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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: Single-channel studies have shown that there exist a multiplicity of conducting states in Gramicidin A (GA). In an earlier work presented at this symposium, it was proposed that such a multiplicity may be expected from different long-lived side-chain distributions available for the channel molecule. In order to test this hypothesis, Leu5-Gramicidin A was synthesized and the effect of replacing the L · Ala5 residue by L · Leu5 was analyzed. First, molecular mechanics calculations on Leu5-Gramicidin A are presented. Then the single-channel conductance sweeps obtained for Leu5-GA are automatically analyzed in the computer using specifically developed algorithms. The results show a dramatic decrease in the multiplicity of states due to the Leu5 substitution. This experimental result is discussed in the light of structural concepts emerging from molecular mechanics calculations.

Notes: The Hamiltonian formulation of chemical kinetics is applied to all closed, single-step, integer-order chemical reactions. In all cases, the dynamics of the Hamiltonian leads to the correct phenomenological rate equation. The relationship between reaction order and the form of the reaction potential is discussed.

Notes: Pb2+ specifically cleaves yeast tRNAPhe in orthorhombic crystals at phosphates P18 and P60 in the dihydrouridine (D) and pseudouridine (T) loops, respectively. Although there are three major lead binding sites in the tRNA, it appears that both cleavages are affected by the same lead ion. The P18 site is apparently the same site that is hydrolyzed by Pb2+ in solutions of the tRNA and is the major cleavage site in crystals. It is shown from P32 labeling studies with polynucleotide kinase that the products of Pb2+ cleavage have the 5′-hydroxyls on G18 and C60, and consequently the 3′ phosphates are on D17 and U59. The OH- in the first coordination sphere of the hydroxo complex Pb(OH)+ either directly or through a water molecule abstracts the proton of the 2′-OH of D17. This promotes a nucleophilic attack by 2′-O- on P18 with subsequent cleavage of the P—O5′ ester bond to generate the major Pb2+ cleavage product pG18-A76. The anchoring of the Pb2+ by the T-loop and D-loop residues seemingly provide the right environment for the generation of the hydroxo complex required for the hydrolysis. Additionally the strain of the phosphodiester conformation at P18 enhances the cleavage at that site. The Pb2+-catalyzed cleavage of tRNA exemplifies a mechanism used not only for the hydrolysis of transfer RNA but one potentially used by other RNA-catalyzed reaction utilizing metal ion cofactors.

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: By use of computer algebra and expansions of orbitals about a single center in spherical harmonics with a matrix representation for the α-function coefficients it is possible to produce formulas for each term of an infinite series that represents the value of a three-center exchange integral. Only seven terms are required to get six decimal digits for triatomic hydrogen. This method is readily generalized to solve all three-center exchange integrals over Slater-type orbitals.

Notes: The simulated ab initio molecular orbital (SAMO) method band structures of six fluorinated and six chlorinated polymers derived from linear polyethylene are presented and compared with extended Huckel and CNDO/2 studies and with the results of ESCA spectroscopy.

Notes: The summation of the perturbation series for the hydrogen Zeeman effect using the renormalized series technique is studid. Improved results are obtained compared to those obtained from the unrenormalized series; the method has the advantage of not requiring any information on the largeorder behavior of the perturbation series coefficients.

Notes: The two lowest bound excited states of the Be- ion, 1s2 2s2p2 4P and 1s2 2p3 4S0, and their respective thresholds, Be 1s2 2s2p 3P0 and Be 1s2 2p2 3P, and the thresholds of these, Be+ 1s2 2s and Be+ 1s2 2p, have been examined using many-body methods. Here, we present the electron affinities (EAs) or ionization potentials, fine and hyperfine structure, and the electric dipole transition probabilities associated with these states and compare them with existing theory and experiment when available. Based on our new EA, a suggestion is made as to why no negative ion transition has yet been seen in the laboratory.

Notes: We derive theoretical experessions for molecular third-order frequency-dependent susceptibilities which represent dc electric-field-induced second-harmonic generation. Our results are valid also if some of the molecular eigenvalues are degenerate as long as the molecular ground state is nondegenerate. The results are in suitable form for quantitative applications, either to small atoms or molecules or to large organic conjugated or aromatic molecules.

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: Current computer hardware developments, in particular, vector processing and parallel processing, are likely to open the door for new applications in quantum chemistry. One applied field that is expected to evolve is a computer-based approach to quantum-chemical synthesis design. Whereas some of the computational difficulties still appear formidable, there are reasons to be optimistic: besides the direct impact of computer hardware developments on existing methods, new theoretical approaches such as density functional theory and numerical molecular wave functions may also become feasible. The topological model of energy hypersurfaces, reaction topology, and quantumchemical manifold theory of reacting systems form a possible framework for a global analysis of a set of all reactions involving a fixed set of nuclei and a fixed number of electrons. The apparent bottleneck for the application of the topological method is the actual computation of the catchment regions (open sets) of reaction topology Tc. In this study some properties of catchment region boundaries are described which lead to computational simplifications. Whereas the ultimate goal of the proposed analysis is to serve as an aid in future quantum-chemical synthesis planning, nonetheless, the boundary networks and sum rules developed in this study may also be of some immediate interest in local surface analysis.

