ALBERT

Notes: The mapping between the local one-body potential and the ground state density is discussed. The role of degenerate ground states, which form a set of measure zero in potential space, is shown to be amplified by the unitary transformation between degenerate densities, forming a space filling set in density space. A numerical experiment demonstrating these features is carried out. No indication of non-V representable densities is encountered.

Notes: In this paper we present a simple method within the coupled Hartree-Fock framework to calculate the 1s2s 3S state of helium and heliumlike ions. The results are in very good agreement with those obtained by the use of multiterm correlated wave functions. Some interesting observations associated with the wave function are presented.

Notes: A scheme for obtaining approximate solutions of the electronic Schrödinger equation is formulated within the context of the method of moments. The flexibility of the method of moments is utilized in the construction of a model based on an antisymmetric product of geminals (APG). This APG model is compared with a model based on an antisymmetric product of strongly orthogonal geminals (APSG). As a test example the advocated APG model is applied to the ground state of ammonia. Our best APG function recovers 37% of the total molecular correlation energy to be compared with an estimated 31% for the best APSG function.

Notes: The shape of correlation holes in many-electron systems is at present scarcely known, even where correlated wave functions are available. We investigate here the kind of electron correlation brought about by configuration interaction (CI), within a given basis set, in the wavefunction of a polyatomic system. The model ring system H6 (in two different bonding circumstances) and H14 have been chosen for a detailed study, because of their paradigmatic importance. We set out the equal-spin and different-spin correlation holes as obtained from complete CI calculations in H6 and partial ct in H14, both within a minimal basis set. We basically find the spinless correlation as being short range, while the spin-dependent correlation holes show long-range oscillations of antiferromagnetic character. We also present a natural spin-geminal analysis of the two-body reduced density matrices in these systems; we find a peculiarity possibly related to the long-range correlation discussed above. Finally, we compare the electron correlation as given from our CI wavefunction to other pictures of electron correlation, as obtained essentially from alternant molecular orbital wave functions and from the electron-gas literature.

Notes: Some physical and chemical properties of the metabolites of the cancerostat cyclophosphamide (trade name: ENDOXAN) have been calculated with an appropriately prepared CNDO/S-CI method. The ground state properties (e.g., charge densities and free valences) do not indicate a significant change, compared with the results of cyclophosphamide, and the same fact is also true for the energy levels of the two lowest excited singlet and triplet states. With respect to the dipole transition moments only the metabolite N-mustard-diamido-phosphoric acid (Friedman acid) differs drastically from cyclophosphamide and the other metabolites. The chemical reactivity has been considered under the aspect of singlet-triplet transitions between quasidegenerate singlet and triplet states. Again Friedman acid behaves quite differently from the other compounds, and only this metabolite exhibits the remarkable ability to act as an alkylating agent via splitting off chloride ions.

Notes: A new convenient and efficient finite-difference (FD) method is developed for solving the pair radial equations (PRE) of many electron perturbation theory (MPT). This method can be interpreted as the FD analog of the well-known Fourier method. The method is used to solve PRE arising in the second order of MPT based on the hydrogenic and Hartree-Fock (HF) zero approximations. Being very simple programmed our method gives results comparable with the most accurate variational calculations.

Notes: Static dipole and quadrupole polarizability (αd and αq, respectively) values of coupled Hartree-Fock quality have been calculated for the alkaline earth atoms Be(2s), Mg(3s), Ca(4s), and Sr(5s) using a method based on the many-body perturbation theory. The present values of αd and αq for Be and αd for Mg are in excellent agreement with the other available results of similar accuracy. The CHF calculations of αd for Sr and αq for Mg, Ca, and Sr are being reported for the first time.

Notes: The time-independent Schrödinger equation for a one-dimensional square step potential with impenetrable walls was solved to prove the suitability as an oscillator potential. The mathematical structure of the eigenvalue conditions and the number of eigenstates within one potential step are discussed.

Notes: A direct method for calculating resonant states in reactive scattering is suggested, permitting us to obtain the characteristics of multichannel resonances (partial width amplitudes). The method is based on the construction of a Laurent expansion of the scattering matrix S(∊ -iΓ/2) in the complex plane. The position of the poles of the S matrix are derived by solving the dynamical problem with complex energy values. The residue at the pole gives all the information concerning the partial widths. The method is applied to a linear triatomic reactive scattering problem. The properties of the resonant states in the H + H2 system are calculated as an example. Two broad resonances are found which have not been reported in previous calculations. The interference of overlapping resonances is shown to have a profound effect on the energy dependence of the transition probabilities.

Notes: The amount of work needed to evaluate the matrix elements in a configuration interaction calculation can be very large. This is especially true if the phase associated with bringing determinants into maximum coincidence is evaluated at the determinant level. A method is presented which allows the phase to be determined at the occupation level for arbitrarily coupled configuration state functions.

Notes: Comparison of the molecular Q-optimized and molecular gradient optimized carbon basis sets for CH4 showed that molecular Q optimization is an excellent substitute to the more expensive molecular gradient optimization. The parameter Q of the Q optimization is related to the population (i.e., net charge) on the atom.

