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Notes: Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree-Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.

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 ground state wave function of a model potential consisting of a zero-range square well joined to a Coulomb tail is used in a two equivalent centre problem to evaluate the overlap integral (S) and the resonance integral (β). It is shown that an extended Linderberg relation of the form β = K/R (dS/dR) is generally well obeyed. The extended relation has been used within a LCAO framework to obtain dissociation energies of the homonuclear diatomic molecules of the alkali atoms.

Notes: MSW-SCF-Xα calculations have been carried out to obtain ionization potentials (via Slater's transition state concept) and charge distributions for HNSi. The results are interpreted and compared with previous ab initio and CNDO/2 studies.

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 molecular electrostatic potentials for several small molecules were investigated using PCILO wave functions at different stages of the perturbation expansion. The utility of the localized picture within the PCILO framework can be shown, even at zeroth order only. For simplicity the approximation of fixed standard bond polarities could be introduced in order to reproduce shape and values of the potential with a sufficient degree of accuracy.

Notes: Theoretical aspects of the MS Xα method are analyzed. It is shown that real field self-consistency is not achieved in an MS Xα calculation and some consequences of this fact are discussed. The approximations involved in the use of the transition-state procedure to evaluate ionization and excitation energies from a MS Xα calculation are presented in some detail and commented.

Notes: For arbitrary k, the separation of spin variables is performed in the reduced density matrix of the kth order (RDM-k) on the basis of the Fock coordinate function method. The independent spatial components of RDM-k are analyzed. For RDM-k of the total spin eigenstate, their number is proved never to exceed its spin multiplicity 2s + 1. Integral and other nontrivial interrelations between spatial components are established which turn out to be the necessary and sufficient conditions of spin purity of a wavefunction corresponding to a given RDM-k. It is shown that the r-rank k-particle spin distribution matrix Fkr, defined as a spatial coefficient at the spin-tensorial operator of rank r in the RDM-k expansion, can be obtained by reduction of the (k + r)-particle charge density matrix Fk+r0. In particular, all spatial components of RDM-2 are explicitly expressed in terms of the four-electron charge density matrix only. This allows us to purpose some approximative formulas for the McWeeny-Mizuno spin-orbit and spin-spin coupling functions in the case of the weak spin contamination.

Notes: Following an interpretive formalism presented earlier, chemical binding in the H2+ molecule has been studied in terms of the variations, with respect to R, of electrostatic field and stress components at five selected points on the interuclear axis. At three points phenomena analogous to those recorded earlier for H2 have been observed. In particular, the existence of extremal relationships for the difference density field and the total field, as well as for the corresponding stresses, at R ≃ Req for certain specific points on the internuclear axis has been confirmed. As in the case of H2, chemical binding in H2+ occurs due to local variations of electrostatic pressure from point to point in such a manner as to cause the vanishing of either the total electrostatic force density or the difference force density at certain points on the internuclear axis.

Notes: (5s, 2p) and (7s, 4p) Gaussian basis sets are presented and evaluated for first- and second-row atoms, respectively, appearing in biologically active molecules. The exponents of the valence shell primitives are taken from larger bases, where the valence shell is better represented, in order to avoid the overemphasis on the core, which occurs in small bases when all exponents are optimized. Contraction coefficients are given for constructing double zeta and minimum molecular basis sets. The basis sets are evaluated by applying them to 19 molecules containing first- or second-row atoms. The results indicate that they are competitive with larger bases for the calculation of properties mainly dependent on the valence shell electrons. In particular, proton affinities seem to be quite reliably reproduced so that they can be used for investigations involving reaction or interaction with proton donors.

Notes: Specific electronic properties related to the metabolic transformation and adduct formation with DNA were calculated for a series of five aflatoxins, AFB1, AFG1, AFP1, AFM1, and aflatoxicol (AFL), as well as for two precursors of AFB1, versicolorin A and sterigmatocystin. The aim of this study was to investigate to what extent such electronic parameters determine relative apparent mutagenic and carcinogenic activities of these compounds. Using two semiempirical all-valence electron methods, IEHT and INDO, the results obtained indicated that for all these compounds the 2,3-vinyl ether double bond is highly susceptible to epoxidation, and this susceptibility is independent of the remaining ring structure and substituents. Further, the epoxides in turn readily form highly electrophilic carbocations whose stability and reactivity are not significantly influenced by chemical structure changes among the seven analogs studied. The results also suggest that major detoxification pathways mitigated by cytochrome P450 metabolism are not likely. Thus differences in potencies do not appear to be caused by differences in electronic properties related to the metabolic transformation and adduct formation, and could be the result of other properties such as lipophilicity and steric effects on enzyme activity.

Notes: Molecular electrostatic potentials are calculated for a single phospholipid molecule (1,2-dilauroyl-phosphatidylethanolamine) and for its model monolayer. For the single molecule the magnitudes of the positive and negative potentials associated with the amino and phosphate groups of the polar head are comparable. For the monolayer a dominantly positive surface potential is obtained.

