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Notes: This paper serves a twofold purpose. First, Löwdin's inner projection in both nonperturbative and perturbative forms is applied to the quartic anharmonic oscillator. Inner projection with perturbation theory yields rational approximations to Brillouin-Wigner-type perturbation expansions. These lower bounds are compared with [N - 1, N] Padé approximants to the Rayleigh-Schrödinger perturbation series for this problem. These Padés are also expressible as the even convergents, w2N, of a Stieltjes-type continued fraction. The latter representation has certain advantages with respect to its Padé counterpart. Inner projection without perturbation theory provides significantly better results than the perturbative version. The application of inner projection techniques to a perturbed hydrogen atom is not straightforward. The usual problems associated with the continuum spectrum of hydrogen are present. By means of a nonunitary “tilting” transformation associated with the Lie group SO(4, 2), these problems may be bypassed. In the SO(4, 2)-reformulated eigenvalue problem, a reinterpretation of the basic variables, as developed by Silverstone and Moats, yields a new Hamiltonian that permits direct use of the inner projection method. This method has been applied to the ground state of the hydrogen atom in a magnetic field, using both four- and eight-dimensional basis manifolds. This represents the first application of inner projection to this problem.

Notes: A comparative study of quasirelativistic equations used in atomic structure calculations has been performed. A uniform derivation of all the equations is presented, and some of their specific features are discussed in detail. Electron density distributions, orbital energies, and expectation values of rn obtained with different methods are compared with the ones resulting from the Schrödinger and Dirac equations. The most accurate are found to be the equations of Wood and Boring and of Barthelat, Pelissier, and Durand. (They reproduce almost exactly the Dirac electron densities and expectation values.) The simplest, though least accurate, equation is proposed by us. It gives the relativistic energy corrections with about 6% accuracy and retains exactly the form of the nonrelativistic Schródinger equation. Consequently, its application in analytical SCF-CI calculations does not require any additional integral calculation.

Notes: The representation matrices of the unitary group generators Ek1 are equivalent to the representation matrices of cyclic permutations (k, k ± l, …, l ∓ 1, l). A method is presented for simultaneous computation of matrices corresponding to all different generators at a cost of less than one multiplication per nonzero element. The number of operations necessary for calculation of individual matrices for single generators or for products of two generators is at most proportional to the number of matrix elements of the final matrix. This approach eliminates the need to store the representation matrices in CI calculations.

Notes: Ab initio molecular orbital calculations using a 3-21G basis set have been used to optimize geometries for pyrrole, CH3(X)CCH2, CH3(H)CCHX (both cis and trans), c-C3H5X, and CH2CHCH2X, where X is CN and NC. In all the alkenyl derivatives methyl groups are found to adopt the conformation in which the methyl hydrogen eclipses the double bond. 6-31G*∥3-21G level calculations show the alkenyl cyanides to be of similar energy to pyrrole, but the isocyanides are ∼20 kcal mol-1 higher in energy. For both substituents the cyclopropyl derivatives are higher in energy by ∼10 kcal mol-1. At the 6-31G* level ring strain is 27.7 kcal mol-1 for the cyanide and 30.6 kcal mol-1 for the isocyanide. Data on the relative energies of RCN and RNC are compared when R is (i) a saturated hydrocarbon, (ii) an unsaturated hydrocarbon, (iii) an α-carbenium ion, (iv) an allyl cation, and (v) an α-carbanion.

Notes: The electronic absorption spectra of some benzohydroxamic acids have been analyzed and interpreted using the results of molecular-orbital calculations. Charge density distributions, dipole moments, and the extent of delocalization of the MOS were used to interpret the observed solvent effects. Comparison between the spectra of benzohydroxamic acids and that of simple amides led to conclusions regarding the structural differences between the two classes of compounds.

