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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: 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: 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: 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: 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: 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: 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: 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.

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: A recently proposed orthonormality constrained orbital optimization technique is operationally modified further by coupling it to a gradient biased method, namely the steepest descent procedure of McWeeny. The hybrid technique developed in this way is shown to have better convergence properties in closed and unrestricted open-shell calculations. The technique can be adapted to MCSCF procedures as well. The important role played by "orbital symmetries" in the operation of the method is analysed. Similarities and differences of the present method with the orthogonal gradient method are pointed out. Possible avenues of circumventing convergence difficulty that one may encounter in pathological cases, particularly in ab initio calculations involving extended basis set, are suggested.

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: Formulas can be automatically generated for all two-center Coulomb integrals over Slater-type orbitals by means of the “C-matrix” single-center expansion method with use of “computer algebra.” The formula coefficients may be stored in two-dimensional arrays.

Notes: The conditions for instability of solutions of Hartree-Fock and projected Hartree-Fock equations are derived in a form involving finite real symmetric matrices. These conditions are also expressed in terms of the Fock-Dirac density matrix, both at the spin-orbital and at the orbital level. The particular variations which give rise to the so-called singlet and triplet instabilities are described.

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: The well-known Hausdorff similarity transformation is used to derive a number of identities for exponential operators. The method does not give new results, but is shown to be a simple alternative to Feynman disentangling, parameter differentiation-differential equation, coherent states, and Lie-algebraic-matrix techniques.

Notes: The connections between open shell Brillouin-Wigner perturbation theory and the Van Vleck unitary transformation formalisms for generating effective Hamiltonians are explored. An explicit expression is obtained relating the generator Ŝ of the unitary transformation eiŝ with the amplitudes to be found from perturbation theory. The “renormalization effects” needed to produce the explicit “orthogonal-Hermitian” form of the effective Hamiltonian in perturbation theory are related directly to the generator of the unitary transformation. The conclusions reached previously by Jørgensen and Brandow regarding the identity of the effective Hamiltonians of the formalisms are explicitly verified for the case that the generator Ŝ satisfied the Kemble condition. The procedure suggests how the powerful techniques of perturbation theory can be used within the unitary transformation framework to guarantee properly renormalized wave functions.

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: Several useful “redefined zero-order Hamiltonian” variants of the Rayleigh-Schrödinger perturbation theory are derived by exploiting the freedom of choice for the orthogonality integral between zero- and first-order wavefunctions. It is found that the more common Hamiltonian repartitioning schemes follow quite naturally, as a consequence of certain consistency requirements. The strategy adopted may as well be employed to derive various newer and profitable zero-order Hamiltonians depending on the nature of the problems. This implication is strengthened by demonstrating the calculational success of one such derived scheme. Feenberg's “scale-changed” Hamiltonian approach is also reinterpreted in the present context.

Notes: The exponential transformation of the molecular orbitals, that has been previously used to achieve a process with a convergence of quadratic quality in SCF closed-shell calculations [J. Chem. Phys. 72, 1452 (1980)] has been extended to UHF determinantal wave functions built from different orbitals for different spins. Explicit formulas are given for the first and second derivatives of the energy to be varied. The method is illustrated by UHF calculations for systems described as standard singlets (Li2 and F2) or triplets (NH) at the RHF approximation level, as well as for CH, CH2, CH3 molecular fragments in their valence states.

Notes: The development of a flexible intra- and intermolecular empirical potential function is described, which is designed for investigating the geometric structure of large molecular systems. The intramolecular components in the potential consist of harmonic bond stretching and angle bending terms, out-of-plane deformation terms, and torsional terms; intermolecular components include nonbonding, hydrogen bonding, and electrostatic terms. Bond lengths, angles, and torsional angles are predicted to within 2% of experiment, with most cases being within 1%. The suitability of the intermolecular potential was tested by crystal packing calculations; in all cases the results obtained were in excellent agreement with experiment.