Notes: The protonation energies (pE) of histamine and methyl histamines were calculated by using the CNDO/II method. After correction for hydration energies, the variation of the pE values has the same trend as that of the pKa1, values determined in aqueous solution. However, there is no apparent relation between the calculated pE and the biological activities for the above-mentioned compounds. On the other hand, it was found that the relative stability of the two tautomers did reflect the H2-receptor agonist activities. The smaller the energy of the N(1) - H tautomer, the greater its H2-receptor activity.

Notes: The imidazole C-2 proton NMR signals of six of the 14 histidine residues per subunit of pyruvate kinase (Mr = 237,000) are detected at 250 MHz using 16-bit analog-to-digital conversion, and their pK′ values have been determined. One of these residues [his (3)] is very near the binding site of the divalent cation activator as indicated by a Mg2+-induced decrease in its pK′ in the presence of K+ and P-enolpyruvate, and by the selective paramagnetic effects of the activator Ni2+ or the substrate β,γ-bidentate CrATP on the relaxation rates of the his (3) signal. Another histidine residue [his (2)] is near the adenine portion of the nucleotide substrate binding site as indicated by paramagnetic broadening by CrATP of the his (2) signal, a nuclear Overhauser effect (NOE) on the adenine H-2 proton of enzyme-bound MgATP upon irradiation of the his (2) signal, and the loss of ATP binding detected kinetically, after selective chemical modification of his (2) as detected by NMR. Intermolecular NOE studies of enzyme-bound MgATP indicate the distance between the adenine H-8 proton and the ribose protons of the substrate to increase in the order H2′ = H3′ ≤ H5′ 〈 H1′ 〈 H4′. These findings are in good agreement with the conformation of enzyme-bound ATP previously and independently determined by distances from Mn2+ at the active site to the protons of ATP.

Notes: The problem of viscous damping of vibrating DNA polymer in aqueous solution is solved in the low-amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. The viscious damping is found to be a strong function of frequency, singular both at very low and very high frequencies. All acoustic modes are overdamped, implying that the observation of well-defined resonances in DNA requires highly structured water or very dry material.

Notes: The nucleotide building blocks of nucleic acids show a preference for two major conformational motifs mainly determined by the sugar puckering and the concerted changes in the glycosyl sugar-base torsion angle: 3E-low anti (χ) and 2E-high anti (χ). The backbone C4′—C5′ bond torsion prefers the gauche1 range while the C5′—O5′ torsion displays a somewhat broader trans range. Thus the two preferred sugar-base-backbone relationships are: 3E-anti-gauche+ and 2Eanti- gauche+. In 5′-nucleotides there is an extreme reluctance for the syn base. Guanine is notoriously peculiar and has a tendency for syn. When the base is syn, the steric conflict with the phosphate is relieved by a concerted rotation around the C4′—C5′ bond to the trans (or gauche-) states, leading to three additional nucleotide motifs: 3E-syn-trans and 3E-syn-trans (or gauche-). The gauche- state is highly destabilized for the 3E., Superhigh χ's are known to drive the backbone into left-handed structures, as exemplified by the unnatural Ikehara polymers [M. Sundaralingam and N. Yathindra, Int. J. Quantum Biol. QB4, 285-303 (1977)].In the recently discovered left-handed Z helices of the alternating deoxy-CG tetra- and hexanucleotides it may be regarded that the C residues assume the preferred “right-handed” conformational combination 2E-anti-gauche+, while the G residues assume the less favored “left-handed” combination 2E-syn-trans., In the latter, steric interactions between the syn base and the 5′-phosphate drive the C4′—C5′ torsion into the trans range, and the electrostatic interactions between the syn base and the 3′-phosphate now drive the sugar into 2E (a variant of 3E). The departure from the preferred nucleotide conformations leads to correlated changes in the ester P′O bonds of the internucleotide phosphodiester groups, which alternatively adopt (in Z-DNA) the “left-handed” double gauche (gauche+, gauche+) and the “right-handed” (gauche′, trans) conformations.The pseudorotational mobility of the furanose ring provides a simple and elegant way of understanding conformational fluctuations and flexibility of nucleic acids. Thermal fluctuations capitalize on the pseudorotation property of the furanose ring. Because the furanose ring is linked to the base and the phosphate, these fluctuations are correlated to the rotational mobility of the base and the phosphate and lead to phenomena such as premelting changes, breathing modes, or opening of base pairs. Such motions are instrumental in the polymorphic transitions of nucleic acid helices (e.g. A ⇄ B, B ⇄ C, B ⇄ Z, …) or in functional processes, such as unwinding and fork formation. It is also proposed that concerted changes in the sugar-phosphate backbone torsion angles, akin to a crankshaft motion, can bring about the B ⇄ Z transition without necessarily disrupting the hydrogen bonds.