Notes: The fixed-node quantum Monte Carlo (QMC) method is used to obtain the classical barrier height for the H + H2 exchange reaction. Using a spin-restricted, single-determinant trial function ΨT, the authors find that the reaction barrier Eb is less than 9.69 ± 0.25 kcal/mol. This mean value is below the calculated energy barrier obtained by Liu in the most extensive CI calculations on this system. Furthermore, the QMC saddle-point energy of - 1.65903 ± 0.00040 hartrees at the CI-determined geometry lies 0.00027 a.u. (0.17 kcal/mol) below Liu's best CI value. Finally, spinrestricted and spin-unrestricted single-determinant trial functions are contrasted. Although the variational energy 〈ΨT|H|ΨT〉 for an SCF ΨT must be lower for the unrestricted case, this is not true generally for QMC. In fact, we show that if the unrestricted SCF ΨT has the lower QMC energy, then there exists another spin-restricted, single-determinant ΨT whose QMC energy is lower than the QMC energy of the spin-restricted SCF ΨT.

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: Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac-Coulomb Hamiltonian HDC. However, because the electron-electron interaction mixes positive- and negative-energy states, the operator HDC has no normalizable eigenfunctions. This fact undermines the quantum-theoretic rationale for the Dirac-Hartree-Fock (DHF) equations and therefore that of the relativistic configuration-interaction (RCI) and multiconfiguration Dirac-Fock (MCDF) methods. An approach to this problem based on quantum electrodynamics is reviewed. It leads to a configuration-space Hamilton H+U which involves positive-energy projection operators dependent on an external potential U; identification of U with the nuclear potential Vext corresponds to use of the Furry bound-state interaction picture. It is shown that the RCI method can be reinterpreted as an approximation scheme for finding eigenvalues of a Hamiltonian H+U, with U identified as the DHF potential; the theoretical interpretation of the MCDF method needs further clarification. It is emphasized that if U differs from Vext one must consider the effects of virtual-pair creation by the difference potential δU = Vext - U; an approximate formula for the level-shift arising from δU is derived. Some ideas for dealing with the technical problems introduced by the projection operators are discussed and relativistic virial theorems are given. Finally, a possible scheme for adapting current MCDF methods to Hamiltonians involving projection operators is described.

Notes: Single-configuration relativistic Hartree-Fock values of the first ionization potentials for Cu through Kr7+, Ag through I6+, and Au through Pb3+ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r0, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r0 parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree-Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.

Notes: The problem of bond length alternation in linear extended systems with conjugated double bonds is examined on a simple cyclic polyene model using finite-order many-body perturbation theory. Three different partitionings of the model Hamiltonian are employed, namely the Hückel, Møller-Plesset, and Epstein-Nesbet partitionings. The dependence of correlation energy on bond length alternation is examined in each case, showing an almost constant behavior of Møller-Plesset and Epstein-Nesbet perturbation energies in contrast to a strong dependence on distortion, favoring undistorted structures, for the Hückel perturbation and UHF correlation energies. The origin of an unphysical character of the Hückel perturbation theory and the inappropriateness of the UHF approach for the problem considered are pointed out. The second- and third-order Møller-Plesset and also the second-order Epstein-Nesbet perturbation theories yield results which are similar to those obtained with the RHF method and which clearly favor the bond length alternating structures, leading to the bond length distortion of about 0.045 Å and to the stabilization energy per site (relative to the equidistant geometry) of about 0.03 eV.

Notes: The limitations arising from the use of a frozen orbital approximation applied to 3s and 3p electrons of the iron atom are investigated at the CI level.

Notes: This is the first paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians directly in the spin-orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U(n) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.

Notes: The unitarily invariant decomposition of Hermitian operators is performed by means of Lie algebra.

Notes: A new derivation is given for the Waller-Hartree-Fock double-determinantal spatial wave function. One starts from the single-determinant wave function in which a orbitals are doubly occupied, and decomposes it into a sum of products of spatial and spin functions. The spatial product of the first genealogical spin eigenfunction is a double-determinantal function. The derivation is based on the simple form of U1ƒ(P) when the representation matrix is obtained from the genealogical spin eigenfunction.

Notes: Expressions for the second-row nuclei chemical shifts calculation using a CNDO-SCF wave function are outlined. In collating it with the Pugmire and Grant's equations, a term with a changed sign appears. Both sets of equations are applied to a study of carbon-13 chemical shifts in alkanes down to C7; results are interpreted with aid of the Lindeman-Adams' empirical equation. Expressions proposed are confirmed for an excellent agreement with experimental data.