Notes: The salient features of generalized second-quantization representations for nonrelativistic systems of composite particles are reviewed and their application to a reformulation of the quantum theory of reactive collisions is discussed. Such representations allow the properties of the bound composite states to be built explicitly into the algebra of states and observables. A single unperturbed Hamiltonian simultaneously describes the free propagation of the various species of bound composites as well as of their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes. The inclusion of the binding of all composites in the unperturbed Hamiltonian cures the divergences in the Born series arising from bound-state poles. Unstable composites can be included in a natural way, leading to an explicit representation for the kinematics and dynamics of their decay and their contribution to collision phenomena.

Notes: Based on the all-valence ZDO SCF approximation a procedure for estimating the basis set superposition error (BSSE) in semiempirical CNDO/INDO methods has been proposed. The results of the calculation show that the BSSE effect may improve the results obtained from the standard CNDO/INDO supermolecule calculation. The estimated BSSE effect enables one to explain some recently reported artificial structures for water and ethylene dimers.

Notes: An approach based on the topological distance matrix is used for algebraic characterization of bridged polycyclic compounds. The classical bridged structures which have external bridges between cycles were examined together with the more complicated three-dimensional polycyclic systems regarded as containing internal bridges. Thirteen rules are given for characterizing the main types of structural rearrangements in these compounds. The important topological characteristic of (poly)cyclic systems, the molecular cyclicity, is examined in the polycyclic condensed, spiro- and bridged structures, respectively.

Notes: The accuracy of a new effective one-body potential is assessed by the study of the electronic structure of atoms from He to Kr. The exchange part of this potential is obtained from a local approximation. Several simplified representations of the electronic density which lead to analytic Coulomb potentials are tested. It is shown that the introduction of the shell structure of the density is necessary, at least for third row atoms. The screening parameters of the potential are variationally optimized with respect to the total energy of the atom. With the most elaborate form of the Coulomb potential which contains one screening parameter for each shell, the comparison of the results with exact Hartree-Fock calculations is very promising. The relative difference is on the order of 10-5 for the total energy and on the order of 10-2 for the orbital energies. Multiplet splitting is reproduced accurately and F- is predicted to be stable (in contrast some others local potentials) by an amount of 0.046 a.u., compared with 0.050 a.u. for an exact Hartree-Fock calculation.

Notes: The nature of problems connected with binding which arise in the everyday work of experimental physicists and material scientists is illustrated by reference to two different experimental studies. (i) Sliding in crystals of group V elements is found to take place not only along planes cutting the quasimetallic bonds, but also along planes apparently cutting their “covalent” bonds, thus suggesting that a more elaborate picture of the two types of bonds and of their interrelation is necessary. (ii) The physisorption of linear pentatriacontane on alkali chlorides indicates alignment of the paraffin molecules along the [110] directions. This may be associated with polarization of methylene groups by ions in the substrate. This hypothesis must be substantiated by suitable quantum-theoretical calculations, which in turn must be based on an adequate description of the adsorption bond.

Notes: The point of view of chemical engineers concerning the possible contributions of fundamental research to their work is briefly illustrated by reference to catalyst design. Specific questions on which the author is working are mentioned. The growing importance of zeolites and their challenge for fundamental research is also pointed out.

Notes: Which information on the properties of the adsorption complex can be obtained from the application of the standard methods in experimental surface science is discussed. None of the methods gives all the information necessary for a complete description of the chemisorption bond so that the results delivered by as many methods as possible should be taken into account.

Notes: It is the intent of this article to illustrate certain aspects of the present status of electrochemistry as regards theoretical interpretations. First a brief critical review of classical electrochemical kinetics is given and the directions are indicated in which improvement in theoretical treatments are hardly needed. Next, experimental results on the cathodic discharge of tin in darkness and in light are presented, and a tentative explanation based on the assumption that adatoms (and not adions) diffuse on the electrode surface as a result of stabilization by light is presented.

Notes: Relativistic quantum-field theory provides the machinery for calculating wave functions or probability amplitudes depending upon space-time coordinates. The currently accepted theory, however, fails to provide position operators and a means of measuring particle coordinates that are consistent with Dirac's properties of physical observables. This is because it calls for a space position probability distribution at a specified time. This paper shows, however, that space-time event coordinate operators, together with a corresponding measurement procedure, can be found that are consistent with Dirac's requirements. This is done through a reinterpretation of the amplitudes computed by field theory and does not involve any change in that mathematical formalism. The measurement of the space-time coordinates of an event is accomplished by detecting the absorption of a photon by a particle from each of two light pulses designed to overlap at a given point at a given time. If a final emitted photon has an energy whose sum with the final particle energy approximately equals the sum of the mean energies of the pulses, then the absorption of the two pulse photons must certainly have taken place within a distance the order of a Compton wavelength of the small space-time region of overlapping pulses. This is clear from the fact that the high energy required to confine the pulses to very small volumes must throw a particle absorbing them far off the mass shell. Thus the absorption of the two photons throws the particle into a narrowly confined spatial wave function that must decay extremely rapidly - to within a Compton wavelength, a delta function in space-time. This delta function is the eigenfunction of space-time coordinate operators Xμ and is the scalar product of vectors in a Hilbert space spanned by spin-space-time kets large enough to contain the operators of the Poincaré group. These event operators transform properly under the action of Poincaré operators but do not commute with the mass. If the Compton wavelength is not negligible compared to the accuracy desired in the coordinate measurements, individual coordinate measurements are no longer possible. Nevertheless, a large number of repeated coordinate measurements can be carried out to produce a coordinate probability distribution. This distribution can be unfolded to find a true coordinate probability distribution if the charge form factor is known from basic theory. An analysis of laboratory particle detection techniques shows that they actually determine space coordinates and energy rather than spatial coordinates at a given time. When this fact is included, the Klein-Nishina formula can be derived using the electromagnetic four-vector potential as the photon probability amplitude wave. To clarify the meaning of the observables, a mass-momentum measurement is described.