Notes: Ascorbic acid enhances the free radical electron spin resonance signal obtained when methylamine interacts with methylglyoxal. Previous ab-initio calculations have shown that methylglyoxal and other ketoaldehydes may act as possible electron acceptors in Szent-Györgyi's theory of cancer. Ascorbic acid is also known to be involved in cancer.The ab-initio SCF method has been used to study the electronic structure of ascorbic acid and its metabolites. The bulk of the calculations involved the use of α-hydroxytetronic acid as a model for ascorbic acid, and related compounds as models for the ascorbyl radical and dehydroascorbic acid. Complete geometry optimizations by the force method were carried out for the model compounds, using an STO-3G basis set.To obtain an estimate of possible charge transfer involving these molecules, ab-initio “supermolecule” calculations were carried out using formamide and glyoxal. A large number of planar and stacked orientations were considered The anion acts as a substantial donor in many of the stacked conformations, but the charge transfer is rather small in all these systems.

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: In an attempt to account for the selectivity displayed by valinomycin with respect to the binding of alkali metal cations, theoretical computations were performed of the interaction energies of this macrocyclic carrier with Na+, K+, Rb+, and Cs+. Subtracting from these interaction energies the corresponding dehydration energies of the cations yields a set of values of the energy balance, the ordering of which follows the ordering of the binding constants measured experimentally in polar solvents. The possibility of extending the procedure to the alkaline-earth cations Mg2+ and Ca2+ is examined.

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: 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: Aminoacyladenylates play a central part in both protein enzymatic and polypeptide prebiotic synthesis. Previous general studies on aminoacyladenylate conformations were extended to some aspects related to polypeptide prebiotic synthesis. Major conclusions drawn from these quantum mechanical PCILO calculations are: (1) In the presence of an ammonium group the glycylphosphate system forms a double seven-membered ring. This folded conformation possesses an important rigidity. This occurs in neutral or acidic solutions. It agrees with experimental observations showing that there is no polymerization in this case, in the absence of catalyst. Thus the catalytic part of montmorillonite clays, which can break the ring by compensation of the anionic and cationic charges, can be understood. (2) When the amine group remains in its neutral form (in basic solutions), numerous stereo structures are allowed for the glycylphosphate stem, among which a ring of weak stability. This is still in good agreement with the observation of polycondensation at high pH without catalyst. (3) The phosphate linking system is flexible enough to allow the extension of the polypeptide chain between the clay layers. This is in accordance with the mechanism proposed by Paecht-Horowitz in which the phosphate is locked on the edge of the montmorillonite sheet.

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: 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: 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: Local coordinate systems are introduced into open sets of topological spaces, defined for the nuclear configuration space R of polyatomic nuclear systems. The open sets are directly related to common chemical concepts, such as chemical structure, reaction mechanism, and stability of reaction paths. A topological model of molecules and chemical reactions is a generalization of the geometrical model, and is particularly suitable to account for the nonrigid nature of chemical structures. The coordinate neighborhoods defined on R and on its submanifolds represent the extent and natural limits for partial analyses of multidimensional potential surfaces.

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 FSGO molecular fragment technique has been employed to perform ab-initio SCF-MO calculations on morphine and naloxone in the free-base and N-protonated forms. Particular features of electronic structure which have been investigated are molecular-orbital (MO) density distributions, energies and ordering, as well as the correlation of specific orbitals between different molecular species. It has been found that high-energy occupied and low-energy unoccupied MOS are centered on the aromatic moiety of both drugs, enabling the ring to act either as an electron donor or as an acceptor in a charge-transfer interaction. Comparison of corresponding MOs in the free base and the acid cation of both morphine and naloxone demonstrates that the field of the cationic head causes a dramatic downward shift in orbital energies. Thus in the N-protonated drugs the acceptor capability of the benzene ring is greatly enhanced at the expense of its suitability as a donor. Furthermore, the allyl group of naloxone becomes highly activated as an electron acceptor through N-protonation. Investigation of the molecular electrostatic potential of the free-base species has revealed preferred avenues of approach for electrophilic and nucleophilic entities. However, the N-protonated species shows no regions of attraction for electrophiles. In both the free base and the acid cation, the vicinities of the nitrogen atom and the 3-hydroxy group are found to be favorably disposed for electrostatic interactions with receptor entities possessing the proper charge or polarity. Based on the findings with regard to electronic structure, a simple model has been suggested to explain the binding of morphine and naloxone at the opioid receptor.