Notes: The significance of the gramicidin channel, its structural elements, and the importance of the peptide libration mechanism are reviewed. Elemental ionic processes of the single-channel currents are considered, which indicate the possibility of two- and three-site models. Data are presented which demonstrate the absence of interactions required for the three-site model, and the resulting free-energy profile for the two-site model is given for the most probable conducting state. The need to extend analyses to include an understanding of multiple conformational states is outlined, and results from approximate conformational energy calculations are presented showing that there are numerous low-energy conformations for the side chains of gramicidin. Specifically the interactions between L·Trp9 and L·Trp15 side chains and between D·Leu4…D·Leu10 are analyzed to show the existence of several energy minima separated by appreciable barriers. These findings provide the basis for understanding facilitated entry of the second ion into the channel and the occurrence of lipid-dependent dispersion of conductance states. Finally perspectives of the molecular mechanism of anesthetics are discussed relevant to the gramicidin channel mean lifetime and single-channel currents.

Notes: A field-theoretic treatment of biological evolution is presented. This treatment (evolutionary field theory) leads to the decomposition of biological evolution, at the molecular level, into permutational and substitutional evolution. The mathematical distinction between these latter two types of evolution is investigated and a nonlinear/linear classification results.

Notes: Theoretical and quantum chemical prediction of toxicity and toxicology is even more challenging than prediction of pharmacology, which is usually a one-stage event at a target site. For toxicity and toxicology, the concept of the “toxic triggering event” was developed which then leads to the cascade of subsequent physiological events. The strategy for computer-generated predictions in this area includes as the major components chemical automated substructure and “toxicophore” identification by powerful chemical substructure searching techniques developed in Europe, geometry optimizations (desirably by ab-initio intramolecular atom class-atom class pair-pair and three-body potentials), quantum chemical calculations (desirably ab-initio, incorporating optimal strategies for such computations on large molecules) on both the toxicant and its metabolites (the structures of which were generated by computer-assisted tracing of metabolic pathways), generation of the three-dimensional electrostatic molecular potential contour maps around the toxicants and their metabolites and matching of these by reverse image holography for new compounds whose toxicity has not yet been tested experimentally against those with a known toxic mechanism, matching of intermolecular interaction maps of untested compounds with known toxicants combined with matching observed physiologic signs and symptoms with “toxic triggering events” and specific pathologies, and using the concepts of systems analysis and control theory and catastrophe theory to track both the dynamic balance of endogenous biomolecules and interactions with these biomolecules. The necessary program modules are described, and the necessary data bases (both theoretical and physiological) are identified along with the form in which they may be used most expeditiously.

Notes: Classically every physical thing has some geometry or other, but in the quantum theory the notions of spatial structure, shape, and size seem to become hazy if not outright inapplicable. In particular, elementary entities are by definition structureless and seem to have no size or shape other than those imposed by their environmént - as represented, e.g., by the boundary conditions. However, this does not entail that systems of interacting components, such as molecules, lack a geometry as well, as has been argued in recent times. The purpose of this paper is to investigate this claim. Since the solution to the problem whether a quantum-mechanical system possesses a geometry depends critically upon the definition of the latter, we elucidate the notions of extension, shape, and spatial configuration of a system. We do so first classically in terms of the energy density, then quantum mechanically in terms of a suitably constructed position distribution function that depends upon the spatial coordinates (and is thus a field quantity) rather than on the particle coordinates. In this way we construct both classical and quantal concepts of the geometry of a system. We also define the notions of spatial structure and chemical structure of a quantal system. Our quantum-mechanical concepts are quite general and constitute smooth extensions of the corresponding classical concepts. The upshot of this investigation is that a quantal system does have a geometry, albeit not as clearcut a one as a classical system, that is primarily determined by the interactions among its components. (Thus, physics determines geometry of physical systems, not the other way around.) This conclusion is obtained within nonrelativistic quantum mechanics without adding any extra assumptions. Our result vindicates the ball-and-spoke models of molecules and thus shows once again that quantum chemistry, although different from classical chemistry, stays close to the chemist's work bench.

Notes: A perturbation configuration interaction method is formulated for a system in an external oscillating field (PCILOSC). It is closely connected with the static PCILO method and can be used for the conformational analysis of molecules and molecular crystals with localized bonds in external fields.

Notes: As an alternative to the density functional approach to estimating total molecular correlation energies, the equation Ecorr=-0.06593 ∑i=1M Ri-0.3916, where Ri=〈r2〉i½ and i runs over the localized molecular orbitals was fitted to 25 STO-3G data points with a root-mean-square error of 0.025 hartree. Other more general equations were tried but no significant improvement was observed in the fit.

Notes: Ab initio LCAO SCF MO calculations are carried out on the ground state and d-d transition states of CoF64-, CoF63-, and CoF62- complexes with a basis set of more than double-zeta quality. To obtain a better description for the excitation energy of d-d transition states, a ligand field configuration interaction calculation is performed. The calculation is improved further by taking into account the correlation energy in the central metal atom and it gives good results for the observed excitation energies. Especially, the excitation energies for the states which have the same configuration as the ground state agree with observed ones within about 1 kK. The excitation energies of several charge transfer states in the CoF62- complex are also computed at the level of SCF MO calculation and the assignments are made for the four strong bands observed in the energy region higher than the weak d-d bands.