Notes: Some aspects of fiber bundles, sheaf theory, and possible generalizations of the notion of differentiable manifolds are discussed.

Notes: Let two strongly continuous one-parameter semigroups of contraction operators, {Z(t); t≧ 0} and {Z0(t); t ≧ 0}, determine physical evolutions realized in the Hilbert spaces ℋ and ℋ0, respectively. We consider the mappings under Z(t) and Z0(t), when the infinitesimal generators G and G0 belong to a product class, properly defined with respect to an H0-norm. The inversed transform of each side in the identity R(λ, G) = R(λ, -iH0)-iR(λ, -iH0)VR(λ, G), which represents a simple algebraic decomposition of the resolvent of G, converges on Ψ if and only if Ψ ∊ D(G). By iteration an asymptotic series emerges, when t → 0. Numerical considerations of this approximation in its first order may support the form of a deviation from the pure exponential decay when the semigroup is compared with a integral transform corresponding to a certain self-adjoint H0 in ℋ0. The deviation may hardly ever be observed and it is therefore most fruitful to discuss the results inside the framework of the enveloping algebra of the semigroups.

Notes: This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February-March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous - at least at the time - the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.-O. Löwdin.

Notes: A formulation of quantum mechanics is presented based on the theory of semigroups and the associated enveloping algebras of functions defined on countable subsemigroups. The existence of a unique *-involution is not assumed. The fundamental elements of a semigroup are identified with experimental precedures for the separation of subensembles from a given ensemble of experimental systems. Observables are represented as elements of enveloping algebras, and ensembles as density matrices within an enveloping algebra. The statistical properties of ensembles are expressed in terms of traces defined on the semigroup and its enveloping algebras. The elements and generators of the Poincaré group can be defined and interpreted in the usual way. A variety of applications is described, in which the theory of the density matrix plays an essential or effective role. Advantages associated with the resulting freedom from the limitations of Hilbert space are illustrated.

Notes: The nodes where the wave function changes sign in conventional quantum theory can alternatively be regarded as places where the wave function descends to zero but rises again without changing its sign. This behavior is accomplished by adding delta function barriers to the potential energy wherever a node occurs in the wave function. This model is supported by the recognition that the wave functions of a subsystem, which is not truly isolated, are really marginal amplitudes which implicitly average out interactions of the system with its environment. The finite effect of these interactions is to replace the delta function barriers by barriers of finite width and height.

Notes: Interaction energies ΔE accompanying the formation of van der Waals (VDW) systems may be estimated by means of the formula ΔE = ΔESCF + BSSE + ED(r-6, r-8, r-10), where BSSE is the basis set superposition error and ED is the dispersion energy in the expanded form. Twenty one stationary points were located on the potential energy surfaces of hydrogen-bonded complexes; of those, 18 were local minima and 3 were saddle points. Thermodynamic characteristics calculated on the basis of molecular constants, quantum chemically generated, were obtained for 12 hydrogen-bonded complexes and for competition equilibria between VDW molecules. The role of the VDW forces in some rate processes and in a prototype of enzyme-substrate interactions is outlined. In connection with enzymic catalysis, the intramolecular discrimination in 1,2-difluorohydrazine, and the stability of hydrogen-bonded complexes in a cation field is discussed.

Notes: An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule - a factor completely overlooked in the usual scheme of calculations.

Notes: Quantum mechanics is a remarkable formalism for studying problems in the microscopic domain, and nobody has reasonably contested its power. Nevertheless, in spite of the many interpretations which have been proposed, its true meaning is far from being clear. The aim of this preliminary paper is to show that it is possible to conceive within a classical framework an interpretation of quantum mechanics and to make its limits of validity precise.

Notes: When calculating the correlation energy where the effect of higher than double excitations is included by means of many-body Rayleigh-Schrödinger perturbation theory (MB-RSPT) through fourth order the problem of cancellation of exclusion-principle-violating (EPV) diagrams arises. The cancellation of EPV diagrams in fourth order of MB-RSPT is demonstrated for diagrams which include the effect of tetraexcitations.

Notes: A complete development of the PCILO method is presented for the INDO approximation. The introduction of exchange terms in the theoretical treatment is discussed and a detailed analysis of the successive contributions to the total energy is given. The method is applied to various conformational problems (geometry optimization, rotation, and inversion barriers). Its ability to deal with biological systems is tested on the acetylcholine neurotransmitter. Inversion barriers are highly improved with respect to the corresponding CNDO algorithm. A better account of σ-π exchange phenomena can be expected with the presented PCILO-INDO development.

Notes: Scope and limitations of different approaches which enable π electronic systems of topologically equivalent structures to be compared have been examined. Particular attention has been paid to analyses in terms of molecular subsystems.

