Library

Notes: Bacteriorhodopsin, bR, the other photosynthetic system in nature (besides chlorophyll) absorbs light and undergoes a cycle involving intermediates appearing in different time domains (from fractions of picoseconds to several milliseconds). As a result, the protonated Schiff base (PSB) deprotonates, and protons are pumped from inside to the outside of the cell membrane, creating proton gradients that are energetically responsible for making ATP. Using time-resolved Raman and optical spectroscopic experiments, the following results and possible conclusions are obtained. (1) Unlike chlorophyll, bR does not use an antenna system, i.e., each absorbing molecule is a reaction center. (2) Isomerization of its retinal chromophore, which leads to the first step in energy storage by charge separation, occurs on the subpicosecond time scale. (3) The deprotonation of the PSB and a tyrosine, which occur on the 40 μs time scale, is found to have activation energies comparable to H-bond energies. This, together with the fact that the temporal quenching of the tryptophan fluorescence follows the time profile of the deprotonation strongly suggests that the latter process is controlled by protein conformation changes. (4) Cations are found to be required for the deprotonation process and are believed to control the protein conformation required for this process. Possible mechanisms responsible for the decrease in the pKa of the PSB from 13.3 to 〈2.6 during the photocycle, and are thus responsible for the deprotonation process, are discussed.

Notes: Given the invariance of an N-body system under discrete operations of reflection, inversion, a rotation by 2π/n, and the corresponding relations among the derivatives of energy, we have constructed through an invertible transformation a set of active and redundant coordinates. Movement along the active coordinates preserves all symmetry relations. We show that algorithms for locating stationary points or for calculating reaction paths are exactly separable in these active and redundant coordinates. We further show that this formalism is equally applicable when equations of constraints among coordinates are specified for the movement of particles. This includes geometrical constraints on bond lengths, angles, substituent group internal rotations, etc. This formalism enhances the efficiency since (laborious) cartesian derivatives need to be calculated only for the active variables and that the problem is reduced in term of m(≤3N) variables. We apply this procedure to obtain the equilibrium geometry of H2O molecule within the subspace of C2v symmetry configurations ab initio derivatives.

Notes: A possible reaction path for the polymorphic transformation of trans-trans solid diacetamide into its trans-cis from is envisaged. A description of the two crystalline forms in the same crystallographic system is adopted, and the energy profile of the crystallographic reaction path is calculated by using an empirical 6-exp. atom-atom potential method and a 6-13G ab initio procedure for the inter- and intramolecular contributions, respectively. Two barriers appear along the reaction path. The first corresponds to the destruction of the trans-trans chains and the second to the formation of the trans-cis dimers. These barriers, being lower than the acetyl rotation barier, are in agreement with the ability to isomerize diacetamide in solid state. The presence of a small energy minimum between these barriers would suggest the existence of an intermediate crystallographic form.

Notes: A new technique for the study of charge transfer processes is presented. The method is based on electron density differentials and employs multiple scattering Xα molecular wave functions. The method is discussed with reference to an excitation of an electron from the HOMO to the LUMO of bis(glycinohydroxomato) nickel (II).

Notes: Some aspects of the catalytic mechanism of the serine proteases were submitted to ab initio RHF MO studies at a 3-21G basis set level. Analytical gradients were used to optimize the geometry of the molecular partners and to sense the interactions among them when they make up for the active site in chymotrypsin. Reaction fields of graded strengths were used to sense the response of the active site to protein surrounding effects. The catalytic triad (Asp-His-Ser) is reduced to a model dyad represented by ammonia and methyl alcohol. Methyl acetate represents a substrate. One water molecule is added to the model as a local solvation effect. (This molecule plays a central role in the rupture of the acylated enzyme, which was not studied here). The reaction pathways of MeAc interacting with the alcohol and alcoholate were studied to determine the intrinsic properties of this system in the present level of wave function representation. The presence of the dyad alters the interaction potential of the reacting system. The canonical form in vacuo is significantly more stable than the diionic one. The reaction field produces stabilizing effects favoring the catalytic diionic form. The effect of the tetrahedralization in the substrate has been studied. A planar substrate is strongly repelled at distances shorter than 3.0 Å, whereas a tetrahedral substrate can approach the catalytic dyad in the native configuration without apparent steric hindrance.

Notes: Complete geometry optimizations have been carried out with the AM1 method on flavone acetic acid and several of its derivatives. Molecular electrostatic potential maps have been used to predict new com.

Notes: A close coupled treatment in a vibrational adiabatic representation is applied to the study of molecular photodissociation dynamics. The procedure which is developed here involves three steps: transformation from a diabatic to an adiabatic basis set, truncation of the adiabatic basis set, back transformation to a reduced-diabatic basis set. In the two model cases which are studied, dissociation spectra show complicated peaks and dips, patterns interpreted in terms of shape and Feshbach resonances associated to vibrational predissociation with a relatively high potential barrier in the excited state. An important reduction in the number of channels required for a given final accuracy can be reached by using the reduced-diabatic basis set instead of the usual diabatic one. This is very promising for studying energy partitioning in molecular systems with several internal degrees of freedom taking part in the dynamics.

Notes: Conformational preferences of the hypermodified nucleic acid bases N6-(Δ2-isopentenyl) adenine, (i6Ade) and its 2-methylthio derivative (ms2i6Ade) have been investigated theoretically by the quantum chemical perturbative configuration interaction using localized orbitals (PCILO) method.The predicted most stable conformation of i6Ade and ms2i6Ade are such that the isopentenyl substituent is oriented away from the imidazole moiety of the adenine ring. The atoms N(6), C(10), and C(11) remain coplanar with the adenine ring for both molecules. However, in contrast to the predicted cis orientation of the C(10)—C(11) bond with respect to the C(6)—N(6) bond in i6Ade, the trans orientation is favored for ms2i6Ade. The plane of the isopentenyl group is rotated by 120° from that of the purine base in i6Ade, whereas rotation by 60° is favored in ms2i6Ade. The favored orientation of the methylthio group with respect to the C(2)—N(3) bond is trans; however, the alternative cis arrangement is also quite probable. The conformational implications of the methylthiolation of the isopentenyladenine are brought out in the context of the considerably large range of accessible (β,γ) and χ orientations. The compatible roles of i6Ade and ms2i6Ade in tRNA are thus understood, besides their distinguishing features.

Notes: The effect of basis set contraction and elimination of primitive Gaussian orbitals on the He2 interaction energy components have been studied within the SCF counterpoise corrected approach supplemented by a dispersion term calculated within the variation-perturbation scheme. Despite elimination of almost half of the primitive Gaussian functions from the saturated sp basis set and complete contraction of the remaining ones, the components of interaction energy in He2 suffer a remarkably small loss of accuracy except for the short range charge transfer contribution.