Notes: The properties of the algebraic structure of fermion density matrices are studied. The algebraic structure of a density matrix leads to a more varied and detailed classification scheme than that offered by the usual shell structure approach. Investigation of the algebraic structure of fermion density matrices by the methods of algebraic topology leads to a classification scheme based on Betti numbers.

Notes: A self-consistent procedure for the Hückel theory, first indicated by Harris [J. Chem. Phys. 48, 4027 (1968)] has been fully developed. To avoid time consuming repeated orthogonal-nonorthogonal transformations and diagonalization of large matrices, a steepest descent technique has been suggested.

Notes: Previous results on the hypervirial analysis of confined systems are extended. Periodic potentials are discussed and an efficient alternative way to solve the Mathieu equation is proposed.

Notes: Examination of the random phase approximation in relation to the energy weighted maximum overlap model suggests a way of accounting for singlet-triplet splittings in particle-hole spectra. Calculations for the first row hydride molecules are used to illustrate applications.

Notes: The analysis of nonstationary processes, taking place in exciton systems in consequence of the nonconservation of the number of elementary excitations, is presented and it is pointed out to a new possibility of light-energy capturing which exists in ecological systems due to the nonconservation of excitons. It is shown that, due to the nonconservation, the one-dimensional molecular chain is able to capture permanently the light energy of the order of 50 keV to 5 MeV. A part of the captured energy is expected to have a role in internal bioprocesses. It is also shown that the system is a seat where the processes of continuous creations and annihilations of pairs of excitons having opposite momenta take place with a probability of the order of 10-4 to 10-2. Further investigations would allow to identify biological phenomena caused by those processes.

Notes: Semilocal pseudopotentials have been determined for first-row (Li to Ne), second row (Na to Ar), and third-row atoms (K, Ca). Core-valence correlation is included by adjusting the pseudopotentials to experimental energies of ions with a single valence electron. Correlation within the valence shell is taken into account by using the spin-density functional formalism. The approximations involved in this approach are tested for atomic ionization energies as well as binding energies of monohydrides and alkali diatomics, agreement with experiment is usually satisfactory, but in certain applications density functionals should be already included in the fitting of the local part of the pseudopotential. In addition, 3s/3p and 3s/2p basis sets (for first and second row, respectively), designed for use in connection with our pseudopotentials, are given; it is shown that they yield reasonable results for both SCF and correlation energies.

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: 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: We performed ab initio pseudopotential and CNDO calculations on γ-aminobutyric acid (GABA) and its Ca2+ and Mg2+ clathrates. We were particularly interested in the rotational barrier existing between two extreme conformers of GABA and its modification upon metal complexing. We found that the pseudopotential method predicts a coordination of the ions to GABA and that this coordination inverts the rotational barrier observed for the isolated molecule. We also looked into the adequacy of CNDO for the study of this type of coordination and found several shortcomings in its predictions. The biological implications of these findings are discussed and a hypothesis on the role of a GABA-Ca2+ complex is presented.

Notes: The various computational procedures for treating the problem of lattice summations in ab initio crystal orbital calculations are briefly reviewed and the cutoff problem is discussed. Several numerical examples are presented for demonstrating the fast convergence of the total energy per unit cell with respect to the inclusion of further neighbors' interactions, in case reasonable cutoff procedures are applied. The importance of electrostatic considerations for the interpretation of long range effects is stressed.

Notes: Model building, difference spectroscopy, and 1H and 13C NMR experiments have been carried out to study the binding of poly(L-Ser) with the polyribonucleotides poly(A) and poly(U) at pH 7.1. Studies have also been carried out with base paired duplexes poly(A)ṁpoly(U). Peak doubling of Cα and carbonyl resonances in the 13C NMR spectrum of poly(L-Ser) in presence of polyribonucleotides is observed. From the chemical shifts and the linewidth, it is concluded that the interaction occurs through hydrogen bonding between the nucleic acid bases and the peptide backbone. In case of poly(A) and poly(U) the hydrogen bonding scheme with peptide backbone is different from that in the base paired poly(A)ṁpoly(U). The possible binding schemes of double stranded DNA and peptide backbone have been investigated using model building and potential energy calculations. The hydrogen bonding schemes discriminate between various base pairs and their sequence. It is concluded that protein backbone can play an important role in protein-nucleic acid recognition schemes.

