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Notes: The ground state energetics and equilibrium geometries of neutral and positively and negatively charged clusters of Li3, Li2H, Li2Na, Li2Mg, and Na2Li have been obtained from a self-consistent field-linear combination of atomic orbitals-molecular orbital calculations within the Hartree-Fock approximation. The correlation energies are included perturbatively using the Möller-Plesset scheme up to the fourth order. The geometries of all negatively charged clusters are found to be linear with bond lengths that are, in general, larger than their neutral or cationic counterparts. The adiabatic electron affinities and ionization potentials are calculated and compared with earlier theoretical results. The addition of an electron to the neutral cluster is found to stabilize the cluster further against dissociation. The spatial distribution of the electrons in these clusters is studied to determine the extent to which electrons added or taken out are localized in the clusters. Mulliken population analysis is also used to elaborate the charge state of the anionic and cationic clusters.

Notes: A simple proof is given for the thermodynamic inequality F - F0 - 〈H - H0〉0 〈 0 in the case when the two Hamiltonians H and H0 do not commute.

Notes: Electron correlation energies are calculated for a series of small molecules by fourth-order Møller-Plesset perturbation theory (MP4) and by quadratic configuration interaction methods. A method is suggested for partitioning the correlation contributions beyond fourth order that result from single, double, and triple substitutions. Detailed comparison of the results reveals that termination of the MP perturbation series at fourth order is inadequate for some electron-deficient species (inadequate treatment of double substitutions), for triply-bonded molecules (overestimation of the triples effect), and for some unsaturated radicals (poor treatment of single substitutions).

Notes: Some general properties of complex coefficient closed-shell molecular orbital calculations (CRHF) are examined. These types of calculations can be useful for describing systems where the restriction of real coefficients requires multideterminant wave functions. Examples of systems where CRHF calculations are useful are presented. These examples include singlet O2, singlet Cr2, and CH2+4.

Notes: Visualization techniques have proven extremely valuable for understanding the dictates controlling asymmetric organic reactions. A series of chemical reactivity models has been developed, which provide a convenient connection between the structural and reactivity aspects important in chemical systems. Structural information is conveyed through the use of shading, while reactivity information, evaluated at points located upon the structural model, is displayed coincident with structure using the color dimension hue. The utility of the resulting four-information-dimensional image can be appreciated by the speed at which all the information presented is assimilated and interpreted by the viewer. While having been demonstrated to be useful in understanding the dictates of asymmetric organic reactivity, the visualization techniques discussed here should be applicable to the description of problems in molecular interactions and structure-activity relationships in general.

Notes: The kinetics of gas-phase electron transfer reactions for a variety of metal-containing reactants have been studied by using Fourier transform ion cyclotron resonance mass spectrometry. Classes of ion/molecule processes studied include both self-exchange (thermoneutral) and exoergic cross reactions. The molecules investigated include metallocenes and octahedral coordination complexes of the transition elements. In a few cases, direct comparisons of condensed-phase and gas-phase reactivities can be made. The experiments with octahedral coordination complexes are the first studies of Werner-type metal complexes in electron-transfer reactions in the gas phase. Simple theoretical models involving unimolecular rate theory, classical reorganization barriers, and quantum mechanical approaches are used to rationalize the dependence of the overall rates of these reactions on the molecular properties of the reactants. In particular, the role of Franck-Condon factors in charge-transfer reactions is examined, and theoretically estimated factors are compared with experiment for a typical metallocene, ferrocene.

Notes: By calculations on CuCl2-4, CuBr2-4, and NiO10-6 clusters it is shown that a first-order configuration interaction (CI) calculation significantly improves the d-d and charge transfer (CT) spectra of ionic transition metal compounds. The first-order CI introduces delocalization (covalency) effects in the dn states, thus increasing the effective ligand-field splitting which is always underestimated at the Hartree-Fock (HF) level. It is demonstrated that this HF + first-order CI treatment is strongly related to a valence bond model. In this model the delocalization is introduced by explicit interactions with relaxed CT states. After account has been taken of the physically very different atomic correlation effects, a very good agreement with experimental d-d spectra is obtained, using only a small cluster. The effect of first-order CI on CT states is to account for hole localization and polarization effects which lead to reductions in the CT excitation energies in the order of 2-3 eV.