Notes: A characterization of molecular model surfaces is proposed. It is based on a graph associated with the van der Waals surface, defined by the detailed information on the interpenetration of van der Waals spheres of the constituent atoms. This “van der Waals graph” describes the three-dimensional body of the molecule, and it does not coincide in general with the less informative bond graph obtainable from the molecular skeleton.The description in terms of the graph reveals clearly the changes in molecular shape induced by conformational rearrangements. The nuclear configurations can be classified by the graph associated with the molecular surface, and the graph-theoretical analysis provides a rigorous partitioning of the configurational space based on shape properties.

Notes: A systematic collection of spatial domains for reciprocal space integrations is derived for all possible crystal symmetries. This set can be used as a simpler alternative to the conventional Brillouin zones. The analysis is restricted to integrations where the function in the integrand satisfies inversion symmetry in k space. In this case only 24 different spatial domains have to be defined in order to allow for k space integrations in the 230 different crystal symmetries. A graphic representation of the asymmetric unit for each of the 24 integration domains is given. Special positions and the associated weighting factors required for numerical integrations in theoretical solid-state approaches are tabulated.

Notes: The edge inversion process in phosphoric acid, PO(OH)3 has been studied by large scale ab initio molecular orbital theory. Edge inversion of the tetrahedral ground state via a square-planar transition state requires 69.5 kcal/mol (MP-2). Addition of two NH3 solvent molecules to the vacant NLUMO stabilizes the transition state by 45 kcal/mol (MP-2). The value for ΔH(300K) for the reaction 2NH3 + PO(OH)3 → PO(OH)3 · (NH3)2 is 24.1 kcal/mol (MP-2). The complex with two NH3 molecules is an intermediate. Addition of one NH3 to PO(OH)3 leads to an energy lowering of the planar form of 31 kcal/mol. This structure is now a transition state. The value for ΔH(300K) for the reaction NH3 + PO(OH)3 → PO(OH)3 · NH3 is 38.6 kcal/mol (MP-2). The complex of PF3O with two NH3 molecules was studied and is an intermediate. The value for ΔH(300K) for the reaction 2NH3 + POF3 → POF3 · (NH3)2 is only 3.3 kcal/mol (MP-2). Electron-donor solvents clearly will stabilize the edge inversion transition state for tetracoordinate main group compounds.

Notes: In this work the problem of normal vibrations of a molecule isolated in the argon gas and nitrogen gas matrix is considered. Modification of a valence force field to this problem is described, allowing the use of Lennard-Jones-type pair potentials for molecular-matrix and matrix-matrix interactions. For the selection of molecular-matrix pair potential parameters, the procedures based on combination rules are employed. To obtain the vibrational frequencies a monosubstitutional site in the crystal of an argon gas or a nitrogen gas is chosen as the most probable trapping site for the hydrogen cyanide molecule in the matrix of them. A pseudolattice method is applied to cubic 12 argon or nitrogen crystal fragments in order to eliminate the edge effect; we can obtain good results.

Notes: We have extended the study of the description of local correlation effects provided by the different partitions of a configuration interaction (CI) wave function to the first excited state of the helium atom. Our analysis makes use of the local mean values of different moments of the interelectronic distance computed with the CI partitions as well as with Hartree-Fock and Hylleraas-type wave functions.

Notes: The resolution of a double determinant into a sum of spin-free orthogonal spin eigenfunctions is presented; its equivalent resolution of a spin function product θM0 is also given. Furthermore, a more general resolution of a Slater determinant into all spin eigenfunctions with S ≥ M is also obtained. Present work has also provided a method to calculate the linear coefficients in the expression of the primitive θMi in terms of the linear combination of spin eigenfunctions X̃NK (S, M).

Notes: We examine a variety of methods for obtaining the stable geometry of molecules and the transition states of simple systems and summarize some of our findings. We find the most efficient methods for optimizing structure to be those based on calculated gradients and estimated second derivative (Hessian) matrices, the later obtained either from the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton update method or from approximations to the coupled perturbed Hartree-Fock method. For uncovering transition states we find particularly useful a variety of the augmented Hessian theory used to uncover regions of the potential energy hypersurface with one and only one negative eigenvalue of the Hessian matrix characterizing the catchment region of the transition state. Once this region is found we minimize the norm of the gradient vector to catch the nearest extreme point of the surface. Examples of these procedures are given.

Notes: Recently, Perdew and Wang presented an expression for the exchange energy of a many-electron system. This functional has been adapted in the present work in variational density functional calculations of the total atomic binding energy of the Ne atom. For this atom similar calculations have been done earlier using the Dirac expression for the exchange energy. Three different total energy functionals have been considered: (1) the Thomas-Fermi-Perdew-Wang functional, (2) the above functional augmented by (1/9) of the original Weizsäcker correction to the Thomas-Fermi kinetic energy, and (3) the same functional as in 1 augmented by (1/5.3) of the original Weizsäcker correction to the Thomas-Fermi kinetic energy. The electron (number) density of the Ne atom has been constructed from hydrogen-like one-electron wave functions containing three variational parameters. Each of three total energy functionals have been minimized with respect to these parameters. Comparison of the Perdew-Wang and Dirac exchange energies shows that, in each of the three model pairs, the Perdew-Wang exchange energy is larger in magnitude than the Dirac exchange energy. It is also found that the exchange energy obtained by 2, -12.31 a.u., is in excellent agreement with the value of -12.22 a.u. calculated by Perdew and Wang with the Clementi and Roetti near-Hartree-Fock density.

Notes: By using the n + (1/2)l filling rule of the atomic Aufbau principle, where n is the principal quantum number and l is the azimuthal quantum number, a new periodic table is presented, its periods having, in order, 8, 18, 18, 32, 42, 50, … elements. The mentioned rule is proposed instead of the n + l rule (or Madelung's rule) which constitutes the quantum mechanical basis of the current periodic table and predicts periods having, in order, 2, 8, 8, 18, 18, 32, 32, 50, … elements. The new periodic table is called “regular” because its groups are formed according to a single rule (namely, the first elements of each period are placed in the same order as the elements of the preceding period), in contrast with the current periodic table, where no simple rule can be applied for the same purpose. The most characteristic feature of the regular periodic table is the fact that its groups are also related in a periodic manner.

Notes: A rigorous approach to the study of the quality of theoretical descriptions of atoms and molecules is proposed. Theoretical descriptions, i.e., collections of atomic or molecular properties obtained via quantum chemical methods, are associated with information quantities defined with respect to reference theoretical or experimental data. In this way the comparison of two theoretical descriptions is reduced to the comparison of the respective information quantities. An increase in information is interpreted as improvement of the theoretical description. The aforementioned approach should be useful in problems related to classifications and systematic improvements of approximate wave functions and consequently for comparing the performance of quantum chemical methods in calculations of atomic and molecular properties. This approach should also constitute a powerful tool for the construction of suitable basis sets for use in calculations of atomic and molecular properties.