Notes: The transfer of the central proton between the two NH3 units of (H3NHNH3)+ is studied using the 4-31 G basis set within the ab-initio Hartree-Fock formalism. Electron density difference maps are constructed which clearly indicate electronic redistributions which accompany the half-transfer of the proton from its equilibrium position (NH—N) to the midpoint of the hydrogen bond (N—H—N). The overall loss of electronic charge from the proton-accepting molecule originates in three distinct regions of space, while a density buildup of smaller magnitude is observed in a characteristic region centered about the N nucleus. Similar regions are noted for the proton-donating molecule, although the changes are reversed in sign. A partitioning of the total density changes into contributions from the various molecular orbitals demonstrates that the a1 orbitals are associated with density shifts along the H-bond axis. Changes in the N lone pairs are attributed chiefly to the (5a1,6a1) pair and are somewhat attenuated by opposite shifts involving the (3a1. 4a1) pair. Orbitals of e symmetry lead to polarizations of the NH bonds and density shifts perpendicular to the H-bond axis.

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 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: To study the arrangement of substrates at the active site of creatine kinase, we have measured the paramagnetic effects of CrADP, an exchange-incrt paramagnetic analog of MgADP, on the nuclear spin lattice relaxation rates 1 /T1 of the protons of water and the protons and phosphorus nucleus of P-creatine in the presence and absence of rabbit muscle creatine kinase. Relaxivity titrations measuring the paramagnetic effect of CrADP on 1/T1 of water protons at several concentrations of the enzyme in the presence of P-creatine were used to study the binding of CrADP to the enzyme·P-creatine complex. The existence of a ternary enzyme·CrADP-P-creatine complex was confirmed by observing the paramagnetic effects of enzyme-bound CrADP on the 1 /T1 of the 31P nucleus and protons of P-creatine. From the magnitude of paramagnetic effects arising within the enzyme·CrADP·P-creatine complex, using the electron spin relaxation time estimated from the magnetic field dependence of 1 /T1 of fast exchanging water protons, a Cr3+-phosphorus distance of 6.0 Å, and Cr3+-proton distances of 11 and 12 Å, were obtained. These results imply the absence of a direct coordination of the phosphoryl group of P-creatine by the nucleotide-bound metal on creatine kinase but indicate proximity of enzyme-bound substrates and are consistent with van der Waals contact between a phosphoryl oxygen of P-creatine and the hydration sphere of the nucleotide-bound metal. Since the metal ion is coordinated to the γ-phosphoryl group of ATP on the enzyme, the overall migration of the phosphoryl group during phosphoryl transfer is ∼3 Å, toward the nucleotide-bound metal.Creatine kinase failed to catalyze phosphoryl transfer from P-creatine to CrADP as monitored by the disappearance of the 31P NMR signal of P-creatine in a solution containing CrADP, P-creatine and creatine kinase. The ability of an isomer of β,γ-bidentate CrATP to act as a partial substrate and our observation of the absence of phosphoryl transfer from P-creatine to CrADP indicate that metal ion coordination of the transferable phosphoryl group precedes phosphoryl transfer and is a requirement of the creatine kinase reaction.

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: Hemoglobin-catalyzed hydroxylation of aniline may be taken as a model for similar reactions catalyzed by cytochrome P-450. Using ultraviolet-difference spectroscopy and 1H nuclear relaxation techniques, the binding of aniline to hemoglobin was examined. From the magnitude of paramagnetic effects of ferric iron on aniline protons, using the correlation time determined from the magnetic field dependence of water proton relaxation rates, aniline was found to bind to methemoglobins such that the aromatic protons are 8.5 ± 0.7 Å, away from the high-spin Fe3+. A mode of binding is proposed where the aniline molecule is hydrogen bonded to the distal histidine of hemoglobin.

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: The solution conformations of two DNA octanucleotides, (GGAATTCC)·(GGAATTCC) and (AAAGCTTT)·(AAAGCTTT), have been investigated by theoretical calculations of NMR shifts. The calculations of proton chemical shifts have been made, taking into consideration the ring current effects and the atomic magnetic anisotropies of the bases. The computed shielding constants for B-DNA, alternating B-DNA, the Levitt propeller-twisted model and the Dickerson propeller-twist model (based on crystallographic data) have been compared with experimentally available shifts. For the (AAAGCTTT)·(AAAGCTTT) double helix the experimental data are available only for the exchangeable protons HN1 and HN3; thus a complete and detailed evaluation is impossible for this system. For (GGAATTCC)·(GGAATTCC) the results indicate that the A·T pairs are propeller twisted à la Levitt and Dickerson.

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.