Notes: It is well known that a wide variety of molecules compete for binding to the estrogen receptor and act as estrogens and/or antiestrogens. These molecules such as estradiol, diethylstilbestrol, doisynolic acid, the triarylethylenes, and cyclofenyl apparently share little resemblance which could account for their interaction with a common estrogen binding site. Knowledge of the receptor binding of triarylethylene and cyclofenyl prototypes, in particular, relative to that of the other estrogens is critical for understanding their structure-function relationship. We have carried out a study on the receptor binding specificity of triarylethylene and cyclofenyl prototypes. This study has revealed that these molecular types share considerable resemblance in their receptor binding specificity and differ from estradiol and other similar molecules in some important respects. However, comparison of their substructural binding specificities reveals the possibility that the triarylethylene and estradiol prototypes may interact with at least some common regions of the estrogen binding site. Based on this reasoning the comparative receptor binding of estrogens has been rationalized on the basis of a subsite hypothesis for the estrogen binding site. According to this hypothesis, the composite estrogen binding site is composed of essentially five subsites, and that the structurally different estrogenic prototypes can interact with different set of subsites, and thus differ in their binding orientation. The essential difference in the activity profile of estradiol prototypes and the triarylethylene antiestrogens reveals the possibility of a causal relationship between the binding orientation of a ligand and its activity profile. This model for receptor site can thus serve as a working hypothesis to rationalize the structure-function relationship of estrogens.

Notes: Cholesterol and phospholipids are major components of biological membranes. The role of cholesterol in membranes is not metabolic and is known to be a regulator of membrane fluidity which in turn regulates various biological phenomena. We have studied the nature of cholesterol and phospholipid interaction in artificial membranes using 13C NMR spectroscopy. This involved preparation of phospholipids specifically labeled with 13C in the ester carbonyl group. Though the chemical shift data did not provide very useful information the T1 and T2 measurements indicated that previously proposed H bonding between the ester carbonyl group and hydroxyl group of cholesterol seems unprobable.

Notes: A coupled perturbation theory for the antisymmetrized product of separated geminals (APSG) approximation is derived. The variational principle for the APSG wave function in an external oscillating field is employed and a set of equations of the form analogous to the normal RPA is obtained. At this level the reduced resolvent in the form of a spectral expansion is written and it is used for the evaluation of the second-order properties.

Notes: A charge density distribution study, based on ab initio SCF-6-31G wave functions, on the optimized geometry of 1,2-dioxethane indicates its high instability which results from (i) the high ring strain, (ii) the large amount of charge contained on the nonbonded sides of the oxygen nuclei, and (iii) the weak binding character of the charge density in the O—O bond region. The redistribution of the charge density when 1,2-dioxethane undergoes change in its nuclear configuration has been discussed. This redistribution of charge along the reaction path (the dissociation of 1,2-dioxethane to formaldehyde products) shows clearly the preceding nature of the electron cloud. The characteristic features of the charge density distribution of the two Hartree-Fock solutions to which the SCF procedure converges have been analyzed and discussed.

Notes: By applying the projection operator method it is shown that the complicated Hamiltonian of a E ⊗ ∊ JT system with nonlinear coupling coefficients can be written in terms of two Hamiltonians which are simple to handle and transform according to irreducible representations E, A1, and A2 of C3v point group. A variational approach is then used to calculate the ground state energy, using the Hamiltonian that transforms according to E, as an explicit function of the linear and nonlinear coupling parameters. The energies calculated in the strong coupling limit are finally compared with the corresponding previously calculated energies.

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: For the purpose of illustrating methods for treating the chemisorption problem, which take into account bulk properties of the crystal, it is shown how the single-particle Green's function may be used to solve the self-consistent Schrödinger equations for an adatom-substrate system. The absorption problem is then reduced to the solution of a set of integral equations in terms of the infinite crystal Green's function. The method is illustrated using the interaction between an impurity level and surface states in a semiconductor gap and using sp hybridization of an alkali atom on a metal.

Notes: Some aspects of studies on organic solids, polymers, and solid surfaces are discussed in connection with the suggestion that local interactions can constitute an important common feature of these quite different systems, which allows a common treatment of certain properties in cluster-type calculations. The examples of molecular crystals, of the influence of different side groups bound to the backbone of a regular polypeptide, and of the interactions of fluorine and chlorine atoms with a silicon surface are treated in order to illustrate this thesis, with special emphasis on the reduction of a variety of bonding situations to local interactions rather than on details of computations.

Notes: Standard ab initio quantum chemical computations are quite effective in throwing light on binding features of biomolecules, in particular, hydrogen bonds. This is illustrated by a brief survey of recent work, including some interesting preliminary results on dipeptides, tripeptides, and tetrapeptides. Differential-energy maps for analyzing results are presented and discussed. Basic theoretical questions, such as the significance of minimal-basis calculations and localization on a subsection of a macromolecule, are also discussed.

Notes: The anomalous behavior of refractive index and density in the glassy ternary B2O3-BaTiO3-Na2O materials is presented and discussed in terms of Raman spectroscopy results. The slope change in the optical properties as a function of composition takes place within the same range of composition in which the Raman spectra suggest a transition from a bridging type of attack on the glassy matrix by the oxygen present in the basic oxide, to a nonbridging type. The structural modifications of the materials at different compositions are inferred from a detailed analysis of the Raman spectra.