Notes: Generalized Padé approximants are used to extrapolate the total energy of polymers described by alternant Hamiltonians to the bulk limit. The method provides an upper bound to the energy. The origin of (quasi) periodic oscillations of the energy per unit cell as the function of the number of unit cells is enlightened through analysis of the moments of the Hamiltonian.

Notes: It is demonstrated that the total π-electron energy calculated within the “variable β” Hückel method is almost entirely determined by the total π-electron energy computed within the ordinary (topological) Hückel method and the number of the carbon-carbon bonds. This explains the fact that the topological Hückel method is capable of predicting relative stabilities of various molecules, even if they possess different bond lengths.

Notes: In this work, an algebraic method is developed to determine the eigenlevels of radially screened Coulomb potential systems. The method is mainly based on the concept of space pruning. The basis functions are combined in a way such that the resulting approximate eigenfunction and its several images under certain positive integer powers of the system's Hamiltonian (H) remain in the domain of H. Certain structural parameters are introduced into the basis functions to imitate some known behaviors of the true eigenfunctions of the system.The main purpose of this work is not to reproduce the results for screened Coulomb potential systems but to develop a method which does not necessitate integration at any stage and can later be adapted to atomic and molecular systems as easily as possible.

Notes: Two different versions, relativistic and nonrelativistic, of the “shape-consistent” effective potential (EP) formalism are analyzed in ab initio calculations for transition metals. The influence of alternative core/valence partitions on the reliability of the procedure is discussed. The accuracy of EP results for transition metals is shown to depend on adequate choices of the valence subspace and proper inclusion of relativistic effects.

Notes: Molecular descriptors currently used in structure-property-activity studies are based on molecular graphs rather than on a structure as a three-dimensional object. Here we suggest a way to amend graph-theoretic invariants with additional geometric information, thereby providing new molecular descriptors for possible use in quantitative structure-activity correlations. In the approach we assume molecular structures embedded on a regular grid. As an illustration we consider first chains of different length embedded on graphite-like lattice. Subsequently, we consider all possible conformations of hexatriene. Although the cases considered here relate to graphite-like lattice, the approach is general and applies to embedings of molecules on three-dimensional lattices, or, in general, to molecules of arbitrary spatial conformations.

Notes: A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski-Monkhorst [16] ansatz for the cluster operator (Ω = ∑eTjPj, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., Tj ≈ Tj(2). The linear version of this method (MR L-CEPM) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C2ν insertion of Be into H2. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L-CEPM results are slightly below the accurate (FCI) values.

Notes: Two possible mechanisms have been suggested for the formation of soot in fuel-rich flames. The first of these involves reactions of small radicals, the second of small ions. We examine the latter possibility in this paper. Reactions between C3H3+ ions and acetylene were studied by quantum mechanical methods. The results suggest that the linear propargylium cation reacts without barrier. Cyclic C3H3+ does not readily react with acetylene. These observations are in agreement with FT-ICR experiments that suggest one inactive form of the C3H3+ cation. The properties of five different products of the reactions were studied for possible identifications in experiments on flames and on model flames.

Notes: The interaction of a carbonyl group with two adjacent aromatic units is discussed. The outer valence electronic structure of compounds of general formula Ph—CO—Ar, where Ar is phenyl, substituted phenyl, furyl and thienyl, is determined from their gas phase photoelectron spectra. Particular attention is paid to biologically active derivatives of 2-amino-5-chlorobenzophenone.

Notes: Proteins and other macromolecules may be viewed as shape-based (or tactile) pattern recognizers. Biological cells exploit this inherent capability by transducing macroscopic signal patterns impinging on the external membrane to microscopic patterns at the molecular level, via second messengers. The parallelism inherent in the wave function description of these microscale processes in effect serves to increase the computing power of molecular computing systems as compared to macroscopic analogs. The conversion and recognition process is highly reminiscent of measurement. The linking role of second messengers allows macroscopic signals to set the state of the cell (in analogy to state preparation), while enzymatic readout and control of cellular behavior is an amplification process that corresponds to measurement of the microstate at a later point of time. Since the standard time evolution equations are reversible and unitary, while measurement is not, it is conceivable that the study of molecular computing will lead to new insights into the relation between the microworld and the macroworld. The model presented suggests that projection processes that are masked in ordinary laboratory systems are brought to macroscopic significance by the highly nonlinear chain of amplification events in the biological cell.

Notes: Whereas localization of orbitals has long been a tool for a semiclassical interpretation of chemical properties, it is in fact electron delocalization that is a fundamental property of quantum mechanical molecules. A mathematically well-defined measure is suggested for the degree of delocalization of molecular orbitals. It is shown that an orbital set of maximum delocalization exists for which the degree of delocalization depends on the charge distribution of the molecule. Hartree-Fock canonical orbitals are definitely more localized than the most uniformaly distributed MO's giving an equivalent description of the molecule. The changes in the geometrical shape of molecular orbitals are studied passing (quasi-) continuously from the strongly localized description towards the most delocalized picture. In the case of charge-inhomogeneities even the most delocalized orbitals remain rather compact. The degree of maximum delocalization may be correlated with chemical properties such as reactivity. The shape distortion of MO's under the perturbing effect of other ions and small molecules is investigated in several examples.

Notes: The density matrix was computed from the density using basis orbitals which form linearly independent products (LIP). Calculations were performed on the Be atom using LIP bases containing several of the natural spin orbitals from an accurate nonrelativistic 650-term configuration interaction (CI) wavefunction. Calculations were also performed using a basis set of 6 s-type orbitals optimized so that the lowest eigenvalue, d1, of the overlap matrix of products is maximized and the energy of a small CI wavefunction is minimized. The value of d1 in the optimized basis is 1 × 10-7. The density and the potential energy obtained from the 650-term CI wavefunction were accurately reproduced by the density matrix expressed in the optimized LIP basis, but the kinetic energy was somewhat less accurate.

Notes: A theoretical prediction of the absorption coefficients of shallow donor pairs in uncompensated doped semiconductors has been performed within the framework of the Alternant Molecular Orbital method. The interaction between the lattice and the electronic excitation is well understood in terms of the Frank-Condon model. Calculations for the value of the electron-LO phonon interaction parameter S have been extended to include the donor pair excitation. The model has been applied for Si:P and Ge:P.

Notes: Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold v. The remaining part is obtained from a v-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.

Notes: The induction of electronic motion by nuclear motion is described for the particular case of the absorption of infrared radiation by chiral molecular systems. The description is in terms of an effective vector potential, which is obtained by averaging over the electronic coordinates. This effective vector potential can be visualized in a number of ways. Nine of these are tabulated and discussed. Strong evidence is presented that the interaction of rings with radiation can be treated in the same way as the interaction with chains. Evidence is also obtained that the bulk of the induced electronic motion can be determined semiclassically.