Notes: The reaction field (RF) model of solvent effects, implemented within the SCF-CNDO/2 scheme of calculation, has been applied to analyze the proton transfer in the NH3…HCOOH system in the presence of several polarizable media. The aim of such a study was to characterize the tatutomeric equilibrium between the neutral and zwiterionic forms of H-bonded amino acids in aprotic solvents. Qualitative results concerning the energetics of this equilbrium show the stabilization of two different H-bonded complexes, corresponding to two separate minima in the free energy surface. These well known double minima potentials are found to be dependent on both the intermolecular N—O distance and the strength of the reaction field. The behavior of this model is qualitatively consistent with experimental observations of nitrogen-substituted amino acids in solution: both show, for low values of the dielectric constant, tautomeric equilibria where the H-bonded complexes appear to be more stable than the corresponding monomeric forms. The charge transfer process associated with the proton migration along the H-bond is also discussed. It is found that the amount of charge transferred increases with the N—O distance and with the RF strength, In order to test the general approach and compare it with previous work, calculations on the real monomeric systems glycine, β-alanine, and γ-amino butyric acid was also performed.

Notes: Analytical intermolecular potentials for the Fe+-H2O and Feo-H2O systems have been determined from ab initio calculations. Interaction energies for a lot of points along the two potential energy surfaces were calculated using Huzinga's MINI-2 basis set. The results obtained were fitted to an analytical function containing 11 adjustable parameters that we have already used with success for the Fe2+-H2O system. The goodness of the generated intermolecular potentials is discussed.

Notes: The quasirelativistic CNDO/1 method has been in investigating the geometry, electronic structure, and redox stability of metal complexes. The systems of [Co(NH3)6]q and [MCl4]q, M being Ni, Pd, and Pt, have been studied. A modified Germer model of solvation has been implemented into the method. This yields reliable results on the redox stability of complexes in aqueous solutions. The calculated excitation energies resemble the electronic spectra of [MCl4]2- complexes.

Notes: 4-31G wave functions have been computed for five purines and pyrimidines. The calculated deformation densities have been partitioned into atomic fragments, which were integrated to yield atomic multipole moments. The transferability of atomic fragments between related molecules was verified by constructing model maps for uracil and guanine from appropriate fragments of cytosine and adenine. Model electrostatic potentials calculated from the moments of model atoms are similar to the corresponding 4-31G potentials. Comparison of 4-31G and 4-31G** deformation densities of cytosine provides simple rules for estimating the effects of polarization functions on the atomic multipole moments of most atom types occurring in the purines and pyrimidines. These rules were applied to the other molecules and yielded reasonable approximations for their molecular dipole moments. Substituting CH3 for H has little effect on the deformation density beyond the substitution center.

Notes: An adiabatic formalism in the degenerate or quasidegenerate subspaces, which does not depend on the particular form of the switching function g(α, t), is outlined. A general factorization theorem for the dynamic operator Sα(t, t0 | g) is proved. This theorem enables one to formulate the perturbation expansion for the effective Hamiltonian and the wave operator which is free from the adiabatic divergencies.

Notes: A formalism is developed for the construction of relativistic symmetry-adapted molecular basis functions under consideration of time reversal invariance. The theory is applicable to the finite double point groups Cn, Cnh, Sn, Cnv, Dn, Dnd, Dnh, T, Th, Td, O, and Oh. It is based on the LCAO method. A projection operator technique is employed to construct molecular symmetry orbitals from atomic orbitals. The search for linearly independent basis function is simplified by means of group theoretical considerations.

Notes: For the Hartree-Fock ground state of atomic two-electron systems, the variational function of Wilson and Silverstone, φ(r) = (a + kr)-1 exp(-kr) / (4π)1/2, can be optimized in two complementary ways. For small values of the atomic number Z, all intergrals have been calculated numerically and optimization can be performed accurately. However, as Z increases, loss of significant figures is increasingly detrimental to the optimization process. For sufficiently large values of Z, the integrals may be replaced by asymptotic expansions in terms of (2a)-. As a result of optimization, the parameters and expectation values can be given as expansions in terms of (32Z)-1/2. Both methods yield good results for Z ≈ 25, so that the whole range of Z can be treated accurately. The results have been compared with those derived from other analytical two-parameter functions. It is found that φ(r) is indeed the outstanding two-parameter function, at least for small and intermediate values of Z.