Notes: A semianalytic scheme is proposed for the evaluation of Brillouin zone (BZ) double integrals such as are met in the evaluation of Compton profiles (CPS) and the angular distribution of annihilation photons (ADAPS) obtained in single-slit positron annihilation experiments. The difficulty that arises due to the jump discontinuities in the momentum density at the generalized Fermi surfaces (FS +HMC), pF = kF + g, where kF is the electron Fermi momentum vector and g is a reciprocal lattice vector, is addressed.

Notes: Following a paper drawing up a matrix form of the time-dependent Hartree-Fock equations which allow the calculation of the nth harmonic generation, we establish the matrix form of the hyperpolarizability tensor. In case of linear polarization, we show that, if the ground-state orbitals are real, so are the perturbed ones. This involves an easy expression of the hyperpolarizability tensor.

Notes: Fick's law of diffusion has been generalized to include kinetic processes, the transport term of the Boltzmann equation, and nonlocal interaction processes. It is shown that the collision interaction term can be obtained by the introduction of a quantum stochastic potential equation. Some approximations of a nonlocal Boltzmann equation can be solved exactly. The solutions can be applied to problems of molecular pattern in biology.

Notes: Hyperspherical coordinates and a generator coordinate representation are employed to find a simple form of the kinetic energy for a general three-particle problem. An expression is developed for the determination of adiabatic hyperangular states in a local potential using the finite element method.

Notes: The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.

Notes: Mulliken's atomic charges (MC) and potential derived (PD) point charges obtained from STO-3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogenbonded complexes. The results of the above-mentioned models are compared with the more accurate results of segmental multipole moment (SMM) expansion, and it is shown that the PD model is superior to the Mc model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6-31G and 6-31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6-31G** PD charges are compared with the 6-31G** SCF interaction energies available for the nine hydrogen-bonded dimers of ammonia, water, and hydrogen fluoride and a good con-elation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point-charge model. The electrostatic interaction energies obtained using STO-3G PD model are shown to be well correlated to the results of 6-31G and 6-31G** PD models.

Notes: Hartree-Fock energies are reported for about 20 low-lying quartet states of B III. A comparison with experimental transition wavelengths shows that Hartree-Fock energies can be helpful to rule out erroneous assignments but that, in general, their accuracy is insufficient for definite confirmation of proposed assignments.

Notes: Simons has previously derived a simple formula for the linewidth Γ of a resonance state in the continuum from real stabilization graphs under the assumption that the energy curves vary almost linearly near the points of avoided crossing. This formula is now rederived without this restricting assumption under the condition that Γ is still small.

Notes: The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree-Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rn of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.

Notes: A new computation procedure for direct calculation of the density matrix in the LCAO version of the restricted Hartree-Fock-Roothaan open-shell theory is analyzed. It is proved that the procedure is quadratically convergent and stable to the round-off errors independently of the Fock operator spectrum. The dependence of the limit matrix of the initial matrix is examined.

Notes: A consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N-particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.

Notes: The definition of a molecular property as a derivative of the electronic energy with respect to one or more applied perturbations is reviewed. The explicit enumeration of terms entering the derivative formulas is performed by considering in turn the various parameter spaces on which the energy and wave function depend. After deriving general expressions for first, second, and third derivatives for different types of perturbation, the parameter spaces involved in MCSCF and CI cases are identified and used to obtain expressions for the first and second derivatives. An example of an MCSCF third derivative is also given. In addition, the various equation systems defining the perturbed wave functions in each order are derived. Some attention is given to the efficient computer implementation of derivative calculations, and the present work is compared with that of other authors.