Notes: Neutron diffraction can provide very precise stereochemical information about hydrogen bonds and other features involving hydrogen atoms in crystals. This is because, unlike for x rays, the hydrogen atom has a significant scattering amplitude for neutrons relative to other atoms. High-precision studies of a class of molecules, like those on α-amino acids carried out at Brookhaven and Trombay, can provide important information on systematics of the structure, conformation, and hydrogen bonding parameters. Some attempts have also been made to extend these single-crystal studies to some proteins like myoglobin, lysozyme, and trypsin. The large anomalous scattering amplitudes for some stable isotopes like 113Cd and 149Sm and the easy variability of neutron wavelength also provides, in principle, a method for solving the phase problem without crystallizing too many heavy atom derivatives. The combination of neutron and x-ray diffraction data, now being used to study charge density distributions in organic molecules and hydrogen bonds, may be extended in the future to larger molecules of biological importance. The small-angle scattering of neutrons is also a powerful technique for studying large biological particles in solution at low resolution to obtain information about sizes, shapes and distribution of constituents.

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: 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: The self-consistent relativistic Thomas-Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential μ which has the scaling property \documentclass{article}\pagestyle{empty}\begin{document}$$ \mu = Z^{4/3} F\left( {N/Z;\;\varepsilon /Z^{2/3} } \right), $$\end{document} with ∊ = α2Z2, α being the fine structure constant. Combining this with the Layzer-Bahcall expansion for the total energy E(Z, N), namely, \documentclass{article}\pagestyle{empty}\begin{document}$$ E(Z,N) = Z^2 \sum\limits_{n = 0}^\infty {\sum\limits_{m = 0}^\infty {E_{mn} (N)\varepsilon ^m Z^{ - n} } } $$\end{document} it is proved that the coefficients Enm (N) at large N have the asymptotic behavior Nn-2m/3#1/3. The corresponding result for the scaling of the relativistic Thomas-Fermi energy is \documentclass{article}\pagestyle{empty}\begin{document}$$ E_{{\rm TF}} (Z,N) = Z^{7/3} F_1 (N/Z;\varepsilon /N^{2/3} ). $$\end{document} Scaling properties of the higher order terms in Enm (N) and E(Z, N) are also proposed.

Notes: The self-consistent perturbation theory is used to calculate noncontract contributions to spin-spin coupling constants involving protons. Molecular wave functions were obtained with a modified version of the INDO method which includes hydrogen 2p orbitals in its basis set. It is found that in many cases the orbital and dipolar terms are by no means negligible, being particularly important in geminal H—H couplings. Results reported in this paper for this type of coupling, reproduce experimental trends in the series CH4, NH3, and OH2. In general, noncontact terms are found to decrease as the number of bonds separating the interacting nuclei increases.

Notes: Analysis of available data on atoms has led to a relatively simple empirical relationship between the correlation energy and second moment 〈r2〉, a measure of the size of the electron density. With the aid of this simple relationship it is possible to predict correlation energies with fair accuracy given the SCF or Hartree-Fock limit values for the size of the electron density. Preliminary extensions of this work to two- and ten-electron molecules indicate that it may be possible to predict molecular correlation energies to semiquantitative accuracy from SCF data on the electronic distribution.

Notes: An ab initio LCAO SCF MO calculation was performed on planar Fe-porphine with a double zeta basis set consisting of 300 CGTO's. SCF wave functions of several states of Fe-porphine and its cation were obtained. The net charge of Fe is in the range of 1.39 to 1.53. The highest occupied orbital is ascertained to be a pure porphine π-MO, 1a1u. The calculated ionization potentials of the two highest occupied orbitals, 1a1u and 5a2u are 5.98 and 6.43 eV, respectively. They are in good agreement with experiments. The role of the porphine macrocycle on the oxidation of Fe is discussed in terms of gross atomic populations and with contour maps of the density difference.

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: Along the lines of previous work [S. Romano and E. Clementi, Gazz. Chim. Ital. 108, 319 (1978); Int. J. Quantum Chem. 14, 839 (1978); 17, 1007 (1980)], we carried out Monte Carlo simulation on serine-water clusters (the neutral molecule and two conformers of the zwitterion) surrounded by an appropriate dielectric continuum simulating the bulk solvent. Results for clusters in vacuo and in the dielectric continuum were compared; similarities and differences could be qualitatively interpreted as produced by competition among different factors.

Notes: The self-consistent APW-k · p method is utilized to obtain the band structure of NaCl in the “muffin-tin” approximation. Qe have investigated the convergence of many intermediate results, e.g., crystalline potential, matrix elements of the momentum operator, and energy eigenvalues at the Γ point. The summation in reciprocal space, included in the definition of the matrix D of the theory, is performed by direct sum and also by a special points technique. For the convergence criteria used, the results converged after five iterations.

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: Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group Sn, if n is twice the number of occupied and virtual orbitals. Method is illustrated with CI using the localized orbitals of polyenes, CI in benzene, and atomic CI for several reference states.