Notes: Extended Hückel molecular orbital calculations have been made for the silver adatom-pyridine complex in order to reveal the very chemical nature of the surface-enhanced Raman scattering. The variation of the behaviors of the bond orders and charge densities as functions of the Ag—N distance and the net charge on the Ag atom, which is applied voltage dependent, is demonstrated. The calculated optical transition of the system can accommodate the experimental observation that as the wavelength of the exciting line shifts from 4880 to 6328 Å, the surface-enhanced Raman signal is enhanced more. Most interesting is the fact that the calculations reproduce well the experimental observation that there is an applied voltage on the electrode at which the surface-enhanced Raman signal is a maximum. The calculations show that the charge transfer enhanced mechanism is mostly due to the transfer of electrons from the silver atom to the pyridine molecule. Several useful overlap integrals involving d orbitals not available in the literature before are listed in the appendices for convenient reference.

Notes: In this paper, an SPG function, which is associated with an extreme point of the set of N-representable second-order reduced density matrices, is used to perform the calculation of the ground state energy of LiH with the variation of internuclear separation. The result of our calculation essentially is in accordance with that of AGP function.

Notes: A Fifth-order constant denominator perturbation treatment of all single and double excitations occuring in the third-order perturbation wave function is presented for the perturbation configuration interaction using localized orbitals (PCILO) method. Contributions from triple and quadruple excitations which decay back to singles and doubles at third order are automatically included in this theory. This method is computationally very fast, with an execution speed proportional to N3, Where N is the number of orbitals present. A [2,1] Padé approximate involving only singles and doubles contributions through to fifth order is shown to be remarkably accurate.

Notes: Owing to an error in his determination of the repulsion integral and the kinetic energy. Hall's results [1] for the ground state of atomic two-electron systems are wrong. Here these results have been corrected. For Z ≤ 5, the results have been obtained by determining the pertinent integrals numerically: but for Z ≥ 5, these can be found sufficiently accurately from Z expansions.

Notes: By means of the SPG function which is associated with an extreme point of the set of N-representable second-order reduced density matrices, an attempt is made to perform the calculations of the ground states of some atoms with four electrons such as Be. The results show that the SPG function is as suitable as the well-known AGP function for approximating the ground states of atoms and molecules.

Notes: We have analyzed the ability of a tertiary amide group to activate an ortho position on aromatic system toward an electrophilic attack using an ab initio SCF molecular orbital method. The molecular electrostatic potential was used to analyze the electronic nature of the ortho-lithiated intermediate complex and possible sites for electrophilic attack.

Notes: An approach which considers both nuclear and electronic motions for molecular systems is derived using algebraic techniques within the vector model. The dynamical symmetries of the Hamiltonian thus derived are examined and shown to account for the analytic diagonalizability of the LEPS level potential function for molecular systems. The initial application is to the H3 collision system, demonstrating the ability of the model to treat systems without bound states. Extensions to more complicated systems are also considered, and these efforts allow for the determination of the algebraic source of the coupling in the “diatomics in molecules” (DIM) potential surface. In general, these terms in the DIM approach preclude analytical diagonalization of the Hamiltonian, which may also be understood in terms of the dynamic symmetry of the corresponding algebraic description.

Notes: The quantity ∊ = (Φ||(H - E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(∊/∊r), where ∊r corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.

Notes: Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater-Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom-atom pair potentials in the form of the Lennard-Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol.A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.

Notes: In reexamining the thermodynamic parameters of the protein refolding of ribonuclease systems over the temperature range of 220-360° K, based on the Nernst heat theorem, we found that at the temperature 〈Ts〉, the thermodynamic quantities ΔG0〈Ts〉 and ΔH0〈Ts〉 are of the same magnitude, while TΔS0〈Ts〉 approaches zero. Based on the Planck-Benzinger thermal work function, ΔW0(T) = ΔH0(T0) - ΔG0(T). Therefore, ΔH0(T0) = ΔW0〈Ts〉 + ΔG0〈Ts〉 at 〈Ts〉. Within the limits of statistical error, plotted values for ΔH0(T0) at 0° K and 〈Ts〉 are equivalent for each of the three ribonuclease systems we examined. Error-minimizing statistical simulation suggests that a reasonable a priori estimation of ΔH0(T0) can be made at 〈Ts〉, provided that the expansion coefficient of the Planck-Benzinger thermal work function is accurately determined. Values for ΔH0(T0) at 〈Ts〉 were determined to be 34.05 ± 1.30 and 19.49 ±0.42 kcal/mol in 20-S1 [I] and 14-S1 [II] systems, respectively. The value for ΔH0〈T0〉 at 〈Ts〉 in the ribonuclease A conformational transition as a function of pH was determined to be 59.0 kcal/mol. The magnitude of ΔH0(T0) values for 20-S1 [I] and 14-S1 [II] is an effective measure of the ease with which these molecules can be refolded to resemble the native protein structure, with greatest ease of folding at the lowest chemical bond energy. The Planck-Benzinger thermal work function, ΔW0(T), is an effective measure of the energy potentially available for any interaction to take place. ΔH0(T0), a temperature-invariant quantity, is a primary source of the chemical bond energy essential for any reaction to proceed in a biological system, and is indispensable in any consideration of macromolecular interaction. Certainly this function has yet to receive sufficient recognition in the field of thermodynamics. After applying it in studies of ribonuclease refolding and protein-protein interaction, we predict that this new state function will eventually supplant the Gibbs-Helmholtz expression in thermodynamic analysis.