Notes: In agreement with previous calculations by the authors, three definite resonances in the elastic electron-SF6 molecule scattering in the energy range 5-40 eV have been obtained with a multiple scattering method, elaborated originally for molecular bound states and modified here for scattering states. Results with various more-reliable one-electron potentials have been compared with previous calculations and available experimental data.

Notes: While regarding the elementary biological function as a series of elementary acts resulting in either chemical bond formation (breakage) or a changed molecular subsystem state, we would like to focus attention on some of the most essential and general features of this process in terms of the Von Neumann theory of self-reproducing automata.

Notes: The electron mechanism of the nonequilibrium vibration excitation is considered in multiatom molecules with the condition that the bottleneck effect takes place. The quantum-statistical theory states that if the simplest enzyme reaction is proposed on the basis of the vibrational energy recuperation idea, the vibrons emitted in producing the free product and enzyme activate the first stage of the formation of the Michaelis-Menten complex and the multiphonon feedback mechanism is realized. Resulting solutions are applied to explain some biochemical and genetic effects.

Notes: Electrostatic interaction energy has been studied for the DNA base pair-RNA base complexes inside the deep groove of the DNA. The allowed region has been continuously scanned in order to find out a minimum energy configuration for each complex. A comparative study of the interactiion energy values and the site of association has been carried out. It has been found that the Watson-Crick G—C base pair shows a definite specificity similar to the model proposed by Zubay or Riley, while for the A—T pair, no specificity can be assigned on the basis of the interaction energy studies alone. Instead, an assumption for a hypothetical backbone directed by the G—C pair specificity, has been adopted to assign a specificity to the A—T pair. As a consequence of these studies, a model for transcription without unwinding of the DNA double helix has been developed.

Notes: The three dimensional structure of human carbonic anhydrase-B has been model fitted to electron density maps in an interactive graphics display and improved by real space refinement and restrained least-squares refinement. The crystallographic R factor for the 5 to 3 Å data dropped from 41.5% to 36.5% after four cycles of least-squares refinement. The important residues involved in the function of the enzyme showed improved positional parameters after the refinement. Thus GLU106 and THR199 oxygen atoms are within hydrogen bond distance of each other after the refinement. Whereas they were very close to each other before the refinement. The procedures involved in the refinement and the implication of the structure to the mechanism of action of the enzyme are brought out.

Notes: Introducing the concept of the “dinucleotide” as the helical repeat, theoretical attempts have been made to determine possible single and double stranded helical structures by using helical parameter calculations and model building investigations. By virtue of its flexible framework, the dinucleotide repeat offers a much greater scope of finding new secondary structural forms for nucleic acids. Considering only those conformations which show tendency for at least partial base overlap as does the dinucleotide helical repeat, it has been possible to predict poly(dinucleotide) helical models in which successive phosphodiesters as well as nucleotide conformations alternate. More important, the recently found left-handed Z-type polynucleotide helix is characterized rather uniquely on the helical parameter plot. The results further suggest the possibility of other Z-type helices obtainable by alternative conformations for the exocyclic C4'-C5' bond and sugar pucker. Near neighbor long range conformational correlations between the dinucleotide repeat and the phosphodiester linking them have been established similar to poly(mononucleotide) helices. Need for considering higher repeats such as trinucleotide has been suggested to obtain models for looped out helical conformations.

Notes: A procedure for calculating the molecular electrostatic potentials on surface envelopes surrounding macromolecules is presented. This new representation of potential is employed in studying B-DNA double helices and, from the results, deductions are drawn on the interaction specificities of B-DNA with electrophiles.

Notes: The results of calculations of the transition energies and polarization in nucleotide bases performed by the CNDO/S CI method are compared with experimental data for long-wavelength and vacuumabsorption bands. The calculations and the analysis of experimental data testify to the existence of n - π* transitions in the first absorption bands of the bases. The study of double-stranded polynucleotides and DNA hypochromism based on the theoretical electronic characteristics of the bases and perturbation theory is performed. The role of stacking and complementary interactions within the hypochromic effect is cleared up. Two mechanisms for the shift of the fluorescence band maximum are investigated: two-proton transfer along H bonds and excimer formation. The study of H-bond potential curves shows the disadvantage of two-proton phototautomerism in the nucleotide base pairs in contrast to model systems. The possibility of excimer state formation in stacked homo- and heterodimers of nucleotide bases is shown within the extended-Hückel treatment. The nature of excimer minimum for the excited-state potential curve is analyzed.

Notes: The quantum-mechanical virial theorem (in diagonal and nondiagonal forms) for molecules in an external, weak, uniform electric field is used for obtaining the analytical expression of the potentialenergy surface in the Hartree-Fock-Roothaan one-determinantal approximation. The polarizability tensor components of the H2O molecule are computed on this basis. The dependence of basing the atomic orbitals upon the intensity of the applied field lead to good coincidence of results with the data of near Hartree-Fock calculations.