Notes: Ab initio MODPOT/VRDDO/MERGE calculations have been carried out for all the different position isomers of nitrocubane from mononitrocubane through octanitrocubane for a perfect symmetrical cubic cubane skeleton and for mononitrocubane through septanitrocubane for the almost cubic experimentally determined cubane skeleton. These calculations were carried out with our own rapid efficient ab initio programs which also incorporate a number of desirable computational strategies for calculations on large molecules. The skeletal total overlap population of the cubane skeleton (a theoretical index we showed years ago to be sensitive and predictive of stability of energetic molecular frameworks) indicates that successive nitration seems to increase the stability of the cubane skeleton. Successive nitration also seems to increase the total overlap population of the C—NO2 bond. There are subtle differences depending on the exact positional isomer for a constant number of nitro groups - but the overall trend is definite. We have also generated electrostatic molecular potential contour (EMPC) maps around these nitrocubanes. These maps are indicative of preferred positions of electrophilic and nucleophilic attack as a function of the number of nitro groups or their positions. These EMPC maps can also indicate, to a first approximation, a limit on how close these molecules may be able to approach each other in a crystal.

Notes: The well known one-to-one correspondence between the eigenstates of the total spin for a system of spin-½ particles and irreducible representations of the symmetric group with up to two rows in the Young shape is the basis of interesting formal developments in quantum chemistry and in the theory of magnetism. As an explicit manifestation of this correspondence the class operators of the symmetric group are demonstrated to be expressible in terms of the total spin operator. This correspondence does not hold for higher elementary spins. The extension to arbitrary spin is investigated using Schrödinger's generalization of the Dirac identity, which expresses the transpositions in terms of two-particle spin operators. It is shown that additional operators, which for σ = ½ reduce to the total spin operator, are needed for a complete classification. Some aspects of the formalism are developed in detail for σ = 1. In this case a classification identical with that provided by the irreducible representations of the symmetric group is obtained in terms of the eigenstates of two commuting operators, one of which is the total spin operator.

Notes: Based on the literature values, the pK1 and pK2 for pyrazine and its six methyl derivatives, the correlation with electron density on the nitrogen atoms N1 and N4 was found. The effect of methyl group was proved to be additive. The total electron density, π-electron density, and dipole moments for compounds under study were determined by the CNDO/2-MO method.

Notes: We have studied the effect of Hubbard interaction on solitonic excitations in the polymer trans-polyacetylene. These excitations are modeled using the Su, Schrieffer, and Heeger (SSH) Hamiltonian. Within this framework, we have calculated the full configuration interaction and restricted Hartree-Fock energies of solitonic excitations in trans-polyacetylene chains with 4-10 carbon atoms. These results are extrapolated to longer chains, and it is shown that the correlation energy for these chains approaches 3%. Thus, our calculations provide a justification, hitherto absent, of the accuracy of the Hartree-Fock calculations reported in the literature.

Notes: The collisional exchange of energy between He atoms and a strongly polar diatomic, the LiH target, has been studied theoretically over a range of relative energies that had been previously sampled by experiments with molecular beams. The relative importance of the rotational and/or vibrational channels is examined by studying in detail the effect of the interaction via a model potential coupling parameter. The different behavior exhibited by differential cross sections (total and partial inelastic) is also analyzed in terms of the strength and shape of the interaction anisotropy.

Notes: Model ring systems 2′-deoxy-2′-fluororibofuranose and deoxyribofuranose have been investigated using ab initio calculations with the 3-21G basis set. The energy barrier to pseudorotation between the N and S states has been evaluated for the three preferred orientations of the (3′)-OH group. Positions of the energy minima and the transition state have been optimized with respect to the (3′)-OH orientation. The barrier to pseudorotation of 2′-deoxy-2′-fluorofuranose is high and asymmetrical (ΔEN→S ≈ 20, ΔEN←S ≈ 8 kJ/mol), whereas the barrier of 2′-deoxyfuranose is lower and almost symmetrical (ΔE ≈ 11-12 kJ/mol). The results obtained show that the preferred configuration of the 2′-deoxy-2′-fluororibo-furanose (N state) is stabilized by an internal O(3′)-H…F interaction in accord with the crystallo-graphic data.