Notes: We have investigated the impurity states in direct gap doped semiconductors via the alternant molecular orbital method with application to n-CdS. Good agreement compared with available experimental data and other calculations for resistivity and metal-nonmetal transition critical point are found. For spin susceptibility we have done an extensive calculation with and without correlation or disorder effects. Such calculation suggests experiments on concentration-dependent susceptibility in n-CdS.

Notes: The possibility of obtaining itinerant antiferromagnetism in the new high Tc superconductors is explored by means of self-consistent spin-polarized calculations for the nonsuperconductor YBa2Cu3O6, which is related to the 90K superconductor YBa2Cu3O7-δ and for models of doped copper oxide planes. Investigation of both the ferromagnetic and antiferromagnetic ground states reveals the former to be unstable and the latter to be stable. Our calculations show that for metastable antiferromagnetic ordering of copper magnetic moments in the CuO2 plane, there is a Peirels-type antiferromagnetic gap around the Fermi energy, and YBa2Cu3O6, in particular, is semiconducting as observed experimentally. Comparison is made with recent neutron diffraction studies.

Notes: An approximate relation between the static-density response function and the fukui function is used to develop a perturbation approach within the framework of density functional theory. It is shown that the approximate relation describes correctly the equivalence between the representation of the energy in terms of the electronic density and the external potential, and the representation in terms of the number of electrons and the external potential. The perturbation scheme is applied to calculate the first and second order corrections to the energy of a two-electron atom. The results show that the present approach incorporates part of the correlation energy.

Notes: β-Endorphins are 31 amino acid endogenous opioid peptides with high receptor affinity and antinociceptive activity. Because of their importance as neurohormones and the significant experimental effort that has been made to understand their structure activity profiles, we have begun to develop procedures that could be useful first to identify low-energy conformers of β-endorphins and ultimately their bioactive form. In the initial studies reported here, we have identified plausible initial structures of the full peptide by calculating and comparing the conformational preference of all possible extended tetrapeptide fragments of β-endorphin starting from each of the first 28 residues. Comparisons of fragment energies suggested two types of compact folded β-endorphin conformers were plausible: a helix-turn-helix and an antiparallel β-sheet conformer. These structures, as well as an extended α-helical and β-strand conformer, were assembled and total geometry optimization performed using the empirical-energy-based program AMBER. The results yield an α-helical structure as the lowest energy form consistent with recently reported NMR studies of β-endorphin. The two more compact folded structures obtained, however, are reasonable starting conformations for further planned molecular dynamics simulation studies and could yield competing low-energy structures as candidates for the bioactive form of these peptides.

Notes: The need to perform a numerical integration of the exchange-correlation functional because of its non-analyticity severely complicates the accurate application of local-density functional methods to molecules and clusters. The optimal choice of grid points for this integration and the estimation of the error made by the choice are subtle considerations. In particular, because the position and/or weighting of each grid point must change when the nuclear positions change, these errors are most noticeable when different geometries are compared. We have determined a method of grid point selection and weighting that reduces these errors. We have also determined a simple method of estimating the extent of the error made in the particular density of points used for the grid. These results are illustrated for a selection of small molecules.

Notes: All bicyclo[p.q.0] conjugated hydrocarbons are found to fall into ten homolog classes each characterized by the numbers of nonbonding, bonding, and antibonding molecular-orbitals of its first prototype and by the prototype itself. The energy level patterns are obtained by the new “structural covariance” pictorial rules directly from structural formulas. The HOMO-LUMO types, aromaticity or three types of nonaromatic behavior, and reactivities towards nucleophiles or electrophiles thereby also result.