Notes: Double-helical polynucleotide conformations, poly(dA)·poly(dT), poly(d(A-T))·poly(d(T-A))·poly(dG)·poly(dC), and poly(d(G-C))·poly(d(C-G)) are analyzed by the atom-atom potential method. The energy optimization is carried out in the space of eight independent geometric parameters using analytical procedures for the constraints, taking into account the flexibility of the β-D-deoxyribose rings. At the first stage, the full screening of atomic partial charges was assumed. The structures of the calculated B and the A forms of DNA are characterized by low energy and absence of short contacts; the dihedral angles are near the average values in the monomers. With the typical energy difference of 3-5 kcal/mol nucleotide pairs in all cases, the B form is more preferable as compared to the A form. At the final step the effect of the Coulomb term is evaluated for poly(dA)·poly(dT) using various values of the effective dielectric constant (ε = 28, 24, 20, 18, 14, 12, 10, 8, 6, 4, and 1). If ε ≤24, the energy optimization leads A to B. We discuss the stereochemical details of the intermediate conformations on the A-B path and hypothesize the nature of stability of the A and the B forms and the mechanism of the A-B transition.

Notes: PCILO computations have been carried out on the conformation of 3'-deoxyadenosine (cordycepin) and 3'-amino-3'-deoxyadenosine. These nucleoside antibiotics results as a consequence of modification in the sugar part of adenosine. Both C(2')-endo and C(3')-endo sugar puckerings have been considered in the computations and the results obtained indicate that these nucleoside antibiotics have very similar conformational preferences as compared to those of the parent nucleoside adenosine. This similarity which is quite marked in aqueous solution has important biological significance.

Notes: In traditional quantum electrodynamic derivation of a intermolecular van der Waals force, the molecules are assumed to be localized clusters of electrons. In this paper we have assumed the molecules to be localized clusters of bosons and have shown that the expression of the potential remains formally the same. This vindicates, through a microscopic derivation, the established concept that the van der Waals interaction is essentially a macroscopic phenomenon.

Notes: This paper summarizes our findings on the effects of protons and neutral salt ions on intermolecular interactions and the self-organization of nucleotide systems in aqueous media, both at monomer and polymer levels. To gain quantitative information about these processes, methods were developed to determine the thermodynamic parameters of monomer association from the data obtained by various experimental techniques (NMR, UV spectroscopy, and spin labeling) and to estimate the individual contributions of base stacking and H-bonding in ordered structures of polynucleotides and their complexes. The main results obtained using these methods are as follows. (i) A difference was discovered in the effects of positive and negative charges on the stacking interaction between ionized and neutral molecules of nucleic heterocycles. Protonation strongly decreases the heterocycle ability to form ordered stacks whereas deprotonation slightly affects stacking. (ii) Base-phosphate interaction, which has not yet really been investigated, was studied. This interaction, along with base stacking, governs nucleotide association in water media. It appears upon protonation of the base moiety and increases with decreasing ionic strength. (iii) Base stacking was found to become stronger under the action of salt anions stabilizing the water structure and it became weaker under the action of destabilizing salt anions, both in monomer and polymer systems, which is indicative of an indirect mechanism of the anionic effects. It is essential that small salt ion additives acting by such a “distance” mechanism can affect the formation of ordered structures in nucleotide systems as strong as the direct interaction of the bases with protons. (iv) The results obtained suggest that an increase in solvent entropy upon the self-organization of nucleotide systems in aqueous media may be an important factor promoting these processes. (v) As follows from our data, specific weakening or strengthening of intermolecular interactions by protons and salt ions at small, physiological-range changes in pH or solvent salt composition seems to be an effective regulatory mechanism for the functioning of nucleotide systems.

Notes: Intensities of a1Δg←X 3∑g- and b 1∑g+ ← X 3∑g- transitions in molecular oxygen have been calculated on the basis of the INDO method taking into account spin-orbit coupling by perturbation theory. The transitions are magnetic dipole in nature. The first of them (a - X) steals its intensity from 3Πg-3∑g- and 1Πg-1Δg transitions, which are determined by the orbital angular-momentum operator. This source is not the principal one for the intensity of the second (b-X) transition. Its intensity is stolen principally from microwave transitions between spin sublevels of the ground 3∑g- state. The last source explains the large difference in intensities of the a-X and b-X transitions. Calculated oscillator strengths are in a good agreement with experiment. The same integrals that determine the intensity also determine the parameters of the spin Hamiltonian for the ground 3∑g- state. These parameters are in a good agreement with experiment also, showing the validity of the whole calculation. In a condensed phase the investigated transitions are enhanced by intermolecular exchange interaction. It is known that an external heavy atom (EHA) enhances the b-X transition of oxygen in solution, but does not influence the a-X transition. In the collision complex O2-EHA, which has a geometry without inversion symmetry, the microwave transitions between spin sublevels of the “3∑g-” state obtain electric-dipole moments, which are stolen from the charge-transfer transition. This mechanism explains the selective effect of EHA.

Notes: The energy of (H2O)3 has been calculated for 29 geometrical configurations of the trimer using the SCF LCAO MO method and extended as well as minimal basis sets of Gaussian functions. For two configurations two intermediate basis sets have also been tested. The results show the nonadditive component of the interaction energy to be small. They also indicate that fairly reliable results for the trimer can be obtained using minimal basis sets and the counterpoise method to eliminate the basis set superposition error. The nonadditive contribution to the interaction energy is shown to be mainly due to the long-range induction interaction.