Notes: Using a graph theoretical approach we have analyzed the aromatic stability of macrocylic systems having ten and fewer fused benzene rings. The approach requires construction and examination of Kekule valence structures of the macrocyclic systems considered. The Kekule valence structures for a molecule were systematically derived and the conjugated circuits in the individual Kekule formulas were enumerated subsequently. The counting results is the expression for molecular resonance energy, from which relative aromatic stabilities can be established. We report also on molecular local features, including ring benzene characters and Pauling bond orders.

Notes: A general technique will be outlined which provides a systematic means for fitting polyatomic potential energy surfaces. Use is made of both ab initio energy and gradient data to fit the surface about an N-dimensional reference curve connecting stationary points. The reference curve may be modified iteratively during the course of the fitting. A particular iteration will specify a new set of points which need to be calculated to improve the accuracy of the surface. An application of this method to a model potential energy surface is discussed.

Notes: Many-body perturbation theory, configuration interaction, and coupled-cluster methods are used with different basis sets to analyze the role of correlation and basis set size effects on the calculated electron affinity of HC2. Utilizing an extended basis set consisting of 83 contracted Gaussian-type orbitals, a CCD calculation gives the value of 3.21 eV for the adiabatic electron affinity of HC2 in excellent agreement with a previous theoretical result of 3.18 eV obtained by eighth-order perturbation theory and in good agreement with the experimental result of 2.94 ±0.10 eV Partial inclusion of single excitations, up to the fourth-order level [CCD + S-MBPT(4)] improves the above theoretical result of 3.21 eV to 3.15 eV. The stability of the results with respect to further increase of the basis set size and the amount of correlation corrections is briefly analyzed.

Notes: Two mapping operators are used to relate the eigenstates of two distorted and displaced oscillators. It is found that these operators satisfy a nonabelian two-dimensional algebra. We exemplify the method by calculating the Franck-Condon integral for the case of two harmonic oscillator wells.

Notes: The problems involved in determining the mechanisms of reactions by quantum mechanical calculations are discussed. Various precautions must be taken if the results of any calculation are to be chemically meaningful. Ab initio studies of reactions must also be carried out at a high level, using large basis sets and allowing for electron correlation. Such calculations are usually restricted to the simplest example of a reaction, which is often untypical. More information can usually be obtained at far less cost through AM1 calculations for a number of examples of a reaction for which experimental data are available. These points are illustrated by recent studies of the Cope rearrangement.

Notes: γ-Aminobutyric acid (GABA) is an inhibitory transmitter used by interneurons in the central nervous system (CNS). In aqueous solution GABA exists as a zwitterion, but in the gas phase the stable form of GABA is a nonzwitterion. Since zwitterions are difficult to transport into the CNS, details of the mechanism for the transformation between nonzwitterionic and zwitterion forms of GABA provide potentially important suggestions for enhancing transport of GABA and GABA analogues into the CNS. A mechanism for the conversion of GABA into the zwitterion form upon aqueous solvation is suggested as a multistage process by simple quantum chemical simulation. Initially, hydrogen bonding at the carbonyl oxygen is followed by attack of water at the carbonyl carbon and results in the formation of a triol. Hydrogen bond bridging, through solvent, from the triol end of the molecule to the amino terminus, facilitates N-protonation from the solvent. The latter appears to trigger rearrangement of the hydrogen bonding at the triol function, thus giving the anionic precursor to the zwitterion. This mechanism is based upon full INDO calculations using a supermolecule composed of GABA and 14 water molecules and resembles part of one of the mechanisms for the hydrolysis of esters as well as a process for the hydration of aldehydes.

Notes: This paper analyzes the use of electric-field-variant (EFV) atomic orbitals in calculations of molecular polarizabilities using the finite field approximation. It is shown that, in the absence of an external electric field, the optimal positions of the orbital centers which minimize the total energy are already shifted with respect to the atomic sites and that these optimal positions constitute a better starting point to compute molecular polarizabilities by the finite field method. The technique is applied to the hydrogen molecule and to the alkane series CnH2n+2, n = 1, 2, 3, 4, 5, 6 in the framework of a floating spherical gaussian orbital-EFV basis.

Notes: Toward the goal of efficiently computing field lines for molecular vector fields, where each field-point calculation is computationally intensive, a few appropriate algorithms for calculating vector field lines are presented and compared for various representative applications. Among these algorithms are the first-order tangent-line method (TL), the fourth-order Runge-Kutta method (RK4), the infinite-order Bulirsch-Stoer method (BS), the second-order Taylor's series method (TS2), and the second-order “curvature-following” method (CF). The TL and the RK4 are well known. The TS2 and the CF are new. The RK4, The TS2, and the CF are appropriate for obtaining high accuracy with few field-point calculations. The TL is definitely not appropriate for this purpose, and the BS is so appropriate only at the highest level of required accuracy. The CF uses the value of the vector field and its gradient at the given field point in order to locate the center of curvature of the field line at that point and, thereby, to extrapolate the field line, as an arc of a circle, to the next field point. The TS2 uses the same information, but extrapolates the field line as a segment of a parabola whose vertex is at the field point. The BS is an infinite-order extrapolation on successively finer scale iterations of the lowest-order Runge-Kutta method. All of these methods are compared for the velocity field of a rotating disk, for the vector field of a point dipole, and for electric field of a high-speed orbiting charged particle. For all of these fields, the field lines are exactly expressible in analytic form, so the absolute errors of these different algorithms can be appraised. As several of these methods allow a rather large step size, it was found appropriate to use a continuous-(geometrical)-curvature interpolation scheme to interpolate between the field points on the generated field lines. One prefers this scheme to the use of cubic splines when the physical fields should have their “geometrical pictures” (even under approximation) invariant to an arbitrary change of the coordinate system used in the calculation. These methods have also been used to generate field lines for the approximate and the exact fields of a half-wave antenna. In this case, one sees very large differences in the structure of the field lines of the approximate and the exact fields, in the near-field region, and also sees the manner in which each of these differences diminishes to zero as the field point approaches the far-field region; features that would have been very hard to observe by purely analytical methods. It is hoped that these methods for field line generation might have application for the field lines of the gradient of the molecular density (as in Bader's theory of atoms in molecules) and for the field lines of the electric fields of nucleic acid molecules.

Notes: The results of applying the simulated annealing method to find the lowest energy structure of the decane molecule are analyzed. The algorithm is found to be both efficient and economical. Some preliminary results are presented for a molecule of biochemical interest, Met-enkephalin.