Notes: Ab initio molecular orbital calculations were performed on a series of phosphazene trimer molecules to elucidate the electronic structure of these systems. The role of the d orbitals was analyzed from comparison of the molecular orbital contour calculations performed both with and without d orbitals in a split valence basis set description. The results indicate that, although the major geometric aspects of these systems can be described without invoking the use of d orbitals, these orbitals are essential to properly describe the electronic structure. The d orbital involvement in out-of-plane π bonding contains elements of both the classical Craig, Paddock, and Mitchell [1-3] and Dewar et al. [4] bonding schemes; the d orbital effects on in-plane bonding modes are also substantial. The charge distribution in these systems is best described as a zwitterionic form, because a significant amount of charge accumulates on the ring nitrogens.

Notes: The titled isomerization has been studied at the HF/3-21G level. The changes in thermodynamic functions, equilibrium constant K(T), conversion efficiency C(T), and the rate constant k(T) for the isomerization have been calculated using our energies of the reactant (R), transition state (TS), and product (P), their harmonic vibrational frequencies, and the classical and corrected barrier (by vibrational zero-point energies). In the range of temperature, 300-1200K, ΔH 〈 0, ΔS 〉 0 and ΔG 〈 0; i.e., it is exothermic, increasing in the entropy, and spontaneous reaction. ΔS≠ 〈 0, log A is about 12.0 ±0.15 (s-1), but the k(T) is from 2.627 × 10(-33) to 6.933 × 10(8) (5-1); i.e., it passes through a tight TS, the A factor changes little, but the rate constant varies rapidly with the temperature. These results agree with the fact that the isomerization occurs readily at high temperature. Furthermore, Newman's mechanism, 2SiH2 → (H2SiSiH2)* → (HSiSiH3)* → Si2H2 + H2, is supported. Similarly, the isomerization, HDSiSiH2 → HSiSiDH2, is also studied.

Notes: A generalization of the Fourier convolution theorem is used to iterate the many-particle Schrödinger equation in momentum space. The method is applied using hyperspherical coordinates, with many-dimensional hydrogenlike wave functions as the starting point for iteration. The problem of angular integration is converted into a problem of differentiation by means of the theory of harmonic polynomials.

Notes: A complete active space MCSCF (multi-configuration self-consistent field) scheme (CASSCF) using relativistic effective potentials followed by configuration interaction and relativistic CI calculations provides a very good description of the electronic states and potential energy surfaces of transition metal dihydrides. Such calculations are of considerable value not only in our understanding of the transition metal-hydrogen bonding but also in the prediction of the barrier to insert the metal atom into the H2 bond. All-electron CASSCF/CI calculations are carried out on twelve electronic states of CoH2. Comparable RECP-CASSCF/CI calculations are also carried out to show that the RECP-CASSCF/CI calculations provide an accurate method for the investigation of transition metal compounds. The general method of RECP-CASSCF/CI calculations for molecules containing heavy atoms is described. The calculations on CoH2 are compared with similar calculations on ScH2, YH2, PtH2, and PdH2. A critical comparison of all these transition metal hydrides reveals that in general the low-spin excited metal atom inserts into H2 spontaneously while the high spin ground state atom has to surmount a large barrier.

Notes: The potential energy curve for the metastable 4IIg state of the He-2 anion is obtained from fully numerical Hartree-Fock (HF) calculations and is used to evaluate the spectroscopic constants. The resonant 4Σ+g state of He-2 and the excited a3Σ+u state of He2 are also investigated. The 〈R2〉 expectation value calculated for numerical orbitals indicates a diffuse character of the anion wave functions.

Notes: Since it became possible to study experimentally the evolution of a metal and the transition from atomic and molecular to surface and bulk properties, the study of clusters, especially metal clusters due to their role in heterogeneous catalysis, represents a highly active research area. On the other hand, clusters serve also as very useful models in solid state physics to investigate impurity, surface, and interface problems. Both cluster aspects will be discussed in addition to the role of cluster calculations in aperiodic polymer and band structure computations. We also report results of Li-cluster studies. Correlation effects, calculated with the coupled cluster method, are discussed in connection with the onset of Pierls' distortion in Li-rings. Finally, it is demonstrated how the cluster model is used to investigate polymer-metal surface interactions and how these interactions influence and change the polymer conformation.

Notes: It is shown by using the Z-1 perturbation expansion in the limit of large nuclear charge, that the leading term in the chemical potential of neutral atoms is given by the summation of two oscillatory terms that have an amplitude proportional to Z-1/3, are periodic in Z1/3, and have slightly different phases. It is further shown that for atoms in the periodic table the position of the point where the derivative of the energy with respect to the number of electrons becomes zero will have a strong influence on the phases of the oscillations but not on their amplitudes.

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.