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: In this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many-electron systems. Since the states of a many-fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two-body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin-dependent operators from the known matrix elements of certain spin-independent two-body operators. In particular this implies a segment-level formula for the matrix elements of the U(2n) generators in the spin-orbit basis.

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: Compact, convenient expressions for the electron density are derived using a fitting functional. Results are given for H2O, CH4, HF, NH3, and PH3, and show the accuracy obtainable using differing numbers of functions on each center. The definition of an atomic charge using these expressions is discussed and it is shown that the Bader virial-partitioning definition, in which the density is integrated over a volume around each nucleus, leads to convergent results.

Notes: The generalized Hellmann-Feynman and curvature theorems are derived for the generalized Sturm-Liouville-type eigenvalue equation which is widely encountered in many branches of physics. In classical mechanics, the Sturm-Liouville eigenvalue equation primarily arises from applying the theory of small oscillations to vibration problems while, in quantum mechanics, the most important example is the time-independent Schrödinger equation. The generalized theorems, respectively, provide simple useful expressions for the first and second λ derivatives of the eigenvalue where λ is an arbitrary real parameter appearing in the eigenvalue equation. These results, which apply to both classical and quantal systems, include as special cases the well-known quantum mechanical Hellmann-Feynman and curvature theorems for the time-independent Schrödinger equation, thus unifying the formalism. This connection between classical and quantum mechanics is of interest per se, and also because classical eigenvalue equations find application in the treatment of some quantum chemical problems. Two derivations of both generalizations are presented, the first proof applying to exact and Rayleigh-Ritz (linear variational) solutions of the eigenvalue problem, and the second, more general one, to arbitrary optimal variational as well as exact solutions. Necessary and sufficient conditions for the validity of the results are discussed. To demonstrate the insight they afford, several applications of the theorems in conjunction with perturbation theory are described.

Notes: In connection with spin adaptation in many-body perturbation theory, this paper reexamines the use of spin graphs in view of a Hugenholtz-like representation where both the orbital and the spin parts coexist. Together with the idea of essentially distinct diagrams, this representation leads to an economic handling of spin adaptation. As a side issue, the appropriate generalization of the Epstein-Nesbet partitioning for spin-adapted perturbation theory is obtained. Compact formulas up to fourth order of the ground-state energy, and up to third order for excitation energies and ionization potentials are given.

Notes: The unitarily invariant decomposition of Hermitian operators for a boson system is performed by means of the symmetry of group SO(2, 1) and the decomposition is also closely related with Lie algebra.

Notes: This is the final paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians. In this paper we derive the reduced matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables a direct evaluation of the matrix elements of spin-dependent Hamiltonians in the spin-orbit basis. An alternative (indirect) method, which employs the use of U(2n) ↓ U(n) × U(2) subduction coefficients, is also discussed.

Notes: This paper lays the algebraic foundation of a unitary group approach to many-body theory. We define a set of second quantized spin-shift operators which are used to construct spin-adapted many-electron configuration functions. We investigate the particle-hole transformation, normal ordering, and contraction of spin shifts. This gives an orbital Wick's theorem reflecting the permutational structure of the states spanning the irreducible representations of the spatial unitary group. We study the spinless Hamiltonian, and the relationship between spin shifts and unitary group generators.

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: Theoretical substituent effects upon the acidity of the title compounds were investigated using STO-3G basis sets augmented by diffuse functions for all oxygen atomic centers of the probe groups. The results are discussed in connection with the available gas-phase data within a novel conception of attractive and repulsive substituent effects.

Notes: Isomerization of octahedral complexes XY6, by a mechanism known as diagonal twist (in which two ligands in cis positions, one to another, exchange sites) is considered. Construction of the corresponding isomerization graph is outlined (reported before by Balaban) and the problem of determining its symmetry is considered. Alternative routes for deducing the order of the automorphism group are described. The group is confirmed to be S6 and representative symmetry permutations (one for each of the 11 classes of S6) are shown. Alternative pictorial representations of the 15-vertex graph are also shown.

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: A new procedure for the Fock matrix operator construction is proposed. Its application for RHF calculations on diatomic molecules using Slater orbital basis sets shows that the computation time for the new SCF procedure is proportional to the square of the basis set size.

Notes: In this article we derive a segment-level formula for the matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables the direct evaluation of the matrix elements of spin-dependent Hamiltonians.

Notes: A new method for solving correlation pair equations for diatomics is presented and followed by numerical results for the H2 and LiH molecules. The essential feature of the new approach is a numerical representation of both basis two-electron functions and Coulomb and exchange potentials in pair equations. It is shown that this significantly simplifies the pair function optimization procedure.

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.