Notes: Recently we derived, implemented, tested, and used successfully a new computational strategy for ab-initio MRD-CI (multireference double excitation - configuration interaction) calculations for molecular decompositions of large molecules and intermolecular reactions of large systems. We carry out the ab-initio SCF for the entire system, then transform the canonical delocalized molecular orbitals to localized orbitals and include explicitly in the MRD-CI only the localized occupied and virtual orbitals in the region of interest, folding the remainder of the occupied localized orbitals into an “effective” CI Hamiltonian. The advantage is that the transformations from integrals over atomic orbitals to integrals over molecular orbitals (the computer time-, computer core-, and external storage- consuming part of the CI calculations) only have to be carried out for the localized orbitals included explicitly in the MRD-CI calculations. The challenge arose to extend our MRD-CI technique based on localized/local orbitals and “effective” CI Hamiltonian to the breaking of a chemical bond in a molecule in a crystal (or other solid environment). This past year we have derived, implemented, and used successfully a procedure for doing this. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of yet more further out surrounding molecules. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have defects, deformations, dislocations, impurities, dopants, edges, and surfaces, boundaries, etc. We have applied this procedure successfully to the H3C - NO2 bond dissociation of nitromethane with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many further out molecules have to be represented by multipoles. To check the goodness of the model cluster approximation for crystalline nitromethane, we carried out ab-initio crystal orbital (XTLORB) calculations using our POLY-CRYST program. The difference in the XTLORB total energies between the 4 nitromethane molecules/unit cell and the 3 nitromethane molecules/unit cell (Table VIII), ER = E4 - E3 = -48.0609079 a.u., corresponds very closely to the reduced energy per nitromethane molecule, ER = (-;48.0605)9 a.u., calculated from explicit SCF calculations on the model nitromethane cluster in the multipole field of farther out nitromethane molecules for the model cluster. Thus, the multipole approximation for describing the effect of further out molecules on the SCF cluster energies is quite good.

Notes: The electrostatic interaction is a critical component of intermolecular interactions in biological processes. Rapid methods for the computation and characterization of the molecular electrostatic potential (MEP) that segment the molecular charge distribution and replace this continuous function by a series of multipole moments for each segment have been described. There are two sources of error in these techniques: 1( The truncation of the expansion after just a few terms, and 2) the charge in the segmental distribution that is more distant from the expansion center than the observation point. The first may be eliminated by finite expansion methods where truncation is unnecessary or performed in a manner that gives errors that are acceptably small. The second is inherent in the multipole expansion and results from the assumption in performing the expansion that the distance to the observation point is larger than the distance to all points inside the charge distribution. As the basis functions used in molecular wave functions have infinite extent, this will never be the case and the multipole expansion is never strictly valid. In practice this inherent error limits the range of usefulness of all multipole expansion techniques. To expand this range we have introduced a method that uses exact techniques to compute the MEP for the part of the molecular charge distribution described by the gaussians on each atom with the smallest exponential parameter and uses segmental multipole methods for the remainder of the charge. Using pyrrole with an STO-3G wave function as an example, this method significantly improves the potential in the range 1.4-2.0 Å from atoms with only a small increase in computational effort. If other basis sets are used with more diffuse gaussians the convergence of the multipole expansion will be at greater distances from the atoms and this type of correction will be more important.

Notes: The generating functional Z(N) of the molecular orbital theory of N electrons has been projected into a subspace of atomic orbitals. By application of the saddle-Point approximataions to the corresponding effective action, a set of equations of motion results. These equations are the classical Roothaan's equations of quantum chemistry.

Notes: The recently developed integral discretization technique for the generator coordinate method is applied to discuss some features of Gaussian expanded wave functions. Using the hydrogen atom ground state, it is shown that the nuclear cusp problem has an interesting relation with the generator coordinator weight function, which allows the production of accurate wave functions by an integration criterion.

Notes: We have recently developed a new classification of the amino acid side chains based on doublet acceptor energy levels (DALs). These energy levels, taken as the eigenvalue of the highest occupied molecular orbital in the radical anion, provide insight into the shape of the tunneling barrier in protein electron transfer. We have used this classification to characterize several transfer pathways in myoglobin. We present here a study of the effect of changes in geometry on the doublet acceptor levels. We find that, in general, this influence is rather small for reasonable changes in bond lengths and angles (e.g., those resulting from thermal fluctuations in the protein structure). However, we have found that for serine, threonine and water, changes in geometry that might take place as a result of fluctuations in hydrogen bond geometries lead to rather large changes in DAL. We investigate these correlations in some detail. The relation between protein fluctuations and changes in the shape of the electron tunneling barrier is discussed. Additionally, based on the energetics of changes in the OH bond distance, we discuss aspects of the relation between electron transfer and proton transfer.

Notes: This short communication outlines preliminary work aimed at understanding the recognition of sialylated oligosaccharides by influenza virus haemagglutinin. Initial efforts to model the complex have used the electrostatic interactions between atoms in the binding pocket and (2) as a means of constraining the conformational search in docking these two molecules. Some important features of the lowest energy structure are discussed.

Notes: Ab initio calculations reveal that a cation, in a position equidistant from the two H-bonding oxygen atoms of (HC(OH)O · H · OH2)+, acts to push the proton from HCOOH toward OH2 if the ion is located near the  - OH or C—H group of HCOOH. In contrast, rotation of the cation out of the HCOOH plane, while maintaining its position relative to the two H-bonding atoms, leads to a potential which is little different than that observed in the absence of an ion. These findings are readily explained on the basis of ion-induced internal polarization of the subunit to which the ion is closer. Replacement of OH2 by HCOOH suggests that polarization of the more distant subunit can also be a factor.

Notes: Application of free-energy simulation methods to the calculation of thermodynamic properties for biologically relevant processes will be presented. Attention will be given to the usefulness of thermodynamic methods to explore the accuracy of empirical energy functions. Calculations of aqueous hydration and binding thermodynamics for drug molecules (trimethoprim and other related compounds) to biological targets (the enzyme dihydrofolate reductase) will be presented. In these applications we will discuss differences in “binding modes” for different drugs and the ability of thermodynamic methods to predict these changes. Finally, comments will be made regarding the free energy derivative methods and coordinate-coupled free energy calculations.

Notes: In this paper we have addressed an important problem: how to develop a strategy for identification of the topological indices which are most important in establishing a model for structure-activity analysis. In particular we consider a rational selection of graph theoretical (topological) indices in QSAR. The approach is illustrated by the study of the toxicity of ethers on mice. The indices examined include the connectivity indices based on adjacency matrix, the conceptually related graph distance indices, and an information theoretic index based on partitioning of electrons in various domains. We have outlined the similarities and differences and discuss advantages and limitations among different approaches. Our emphasis is on the problem how to select in a rational way appropriate graph-theoretical descriptors and how to introduce higher “corrections” in order to improve derived correlation.