Notes: An attempt is made to refine the physical background underlying qualitative quantum-chemical concepts that are an essential component of the modern theory of chemical reactivity. The energy of electron delocalization in a transition state (stabilization energy, SE) is used as a measure of chemical reactivity. Using Coulson's integral representation for bond order matrix enables one to present the Woodward-Hoffmann rules and the effects of conjugated substitutents as theorems for a Hückel SE in alternant systems. A part of the results are extended to heteroatomic systems. The validity of the present treatment is discussed in terms of the SCF PPP theory.

Notes: The Fock generating function method is employed for the separation of spin variables into two-particle transition density matrices. Their spatial components introduced by McWeeny are expressed through Schrödinger's coordinate wave functions. Some nontrivial integral relations between these components and the charge and transition spin density matrices are obtained. The interrelation between the mentioned spatial components and the Matsen-Poshusta symmetrized density matrices of an arbitrary spatial function is found.

Notes: Potential-energy curves for CH4·CH4 have been calculated using the SCF LCAO MO method. Six different mutual orientations of the molecules have been considered and several basis sets have been employed. An analytical potential has been fitted to the computed energy values and used in a Monte Carlo calculation to yield a spherically averaged CH4·CH4 potential. The potential, if corrected for dispersion interaction, agrees fairly well with that derived from thermophysical data. At short distances it disagrees with the potentials derived from scattering experiments which, however, are also incompatible with the experimental potential for large distances.

Notes: We present two identities that permit a simplification of some lengthy derivations with spherical harmonics. Examples of their use are given.

Notes: Infrared spectroscopy has been employed to study possible base pair interactions, in nonpolar media, between O6-methylguanine and uracil, cytosine and adenine; and between derivatives of N4-hydroxycytosine and adenine. The association constants of O6-methylguanine with uracil, cytosine, and adenine are well below 1M-1, whereas those for interaction of 1-methyl-N4-methoxycytosine and its 5-methyl derivative with adenine are identical, K = 14M-1. The significance of the latter finding is discussed in relation to the conformation of the exocyclic N4-methoxy group. Quantum chemical calculations, with the aid of the perturbation method, were carried out for the interaction of O6-methylguanine with uracil, cytosine, and adenine, to establish the most energetically favoured configurations for interactions of the free bases, and of the same base pairs in the B form of DNA. The role of the conformation of the exocyclic  - OCH3 group in O6-methylguanine is discussed. The relevance of both the experimental and theoretical results to mutagenesis by O6-methylguanine and N4-hydroxycytosine is examined.

Notes: Possibilities of improving individual contributions to the statistical interaction energy (kinetic and exchange) are examined. A new method of calculating statistical interaction energies is proposed. The exchange term is calculated using a suitably modified second-order gradient correction. For the kinetic contribution the accurate formula corresponding to the first-order perturbation theory is applied. The calculations have been carried out for several pairs of noble gas atoms.

Notes: New theoretical developments based upon hypervirial analysis of enclosed systems are given. Systems which obey unsymmetrical boundary conditions are analyzed. Several results which were given by the authors in two previous communications are generalized.

Notes: The calculus of the overlap integral for two states represented by the vibrational wave functions ψν′a and ψν″b is reduced to that of the Franck-Condon integral ℒ(0, x) = ∫0x ψν′aψν″b (t) dt. It is proved that for “numerical potentials” (as well as for a Dunham potential), this integral is given on each interval by a simple analytic expression in terms of the two potentials. The Franck-Condon factors are well determined by “coupling constants” related uniquely to the coordinates of the turning points of the potentials. An application to the band system BII—XΣ of Nα2 is compared with the usual numerical methods.

Notes: The CASSCF method has been applied to some excited states of the BO molecule. Only portions of the full potential curves could be obtained with the help of the usual two-step procedure. It was possible to complete the curves and to consider other excited states by using an averaged field technique. In this approach the energies were computed with orbitals that were self-consistently determined with first- and second-order density matrices averaged over several states.

Notes: Ab initio MODPOT/VRDDO/MERGE calculations were carried out on carcinogenic 3-methylcholanthrene (3-MCA) and its metabolites. The results for 3-MCA were compared to our earlier similar calculations for carcinogenic benzo(a)pyrene (BP). Both compounds 3-MCA and BP are carcinogenic and are metabolically activated by similar mechanisms but in different positions. Both the calculated wave functions for 3-MCA and BP and the electrostatic molecular potential contour maps generated from these wave functions correctly reflect the similarity of mechanisms of metabolic activation and the differences in position. Our calculated results both for BP and for 3-MCA reflect accurately their experimentally observed behavior. Thus this combination of theoretical techniques can be used with confidence to describe the behavior of the polycyclic aromatic hydrocarbons (PAH's) and their metabolites. The ab initio MODPOT/VRDDO method incorporates two very desirable options into our fast ab initio Gaussian programs: MODPOT-ab initio effective core model potentials - and a charge-conserving integral prescreening approximation which we named VRDDO (variable retention of diatomic differential overlap). For orbital energies and population analysis the MODPOT/VRDDO results agree to essentially three decimal places with completely ab initio calculations using the same valence atomic basis set. For this series of very closely related congeners our recent MERGE technique which allows reuse of integrals from a common skeletal fragment was used. The ab initio MODPOT/VRDDO/MERGE calculations were carried out for 3-MCA, 3-MCA oxides, 3-MCA dihydrodiols, and 3-MCA dihydrodiolepoxides. The metabolites investigated were 3-MCA 9,10-oxide; 3-MCA 7,8-oxide; 3-MCA 9,10-dihydrodiol [trans(axial, axial); trans(equatorial, equatorial); cis(axial, equatorial); cis(equatorial, axial)]; and 3-MCA 9,10-dihydrodiol-7,8-epoxide [for both conformations A and B of the dihydrodiol and for all stereoisomers of the dihydrodiolepoxides relative to below and above the plane: ααα, and ααβ αβα αββ βαα βαβ ββα and βββ (most stable)]. Calculations were also carried out for opening of the C7—O—C8 epoxide ring both towards C7 and C8 for the most stable isomer Aβββ (above the ring). Opening the epoxide ring between C7 and O leads to a more stable intermediate than opening the epoxide ring between C8 and O. Again, however, as with opening the epoxide ring in BP 7,8-dihydrodiol-9,10-epoxide there is no buildup of positive charge on C7 in the 3-MCA metabolites as postulated by some cancer researchers, but rather the C7 becomes slightly more negative. Nor is there a buildup of negative charge on the O atom, but rather it becomes slightly more positive. As the epoxide ring is opened further than 90° for the O—C7—C8 or O—C8—C7 angles, there appears to be a possible mixing of configurations that is being investigated further.