Notes: Interactions of catecholamines with acidic sites in the biophase are likely to be involved in the control of the receptors activity as well as in storage and transport mechanisms. In view of the importance of the phenomena a model study of ethanolamine-phosphate complexes was made. The electrostatic interaction energy surface was calculated in the charge density multipole expansion approximation with terms up to quadrupole. The consecutive minimal energy conformation shows the importance for the interaction with the biophase of the catechol ring steric and electronic relation to the side chain.

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

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

Notes: A simple method is presented for the construction of contracted Gaussian basis sets with little or no energy-optimization. The contraction coefficients are fitted by a least-squares procedure to the orbital expansion coefficients of the completely decontracted basis. The method is applied to the construction of minimum basis sets of first-row atoms from (6s, 3p) uncontracted atomic basis sets, and of [6s, 4p] contracted bases from (12s, 8p) uncontracted bases of second-row atoms. The results are better than using the expansion coefficients directly and are usually comparable to fully energy-optimized bases.The method can also be used to generate balanced atomic contraction coefficients from molecular calculations. This is shown with a (7s, 3p) and a (6s, 3p) basis, both contracted to a minimum basis. The contracted basis sets are employed in several small molecules, and the results are compared with calculations done with the decontracted bases and with contracted bases where the contraction coefficients were energy optimized in the molecules.

Notes: Conformational properties of pyrazofurins, which were previously designated as pyrazomycins in both β- and α-anomeric forms, have been investigated by the PCILO method. The results indicate that the most preferred conformation for β anomer is anti-gg, while that for α anomer is syn-gg when intramolecular hydrogen bonding between sugar and the base is allowed. However, in the absence such hydrogen bonding, which mimicks the situation in aqueous solution, both β and α pyrazofurins show exactly similar preference for anti-gg conformation. The biological significance of this result has been discussed. Further the β anomer is energetically more favorable than the α anomer. This result is in agreement with the experimental observations, which indicate that β pyrazofurin is more populated than a pyrazofurin in aqueous solution at room temperature.

Notes: An investigation is carried out of the influence of counterions bound to yeast tRNAPhe on the electrostatic potential and steric accessibility of this macromolecule. Two types of cations are considered, the Mg2+ ions located in the crystal of tRNAPhe, with their waters of hydration, and Na+ ions, which are positioned by theoretical estimation. Possible effects of the counterions on the chemical reactivity of tRNAPhe are pointed out.

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

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

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

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

Notes: In investigations of the molecular determinants for the recognition of drugs by a serotonin (5-HT) receptor in the brain, the commonality in the reactivity patterns of 5-HT congeners has been identified. On this basis a mechanistic hypothesis is proposed to explain the rank order of the affinity of drugs that bind to the receptor shared by 5-HT and LSD (the 5-HT/LSD receptor). This hypothesis describes the relation between affinity and the intramolecular rearrangement needed to make a 5-HT congener recognizable at the 5-HT/LSD receptor. The rearrangement of the congener aligns the electrostatic orientation vector of its indole portion in the direction defined by the vector in 5-HT. To further probe this mechanistic hypothesis the molecular determinants for the action of a new series of tryptamine derivatives was studied in which a methylenedioxy substituent is placed at the 5.6 or the 4,5 positions. The reactivity characteristics of these molecules are presented. The-oretical predictions for their activity on the 5-HT/LSD receptor are discussed. These predictions are based on the comparison of the electrostatic potentials of these molecules with the requirements for 5-HT-like recognition by the 5-HT/LSD receptor, and on simulations of molecular interactions with a molecular probe (imidazolium cztion) which represents a matching receptor site. The electrostatic nature of the complexes that these molecules form with imidazolium cation is revealed by the decomposition of the stabilization energy. It is shown that the affinity of these new compounds for 5-HT/LSD receptors can be predicted and explained on the basis of the working hypothesis obtained previously. Preliminary experimental data on the binding of 5,6- and 4.5-methylenedioxy derivatives of typtamine to the 5-HT/LSD receptors in brain confirm these findings.

Notes: With the empirical atom-atom potential the systems of one and three water molecules surrounding either the lactim or the lactam tautomer of 2-oxopyridine are simulated at temperatures of 198, 248, 298, and 348 K, using Monte Carlo techniques. The results show that the lactam form of the molecule is more stabilized by the water molecules than the lactim form by about 17-29 kJ/mol (4-7 kcal/mol), thus remaining in accordance with the conclusions inferred from experimental evidence.

Notes: Statistical correlations have been examined between two experimental carcinogenicity indices, a mutagenicity index, and several theoretical reactivity indices for a sample of polycyclic aromatic hydrocarbons displaying a considerable range of carcinogenic activities. Salmonella/microsome mutagenicity assay results show no quantitative correlation with either lball indices (r = 0.08) or a mouse-skin tumor index (r = -0.11) for this sample, whereas the two carcinogenicity indices show reasonable agreement (r = 0.84). The theoretical indices, which represent chemical reactivities for several putative carcinogenic “activation” steps, correlate with the cancer indices ( r ∼ 0.6-0.9). but not the mutagenicity index, suggesting a usefulness in cancer prescreening procedures. Similar results are found for a sample of 24 unsubstituted aromatic hydrocarbons. Available hamster V79 cell assay results show good correlations with the carcinogenicity indices (r = 0.87-0.99).