Notes: We investigate, as the function of the width of the quantum well, the effect of the nonparabolicity of the GaAs conduction band on the binding energy of a hydrogenic donor placed at off-center positions in a Ga0.7Al0.3As/GaAs/Ga0.7Al0.3As quantum well. We find, in agreement with Chaudhuri and Bajaj, who have investigated this effect for on-center donors, that consideration of the nonparabolicity of the conduction band of GaAs leads to an enhanced binding.

Notes: Using ab initio RHF-SCF-MO theory with the 3-21G basis set and geometry optimization with a gradient method, trans pentadienyl lithium and sodium have been shown to have a carbon backbone in which the middle carbon atom falls ca. 40° out of the plane of the other carbon atoms. The free anion was found to be planar. Optimization of the dilithium octateraene complex (C8H10Li2) with C2 symmetry gave a structure where the hydrocarbon backbone is distorted out of plane and folded about the lithium atoms. A partially optimized C8H10Li2 where the C and H atoms are constrained to remain in-plane lies ca. 0.6 eV above the folded structure. The consequences of the distortion are discussed for the applicability to longer polyenes and n-doped polyacetylene. In a vibrational analysis of C5H7Li and C5H7Na and of allyl Li and allyl Na, two very intense bands near 800 cm-1 appear which are not present in the flat, free allyl and pentadienyl anions. The similarity to the broad band at 800 cm-1 which appears in doped polyacetylene is discussed.

Notes: Third order diagonal self-energies are augmented with fourth order terms that are easily determined from by-products of a third order calculation. Comparisons are made with the outer valence approximation, a method for estimating fourth and higher order terms. The number of operations needed for all of these procedures is less than the number required for the limited two electron integral transformation. Improved one-electron reduced density matrices are another useful by-product of these calculations. The present methods are applied to calculating the ionization energies and dipole moments of the anions F-, OH-, NH-2, Cl-, SH-, PH2-, and CN-. The basis sets used in these calculations have been shown to be sufficiently flexible in a variety of calculations.

Notes: The manifold of one-particle operators has a rich group structure. It is the Lie algebra of the complex Lie group GL(2s,), (2s = dimension of one-particle spin orbital basis) realized as second-quantized operators acting in fermion fock space. This representation is reduced by the subspaces referring to N particles (N = 0, 1, 2,…). One can associate families of coherent states within each of these subspaces with real forms, Gr, of GL(2s,). These families have isotropy groups, Hr, which are associated with subgroups of these real forms (isotropy groups are the groups of transformations that leave a state invariant). The cosets GL(2s,)/Hr can be given an exponential parameterization that labels the coherent states. This label space is a complex vector space which is in correspondence with the nonlinear manifold of coherent states in the hilbert space HN. These complex variables can be made time dependent, and by utilizing the time-dependent variation principle one can obtain a nonlinear approximation to the time-dependent Schrödinger equation which has the form of classical equations of motion in a generalized phase space P = Grc/Hrc. This classical dynamics can be given a Hilbert space description, where the Hilbert space is a subspace of square integrable holomorphic functions f: ↦ P → and is isomorphic with HN. Different pairs {Gr,Hr} are associated with different families of coherent states. Some examples of these constructions are given, and the structure of the approximate time evolution is discussed and related to time-dependent approximation schemes and generalized random phase approximations (RPA).

Notes: A major impediment to achieving accurate solutions of the momentum-space Hartree-Fock equation in fully numerical form lies in the error caused by the truncation of momentum space. We use a coordinate transformation, which is characterized by P = tan(α/2), thus avoiding this truncation to achieve accurate solutions of the Hartree-Fock equation. Using this approach, we have re-examined the He model problem previously analyzed by Delhalle and Defranceschi [Intern. J. Quantum Chem. Symp. 21 425 (1987)]: The kinetic, nuclear attraction and Coulomb repulsion energies of the He atom have been evaluated using both conventional spherical polar momentum coordinates, (p, θ, ϕ) and the transformed coordinates, (α,θ,ϕ) in order to compare their accuracies. We have performed a number of fully numerical calculations on the H+2 ion in order to examine the influence of the number of points in the mesh on the accuracy of the computed total electronic energy of the diatomic molecule.

Notes: The technique of expanding Löwdin α-functions in a Taylor series has been further developed and applied to the problem of the electrostatic potential due to H2 with given 1s, 2s, 2p Slater-type orbitals. In contrast to other methods, our approach is completely analytic, and capable of arbitrary precision. The ultimate accuracy of our method is dependent upon the number of partial waves used; here by use of only 13 harmonics excellent results are achieved. Our methods are readily generalized to larger molecules.

Notes: The known bounds on the eigenvalues of 2-Fermion reduced density matrices may be improved by considering unitarily invariant properties of the associated natural geminals and of the system 1-Fermion reduced density matrix. The polynomial invariants are particularly important, since they may be introduced systematically according to the degree of the polynomials.

Notes: Vibrational frequencies and IR band intensities for 18 isotopomers of uracil, including deuterated 15N and 18O species, have been calculated using the scaled ab initio force field of Ref. 1. The results obtained are compared with available experimental data, and a number of refinements in former assignments are proposed. The good agreement between the calculated and experimental frequencies confirms the reliability of the scaled quantum mechanical-force field.

Notes: Phenyl acetylene complexes with HF, H2O, and NH3 are investigated with ab initio molecular orbital calculations using the 6-31G Gaussian basis set. HF is found to form a π complex, whereas H2O and NH3 form σ complexes. Observations of experimental spectroscopic shifts are rationalized.

Notes: The energy of an infinite, homogeneous electron gas is examined by second order perturbation theory using a Hartee-Fock rather than a noninteracting particle unperturbed state. The second order energy still diverges for small promotions k, albert than as ln|ln k| rather than as In k.

Notes: The ability to artificially structure new semiconductor materials on an atomic scale, using advanced crystal growth methods such as molecular beam epitaxy and metal organic chemical vapor deposition, has led recently to the observation of new physical phenomena as well as the creation of entirely new classes of devices based on band gap and wave function engineering. In these lectures an elementary introduction is given to the quantum aspects of these new structures.

Notes: In this note we discuss the variational forms of the energy derivatives and the method of obtaining them. We show that perturbation theory can be formulated in terms of stationary energy derivatives and that this formulation extends the idea of the Hylleraas functional to infinite order and excited states.

Notes: Molecular Orbital (MO) calculations by the MINDO/3 method on tumor-inhinbitory nitrosoureas is reported. Electronic structures for 18 chlorethyl nitrosoureas and 30 cyclohexyl nitrosoureas (CCNUS) are related to biological activity in the form of toxicity, therapeutic activity, and increase in life span and chemical reactivity in the form of alkylating and carbamoylating activity. Hydrophobicity, as measured by the logarithm of the partition coefficient (octan-1-o1/water), shows a parallelism with calculated bulk molecular properties. Mechanisms of alkylation and other reactions related to biological action are proposed and discussed.

