycle, it is observed that the electrical oscillations appear to be maximal at or near mitosis. This provokes questions as to why, how, and when such natural oscillations occur.To the question, “Do these natural electrical oscillations reflect essential or merely unnecessary cellular events?,” one is led to assume that they reflected needed processes, for they have persisted through the long evolutionary corridors of time. If, for example, they reflect events necessary to the cellular reproduction sequence, this further implies that there may be an electrical aspect to cellular growth and its control.These experimental findings lead to a testable theory: “cellular reproduction requires electrical oscillations.” Immediate tests of this idea are available in discussing the phenomenon of “contact” or “density” inhibition of cell growth, and in the four phases of mammalian life when cell growth occurs, i.e., during embryonic, normal somatic replacement, wound healing, and oncogenic growth. Several mechanisms whereby such electrical oscillations may arise in living cells are suggested and discussed.

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: Two simple and manageable schemes for integrating the time evolution operator e-iHt are discussed and applied to study vibronic effects in photoemission and optical excitation of model conjugated molecules.

Notes: Current experimental efforts, both with isolated binuclear metal complexes and with modified proteins, are focusing on the role of distance and of bridging groups in intramolecular electron transfer. After a brief overview both of standard and nonadiabatic electron transfer rates (in Hopfield's formulation) and of the current experiments. We consider the possiblility of bridge-assisted intramolecular electron transfer in three specific situations. For the bridged binuclear transition-metal complexes studied by Taube and his students, the tunneling integral T can be deduced by study of the optical intervalence transfer band. Here we discuss semiempirical calculations which suggest that bridge assistance occurs, and determine the size of T. The assistance is via a superexchange-type mechanism, and we suggest that hole-type or electron-type superexchange should dominate in saturated or unsaturated bridges, respectively. For the very strongly coupled Creutz-Taube ion, involving a pyrazine bridge, the electronic structure study of Ondrechen et al. requires the invoking of a three-site model to understand the optical and EPR data; this involves bridge-assisted transfer with a vengeance. Finally, for an oxide-bridged phthalocyanine dimer, the transfer takes place via ring π-π overlap, and no bridge assistance occurs. Thus bridge assistance in T will depend on the geometry and energetics of the specific case under study. One generally suspects, however, that bridge assistance will be found in very long-range (〉6 Å) transfer.

Notes: A nondiagrammatic formulation of the analytical first derivative of the coupled-cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree-Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first-order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non-perturbation-dependent set of equations can be solved instead. This and the first-order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

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: Matrix elements may be viewed as the scalar projection of an operator onto the transition density between the states involved (trace of matrix product equivalent to double dot product). This means that the operator and transition density matrices must “look the same” if a matrix element is to be the large. Using CNDO/S-CI wave functions, we have examined the symmetric part of the first-order transition density matrices (transition bond orders) for a series of aromatic systems whose π electrons are isoelectrornic with the nine-membered, ten-π-electron cyclononatetraene anion, including indenide, indole, benzimidazole, purine, and adenine. The topology of the parent hydrocarbon matrices is not purely even or odd as with alternant systems, thereby precluding exclusive action by vibronic or inductive perturbations.See P. R. Callis, T. W. Scott, and A. C. Albrecht, J. Chem. Phys. 78, 16 (1983). Nevertheless, interesting and useful patterns have emerged. For example, the matrices show, at a glance, how the D9th dictated degeneracy of the so-called Lb and La bands of the parent is retained as accidental degeneracy in some analogs because the crosslinking and heteroatom perturbations have opposite sign and nearly cancel. The first-order transition bond orders between La and Lb vanish so that real one-electron operators cannot couple these states in the parent molecule. This leads to distinctive La and Lb patterns which persist throughout the series, thereby providing a logical and satisfying justification for these intuitively assigned labels which are ambiguous in the Platt scheme: if one keys on the six-membered ring there is a striking correlation between the La,b transition densities, as they have been assigned, and those of benzene.

Notes: The use of raster display systems with refresh memory and read-write color map tables for man-machine communication is described. Particular emphasis is given to the application of such systems in molecular physics. Simple shading algorithms for molecular modeling and methods for the display of surfaces are given as examples. Some aspects of future development are summarized.

Notes: In this theory a chemical reaction is treated as a quantum transition from reactants to products. The approach leads to a Franck-Condon-like factor for the evaluation of product energy distributions. Second-quantization representation is used to enable a Hamiltonian for reaction to be defined. A specific adiabatic method is used to describe the dynamics of nuclear motion. The theory is applied to the reactions HO + D → OD + H and ClI + D → Cl + ID. Polyatomic photodissociation can also be treated by a similar formalism.

Notes: Computational studies are reported of Stieltjes orbitals for Hilbert-space descriptions of discrete and continuum molecular electronic eigenstates. Particular attention is focused on the identification of N → V π(π → π*) and N → Vσ(σ → σ*) intravalence contributions to photoexcitation and ionization spectra in CO and H2CO molecules. Three-dimensional graphical representations of appropriate Stielties orbitals serve to identify the σ → σ* transitions of Mulliken as photoionization resonances above threshold in these compounds, whereas the corresponding π → π* contributions are spectrally localized as familiar discrete excited states. The development illustrates the nature and properties of Stieltjes orbitals, and demonstrates their utility in studies of both discrete and continuum excitation spectra on a common basis.

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 singlet-triplet energy difference in para-, meta-, and ortho-xylylenes is studied as the interaction of two radical centers through the benzene ring. An SCF perturbative procedure adapted to open-shell systems leads to two benzyl-like nonbonding molecular orbitals (NBMOS) and to benzene-like occupied and vacant MOS whatever the xylylene isomer. The superposition of these NBMOS in para-, meta-, and ortho-positions and their interaction with the benzene-like MOS lead, at the configuration interaction level, to the following results: The exchange energy (which favors the triplet state) and the charge transfer energy (which favors the singlet state) are important only in the meta-xylylene; the dynamic (or double) spin polarization favors the triplet in meta and the singlet in para and ortho-isomers; the super-exchange energy (which favors the singlet) is important only in para- and ortho-isomers. The above results are independent of the chosen geometry.