Notes: The single excited doublet states of some small molecule cations calculated by CI method in the framework of semiempirical CNDO and INDO models are correlated with the photoelectron spectra of the parent molecules. The purity of the Koopmans transitions is used to discuss the one-particle interpretation of photoelectron bands by comparison with nonempirical many-body calculations. Furthermore, empirical relations are applied with respect to the evaluation of shake-up energies.

Notes: The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.

Notes: This paper investigates the polarization effects associated with functional processes in photosynthetic membranes.

Notes: Calculations of Kato's equations have been carried out as a function of the coordinates of the system using a number of approximate wave functions in order to determine the effects of the energy, electron density, constraints, and the functional form of the wave functions on how well Kato's equations are obeyed. It is shown that by putting constraints on the functional form of some wave functions, the wave functions will give the exact value of Kato's equations.

Notes: The ab initio valence bond method has been used to study the ground and the lowest vertical valence ionized states of pyridine. On the basis of our calculations the first two ionization potentials are assigned to π and n electron removals, respectively. The final wave functions have been interpreted in terms of valence bond structures by means of an appropriate population analysis.

Notes: Both short-range and long-range intermolecular interaction energies between two prophin molecules, both in their ground state, separated by a range of interplanar distances from 3 to 4.5 Å, are estimated using the standard perturbation theory. The results indicate that a 60° rotated sandwich structure is the most stable conformation for the dimer. Certain translated as well as the perfect sandwich forms are other favoured structures. The stability of the dimer is mainly due to the van der Waals interactions with no significant contribution from the charge-transfer interactions. Biochemical implications of these findings are discussed.

Notes: Proton affinities, geometries with optimized parameters, and net atomic charges are reported for guanidine-, methyl-, amino-, and fluoro-substituted guanidines. The results are obtained using the ab initio SCF method as implemented by the GAUSSIAN-70 computer program with a 6-31G basis set. Basicity is discussed in terms of electron distribution and intramolecular attraction forces.

Notes: The Racah method, proposed for the evaluation of coefficients of fractional parentage (CFP) for single shell configurations, is generalized for the cases of two and more than two shells. On the basis of the generalized Racah method, we have evaluated one-particle CFP for all states of svpμ electronic configurations. Two-particle CFP are expressed through one-particle CFP and Racah coefficients.

Notes: A formalism for the determination of the most favored sites of monohydration and the orientation of water molecules around a solute by means of electrostatic potentials is suggested. The results of this method may serve as starting point for explicit supermolecule calculations. The hydration schemes determined in this way for the tautomeric forms of 2- and 4-hydroxypyridine can be used as a basis for the evaluation of the displacement of the lactam-lactim equilibrium under the influence of the water environment.

Notes: Ab initio MO calculations, using both minimal (STO-3G) and extended (Roos-Siegbahn) basis sets are reported for the systems methanethiol-imidazole, methanethiol-imidazole-formaldehyde, and methanethiol-imidazole-formamide, which, together with a point-change representation of a long α-helix, form models for the active site of papain. It is shown that the large electric field exerted by the helix in the active-site region is responsible for the presence of the essential residues Cys 25 and His 159 in the form of an ion pair RS- ··· ImH+, which is crucial for a recently proposed mechanism for the catalytic action of the enzyme. Also, an explanation is given for the anomalies in measured pK values for these residues. Detailed studies on the (sub)systems show that minimal basis sets lack the flexibility necessary for describing the type of proton transfer involved. We conclude that α-helices are essential parts of enzymes and that they play a significant role in the catalytic process.

Notes: The identity recently presented by Hiller, Sucher, and Feinberg relating the expectation value of a δ-function operator to that of another operator is rederived for the case of the Fermi contact interaction and the required expectation values expressed in terms of the spin-density and conditional spin-density matrices. The ground state of the H atom is considered as an example and it is shown that, for approximation by a linear combination of Gaussian orbitals, use of the identity improves the estimate of spin density at the nucleus by an order of magnitude or more.