Notes: The path of proton motion in protein bacteriorhodopsin is constructed: Tyr 43 → Tyr 26 → Asp 212 → Tyr 83 → Tyr 57 → Tyr 79 → Glu 204 → Tyr 64 → Glu 74. From the position of quantum theory the light-induced isomerization of retinal, the process carrying out the proton and throw-over from the inlet H-bond chain (Tyr 43 → Tyr 26 → Lys 216) to the outlet one (Lys 216 → Asp 212 → … → Glu 74) are investigated. The kinetics of the transition of the excitation from the π-electron subsystem to the vibrational one is studied; the function of the nonequilibrial excitation distribution of the collective intramolecular retinal vibrations is found. The mechanism of deprotonation of Schiff base (transmission of proton to the outlet channel) is considered. The correspondence between the theoretically estimated states and spectroscopically identified forms of bacteriorhodosin (initial form bR, intermediates J, K) is proposed.

Notes: Conformational preferences of model modified nucleic acid base N6-(N-alanylcarbonyl) adenine, ac6Ade, have been investigated using the quantum chemical PCILO (perturbative configuration interaction using localized orbitals) method. The multidimensional conformational space has been searched using selected grid points formed by combining the various torsion angles that take favored values derived from energy variation with respect to each torsion angle individually.The preferred molecular structure is stabilized by an intramolecular hydrogen bond from N(11)H of the amino acid to N(1) of the adenine. The observed crystal structure conformations for the naturally occurring, anticodon adjacent, threonyl analogs, tc6Ade, correspond to the predicted most stable conformation for the model modified base ac6Ade. Three stable, low energy conformations differing in the orientations of the carboxyl group and the amino acid side chain are predicted within 1 kcal/mol of the most stable structure. The possible bifurcated hydrogen bonding of N(11)H with N(1) and either of the carboxyl oxygens is of minor significance.The indicated orientational flexibility for the carboxyl group and the amino acid side chain may enable convenient probing of the molecular environment, in the vicinity of the anticodon in tRNA, by the amino acid substituent, with only modest changes in energy stabilization.

Notes: For Z particles moving independently in an unscreened Coulomb potential energy -Ze2/r, it is known that the total energy E = -(3/2)1/3Z7/3 in nonrelativistic theory as Z→∞. The generalization of this result to d dimensions in the same asymptotice limit is obtained as \documentclass{article}\pagestyle{empty}\begin{document}$$E(Z,d) = - \frac{{2\left({\frac{{d!}}{4}} \right)^{1 - (2/d)} }}{{(d - 1)!(d - 2)}}Z^{3 - (2/d)},$$\end{document} which includes the known result above for the three-dimensional case.

Notes: The pair correlation energies for some nl4f pairs of the ground state of the Yb atom are calculated for the first time. The partial wave (PW) increments to the second-order pair energies are generated using numerical first-order radial pair functions obtained as the solution of two-dimensional differential equations. The analysis of the PWs contributions shows the dominant role of the df, fg, and gh PWs for the 4d4f pair, of the pf and dg PWs for the 4p4f and 5p4f pairs, and of the sf and pg PWs for the 4s4f, 5s4f, and 6s4f pairs. A discussion of the similarities and differences of the structure of the correlation energy found in this paper with those calculated earlier for smaller atoms is given.

Notes: In a dissociation attachment experiment of water, three peaks were observed at 7,9, and 12 eV. The origin of the third peak has been believed to be 2B2. However, the calculated energy of this state is 0.6 eV higher than the experimental value. This discrepancy is quite large compared with the case of the lower two peaks. In this study we propose new candidates for resonant states responsible for the third peak. The configurations considered are (3a1)-1(3pa1)2, (3a1)-1(3pb1)2, (3a1)-1(3pb2)2, (3a1)-1(3pa1)1(3pb1)1, (3a1)-1(3pb2)1(3pa1)1, and (3a1)-1(3pb2)1(3pb1)1 which have the parent state (3a1)-1(3pa1)1, (3a1)-1(3pb1)1, or (3a1)-1(3pb2)1. The energy levels arising from these configurations are calculated by a method of configuration interaction. A Few resonance states, which could be responsible for the third peak, are found. New decay process of these states are proposed.

Notes: It is well known that positive and negative ions derived from the same alternant hydrocarbon have almost indistinguishable electron spectra. Effective charges, bond orders, and many other properties also correlate between the two systems. These «alternancy» properties are due to the particle-hole symmetry, and they can be generalized far beyond alternant hydrocarbons. In general, with each quantum system one can associate a «complementary» system. The eigenstates of the complementary system are related to the eigenstates of the original system in the same way as the anionic eigenstates of an alternant hydrocarbon are related to the cationic eigenstates of this hydrocarbon. In particular, the (N + k)-electron spectrum of the complementary system is the same, up to the uniform shift, as the (N - k)-electron spectrum of the original system; the effective charges in the complementary system are opposite to the corresponding effetive charges in the original system; bond orders in the two systems between vertices of the same and of the opposite parity are, respectively, opposite and the same, etc. Each particle-hole symmetry operator associates with the original system one such complementary system. There is hence a large number of the systems complementary to the same original system. In the PPP model and in various generalizations of this model, systems complementary to conjugated hydrocarbons are Möbius-type alterations of original hydrocarbons. In the case of conjugated heterocompounds, there is a formal replacement of all heteroatoms with some other heteroatoms, with or without an additional Möbius-type change. Such complementary systems may correspond to entirely different molecules, and they also may describe some transition states of these molecules.

Notes: A new semiempirical all-valence method, GRINDOL (Ghost and Rydberg INDO), based on the INDO approximation, is described. Linderberg-Seamans relation (extended to the d and Rydberg orbitals) for the resonance integrals and a new semitheoretical expression for the core-core repulsion term and energy correction including basis-set superposition error (intermolecular as well as intramolecular) has been applied. The proposed method enables calculation of ground and excited state properties. The ground state results (including intermolecular interactions) as well as the spectral properties are in reasonable agreement with relevant experimental (or ab initio) studies for isolated molecules, molecular complexes, and transition metal compounds. The method contains only one adjustable parameter, all two-center integrals and terms are only basis-set dependent. The one-center integrals are evaluated from the respective atomic terms.

Notes: The optical activity of oligopeptides in the conformation of the right-handed α-helix was calculated by the direct semiempirical quantum chemical CNDO/OPTIC method. The oligomers of glycine and alanine from dimer up to pentamer were considered. The comparison with results obtained using the model of interacting groups (MIG) based on the perturbation approach was carried out. The calculational results show that the circular dichroism (CD) of oligopeptide α-helices is essentially different from the CD of the peptide polymers in the same conformation. The comparison between results obtained by the CNDO/OPTIC method and by the MIG leads to doubts about the reliability of the use of the MIG to calculate rotatory strengths of nπ* transitions of oligopeptides in α-helix conformation.