Notes: The problem of a mathematical description of objects showing individual structural variations but belonging to an apparently homogeneous population is considered. As an illustration a characterization of neuronal dendritic fields is outlined. The scheme views a neuron as a graph and is concerned with the characterization of the branching mode of derived graphs. The basic graph invariants considered are distances between all end points, which are enumerated and combined in a sequence. Some properties of the codes are discussed and their use for a classification of objects is illustrated.

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: 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: The molecule-in-molecule method of computation has been applied in a SCF study of the electronic absorption spectra of 2- and 3-phenylfurans and 2,2′- and 3,3′-bifurans. The computed values for the transition energies and band intensities differ for the different isomers and help one to assign the preferred conformer of the studied molecules. Computations were performed on planar as well as nonplanar conformers. The calculated parameters as well as the interaction energy suggest all-planar configuration for the studied molecules. A model potential for the sigma framework for the ortho-hydrogens is considered. The calculated steric repulsion energy is negligible compared to the π delocalization. The height of the rotational barrier was larger for 2-phenylfuran than for 3-phenylfuran, and larger for 2,2′-bifuran than for 3,3′-bifuran. This result is in accord with predictions based on the extent of “π” conjugation in these molecules.

Notes: Quantum mechanical calculations have been made of vibrational transition probabilities in the collinear collision of an inert gas atom with either CO2 or OCS. The dependence of the transition probability on the relative translational energy and the reduced mass is similar to that found for atom-diatom collisions. The transition P00 → 10 (excitation of the first stretching mode) is much greater than P00 → 01 (the second stretching mode). This is largely due to the difference in frequencies but it has been shown that there is an independent mass factor responsible for this difference.

Notes: While the concept of the graph center is unambiguous (and quite old) in the case of acyclic graphs, an attempt has been made recently to extend the concept to polycyclic structures using the distance matrix of a graph as the basis. In this work we continue exploring such generalizations considering in addition to the distance matrix, self-avoiding walks or paths as graph invariants of potential interest for discriminating distinctive vertex environments in a graph of polycyclic structures. A hierachy of criteria is suggested that offers a systematic approach to the vertex discrimination and eventually establishes in most cases the graph center as a single vertex, a single bond (edge), or a single group of equivalent vertices. Some applications and the significance of the concept of the graph center are presented.

Notes: We use an experimental design method for computing a local quadratic form which is adequate to find stationary points and to evaluate the force constant matrix on a k-dimensional potential energy hypersurface. Two types of designs are particularly discussed: the composite and the Doehiert's plane. We give examples for illustrating the methodology. Some thermodynamical properties are deduced from our results. Such a method may be used with every type of theoretical calculations (SCF or CI) and with any program without modification.

Notes: Energy difference formulas for isoelectronic processes are derived using a perturbation series. The perturbed Hamiltonian is written as a function of a perturbation parameter that changes linearly from zero to one between the limits of the isoelectronic process. The perturbation series is based on a zero order wave function obtained when the perturbation parameter has a value of ½. For the description of changes of electronic energy with internuclear geometry, this zero order wave function will correspond to the solution of a Hamiltonian which contains atoms from both internuclear geometries, but with half their normal nuclear charge. Energy differences calculated with this formalism for the stretching of simple diatomic molecules hydrogen fluoride, fluorine, and carbon monoxide and the rotational barrier in ethane are compared with results from restricted Hartree-Fock and integral-Hellmann-Feynman theorem energies.

Notes: Ab initio STO-3G geometries and relative energies for uracil (U) and the tautomer 4-hydroxyuracil (U*) were obtained with the HONDO program utilizing the rapidly convergent method of Murtaugh and Sargent for geometry optimization. ΔE for U⇄U* is 6.61 kcal/mole. The reaction field continuum model for solvent effect indicates a preferential stabilization of U* by 1.0 kcal/mole. The calculated gas phase Kt and solution Kt for U⇄U* are 1.44×10-5 and 1.3×10-4, respectively.

Notes: Procedures for the construction of the eigenvector matrix and the spectrum of 4 × 4 real and symmetric matrices are given. The Lie algebra of the group O(4)† is used as well as the relation to O(3)†. Perturbations are analyzed in terms of the group parameters.

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: 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: 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: 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: For a Coulomb system of particles of charge e, it has previously been shown that the indirect part of the repulsive Coulomb energy (exchange plus correlation energy) has a lower bound of the form -Ce2/3∫ρ(x)4/3 dx, where ρ is the single particle charge density. Here we lower the constant C from the 8.52 previously given to 1.68. We also show that the best possible C is greater than 1.23.

Notes: After emphasizing the importance of absorption spectra of metal clusters, with special reference to alkali halide IR absorption, the equilibrium configurations and the binding energies of alkali halide clusters are discussed in terms of a very simple two-body interaction.