Notes: The SCF theory of multiplet monodeterminantal states is described from a comprehensive viewpoint. In this context, the formalism and derived theorems are developed, as well as the description of a SCF closed-shell-like structure, namely the hypermultiplet. Numerical applications are discussed taking as a model the H2O molecule and its first positive ion. Wave functions of double ζ-quality, with computed molecular properties of 16 states are given.

Notes: Ab initio SCF calculations carried out on the planar cluster CuCl42- suggest that the strong satellites at the high-binding energy side of inner-shell ESCA lines of Cu are due to charge relaxations in the σ-bonding orbitals which mix with Cu 3d. The satellite state with the largest intensity may be described as a one-electron excitation Cu 3d → Cl 3p.

Notes: This paper gives an abbreviated method for the calculation of the density of states of a crystal on the basis of that band theory in which the crystal electron states are represented by the standinglike wave functions classified according to the point-group symmetry species. The crystal is a large but finite sphere filled regularly with atoms, and the wave functions are quantized at the boundary of the sphere. The Bloch theorem is not satisfied in this theory since the wave functions are not basis functions of the irreducible representations of the translation subgroup. On the other hand, a theorem is established that the density of states can be made up of contributions given by all irreducible representations of the crystal point group, any contribution being proportional to the square of the dimension of the irreducible representation. In distinction to a former approach, the band structure is calculated solely from the energy eigenvalues obtained with the aid of the diagonalization process of the Wannier-Slater differential operator. A simple cubic lattice with an s atomic orbital on each lattice site is taken as an example, and the results are compared with Bloch's theory.

Notes: Second order MCSCF theory is presented in a unitary group formulation for any multiplicity without spin projection. Its reduction to lower order theory is discussed, as well as its extension through the use of effective Hamiltonians.

Notes: The limiting of the 〈r12-1〈/〈r1-1〈 ratio in the He sequence is critically examined at different levels of approximations leading to some interesting results.

Notes: We report on the band structure and wave functions of positrons, annihilating with electrons, from the thermalized state k+ = 0. We find that the bottom of the band to which the positron thermalizes in this metal is definitely nonambiguous. It is also found that even though the first few Bloch terms in the wave function can give the gross shape of the positron annihilation curve for this metal, the higher momentum components of high orders are definitely important if one is to assay the fine details of the curve.

Notes: The Silverstone-Stuebing variational principle for the discontinuous wave functions of one-electron systems is generalized for many-electron systems. The variational functional of energy takes real or complex value. The condition that it is real is given. Using the generalized variational principle, a multiconfiguration SCF theory for the composite molecular wave function is formulated. According to the theory, we may divide the whole space into space-filling cells, solve the SCF equations in each cell and build up the wave functions of the system by gathering the wave functions obtained in the cells. For use in the basis-set expansion method, the SCF equations are rewritten as matrix forms in which only one- and two-center integrals appear if an expansion center is located in each cell.

Notes: The four-center nonplanar electron repulsion integrals over 1s Slater-type atomic orbitals are considered by a numerical Fourier-transform method. It is shown that the highly oscillating integrand appearing in the Fourier inversion formula could be successfully treated by using Tchebyscheff quadrature. The resulting formulas are thoroughly discussed with particular emphasis on their numerical features and convergence properties. It follows that the aforementioned integrals may be calculated with a good accuracy with a moderate amount of computing time.

Notes: The behavior of the electron density n(r) and potential energy V(r) near the origin, where an impurity of charge Z is located, is studied using the Lindhard dielectric theory of the free-electron gas. The leading odd terms in the power-series expansion of n(r) and V(r) are obtained. It is shown that the derivative n′(0) = -2Zn0/a0, where n0 is the free-electron gas density and a0 is the Bohr radius.

Notes: This work describes the investigation of the space organization of DNA compact forms and DNA-protein complexes by the small-angle x-ray scattering method. A plane texture was disclosed in dehydrated DNP films. Compact DNA particles formed in the presence of poly(ethylene glycol) reveal ordered structures having a periodicity of 84 Å. Various morphological forms of crystals of CTA-DNA were used to obtain small-angle x-ray patterns of the single-crystal type.

Notes: The individual absorption spectra of various ionic and tautomeric species of some derivatives of nucleic-acid components have been determined by computer handling of the summary spectra of these compounds measured at different pH values. These individual spectra have been decomposed into separate bands represented by log-normal curves and corresponding to different electronic transitions. Using the parameter system calculated earlier for the molecules of the vitamin B6 family, the calculation of the electronic spectra and electronic structure of various ionic and tautomeric species of the molecules studied have been carried out in the π-electron approximation. These properties have also been calculated by the all-valence electronic method CNDOS. The calculated results correlate well with both approximations and with our experimental spectral data. The localization of the molecular electronic excitation studied on the transition to the S1 and T1 states is considered in connection with the reactivity in these states.

Notes: Generalized oscillator strengths and integrated cross sections from threshold to 1 keV are calculated in the Born approximation for the electron impact excitation of O II.

Notes: One-electron properties may be evaluated by configuration interaction methods using analytical differentiation of the total energy with respect to an external perturbation parameter. Dipole moments are reported using such a method for CO and H2CO. Inclusion of single substitutions does not change calculated dipole moments appreciably with this method. The differences between this method and the direct evaluation of an expectation value are discussed.