Notes: Here is presented a method to determine the consistent ground state (CGS) which satisfies the so-called killer condition for the excitation operator. This method may be called an extended application of the procedure employed by Weiner and Goscinski in deriving the random phase approximation (RPA) vacuum.The RPA vacuum is derived by solving the recurrence formula of the configuration coefficients of a multiconfigurational state vector. The role of boson approximation to the primitive p-h excitation operator is also investigated and by using the present formalism the cluster-expansion-type CGS is derived as the RPA vacuum under the boson approximation.Inclusion of the effects of a higher RPA in the CGS leads to the simultaneous equations of the configuration coefficients of the CGS. In including the effect of the second RPA, only the symmetry-broken CGS can exist. When the third RPA effect is involved instead of the second RPA, there can be a symmetry-adapted CGS, in which the picture of electron pairs acquired in the standard RPA vacuum is modified. Thus the exact CGS vectors are analytically obtained in the case of simple model systems of two or four electrons.

Notes: On the basis of an analytical potential energy surface for the electronic ground state of the Na+ + H2 system reported recently, extensive trajectory calculations have been performed to study the collision dynamics of vibrationally inelastic processes at total energies up to ∼3 eV. Special attention is given to the relative efficiacy of translational and rotational energy, respectively, in promoting vibrational energy transfer. Vibrational transitions are found to be substantially enhanced by initial molecular rotation. Furthermore, the applicability of simple models is discussed.

Notes: Quantum mechanical models to treat long distance electron transfer are being developed. The model is based on the theory of R.A. Marcus. Our contribution is in the calculation of the electron coupling factor k. Estimations of the latter number, as well as the bond and solvent relaxation energies, λi and λo, respectively, are necessary to be able to calculate the rate constant for a reaction of the conductivity in an electric field. k may be approximately calculated from orbital energy differences at avoided crossings between orbitals localized in different parts of the system. A novel spectroscopic NDO method is suggested in which one may include any atom of the periodic table. Another problem discussed is the inclusion of electronic relaxation effects of the solvent or protein in the calculation. Applications are made to systems where metal ions are connected by organic bridges of different kinds such as dipyridine with coplanar and perpendicular pyridyl groups. As expected the electronic factor depends strongly on the conformation of the bridge. A strong conformational dependence is also obtained for a saturated bridge of the type NH2 · (CH2)n · NH2. In another study we use an α helix as a bridge between two metal ions. If one glycine in this α-helix is substituted by phenylalanine the electronic factor increases by factors of 1.5-10. It is suggested, however, that larger enhancement factors are possible if an aromatic group is positioned in a favorable way. The CNDO/S method is used to study the charge separation process in a bichromophoric molecule and in the reaction center (RC) of Rhodopseudomonas viridis. In those cases where the electronic coupling is large enough for the charge transfer states to be seen in the spectrum, the calculated results agree well with the experimental ones, but suggest a novel assignment. The CNDO/S results verify that electron transfer is possible through saturated spacers. In the special pair of RC the S1 state is calculated at approximately the correct position. Like the ground state, it has a delocalized character.

Notes: Nuclear configuration and molecular shape are two different concepts. The former refers to the geometry of the nuclear framework, whereas the shape of a molecule is better represented by a molecular envelope surface enclosing the nuclei. Nevertheless, there exist relationships between the molecular shape and the conformational arrangements of the nuclei. For certain changes in the nuclear geometry, the shape of a molecular surface does not change significantly, whereas for some others it may undergo essential topological changes. The characterization and interrelations of these changes provide a rigorous classification of reaction paths and conformational rearrangements for flexible molecules in terms of shape features. In this article we use a recently introduced topological tool to study molecular shape and molecular conformations: the “shape groups” (symmetry-independent homology groups) of a molecule. Van der Waals surfaces are considered as illustrative examples of molecular surfaces. We study the changes in the shape of van der Waals surfaces of hydroquinone, resorcinol, and catechol for a number of two-dimensional conformational problems, where the nonrigid conformational paths have been calculated at the STO-3G ab initio Hartree-Fock level.

Notes: Residues 23-26 (Gly-, Phe-, Phe-, Tyr) of the B-chain of insulin constitute a critical area of the receptor-binding region of the molecule. Three chemically distinct mutant insulins have recently been identified in patients with NIDDM, each involving substitution of either B24 of B25 phenylalanine. Two of the mutations have been unambiguously characterized: a B25 phenylalanine-to-leucine substitution [B25(Phe → Leu)], and the other, a B24 phenylalanine-to-serine [B24 (Phe → Ser)]. We have calculated the preferred conformations of normal and mutant insulins using a global optimization method developed by us earlier. The mutant insulins exhibit significant alterations in conformation and in the average distances between amino acid side-chains as compared to normal insulin. Therefore, the decreased binding affinity of mutant insulin could be either due to an alteration in the nature of the substituted residue (hydrophilic in place of hydrophobic) or to the alteration in one or more critical side-chain distances in the case of a hydrophobic to hydrophobic substitution.

Notes: Using molecular orbital methods, we propose various models of interactions between GABA or analogs (TACA, muscimol, isomuscimol) and an hypothetical receptor molecular fragment, a methylguanidinium ion. The respective geometries of the GABA-, TACA-, muscimol-, and isomuscimol-methylguanidinium ion complexes are optimized using the semi-empirical MNDO method. Stabilization energies of the complexes obtained by substraction of the heats of formation of the optimized complexes from those of the optimized isolated molecules differentiate the behavior of the anionic heads between the agonist and antagonist compounds. Affinity and stabilization are confirmed by computing ab initio STO-3G ionization potentials and interaction energies taking into account counterpoise corrections. Results show a decrease of the interaction energy from GABA and TACA (-54.9 and -49.4 kcal/mol) to isomuscimol (-35.6 kcal/mol), via muscimol (-46.0 kcal/mol). The low interaction energy of the 5-isoxazolols as isomuscimol compared to the 3-isoxazolols, as muscimol, may explain their antagonist character.

Notes: The chain-buildup method is presented for sampling the low energy conformations of polypeptides and enzyme-substrate complexes. This method circumvents the multiple minimum problem. It is shown that the method can compute structures in agreement with experiment.

Notes: Results are presented from Hartree-Fock-Slater (HFS) calculations on harmonic frequencies and force constants of H2O, H2S, NH3, PH3, CH4, SiH4, and C2H4. Both frequencies and force constants were calculated by a numerical (finite difference) differentiation of analytical energy gradients. It is shown by a comparison with experimental data and results from ab initio Hartree-Fock (HF) calculations that the HFS-method provides harmonic frequencies and force constants in at least as good agreement with experiment as the HF-scheme.