Notes: The large vibrational inelasticity observed in proton-O2 scattering at collision energies of ∼10.0 eV and for various angular distributions below the rainbow region is examined in terms of SCF adiabatic potential energy surfaces which exhibit strong O2+ “character” within a specific range of relative distances between colliding partners. The possibility for this O2 distortion during encounters with protons to be responsible for the unusually large inelasticity is discussed and the time factors that are likely to play an important role during the dynamics are also considered and analyzed.

Notes: Atom-metal surface overlap integrals are of utmost importance in surface energy calculations. Direct numerical evaluation of these triple integrals can be very time-consuming. However, we have developed an exact algebraic expression, where formulas for the coefficients are given for both the general case and the special case where the parallel wave vector is zero. Some numerical examples of the overlap for H on Al are given.

Notes: A multiconfigurational variation of moments (MCM) is presented to determine correlated orbital energies. Appropriate multiconfigurational one-particle operators are introduced starting for closed-shell systems from the restricted Hartree-Fock (RHF) scheme and for open-shell system from the unrestricted Hartree-Fock (UHF) scheme. The advantage of these operators is the linear form of the correlation energy in the configuration interaction (CI) coefficients. They obey HF analogous pseudoeigenvalue equations and are therefore a generalization of the HF operator. In principle, the scheme can be extended to a multiconfiguration self-consistent field (MCSCF) procedure for moments. In contrast to the SCF formalism they allow an orbital description of degeneracy and quasidegeneracy of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbital. With these operators, funnels of thermally forbidden Woodward-Hoffman reactions, as well as dissociations, can be described in a physically meaningful fashion by orbitalcorrelation diagrams.

Notes: Molecular-orbital calculations, using the INDO procedures, were carried out on the tautomers of 1, 2, 4-triazole and its benzo-derivative as well as on 1, 2, 5-oxadiazole and its benzo-derivative. Calculations of the transition energy as well as the dipole moment helped to predict the predominant tautomer in an equilibrium mixture. The correspondence between the calculated and observed data is satisfactory. The results of calculations indicated some differences in the electronic structures of the tautomers of a compound.

Notes: Ab initio configuration interaction calculations are reported on the lowest quintet, triplet, and singlet states of FeII(P). Due to the large number of states found, a catalog of the low-lying states is presented. Novel triplet and quintet charge-transfer states are reported as low as 1.3 eV. These states are d5 (S = 5/2) on the iron low-spin-coupled to the radical anion excited porphyrin ring (S = 1/2 or 3/2). Oscillator strengths originating from each of three low-energy triplet states are reported.

Notes: Some accurate results on the length dependence of the excitation energies from the ground state to ionic excited states in the Hubbard model of linear polyenes are obtained based on the method of Lieb and Wu. To this end, it is first shown that singly ionic excited states with “plus” alternancy symmetry in the Hubbard model are described by the wave functions in which the two electron operator [∑n=1N(-)nCnα+Cnβ+] is acted on (N - 2)-electron covalent eigenstates. Then by solving the Lieb-Wu equations the exact excitation energies of the lowest ionic state, which corresponds to the E1+ state in this model, are calculated for systems with up to 50 electrons. The result, together with a correction for the end effect, indicates that the excitation energies do not decrease as 1/N but converge to the limiting value more rapidly when the number of electrons N becomes large.

Notes: A new procedure for construction of spin-adapted DIM bases is described. The procedure is based on the direct diagonalization approach, is quite general, and seems to be especially suited for computer implementation. The structure of the bases obtained by the procedure appears to be favorable for performing symmetry operations necessary in setting up the Hamiltonian matrices in semiempirical applications of the DIM method.

Notes: The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO44-, PO43-, SO42-, ClO4-, and decrease in order of GeO44-, AsO43-, SeO42-, BrO4-. The bond strengths are also obtained for these ions. The hybrid Orbital of VO43-, CrO42-, and MnO4- are of the type d3s as the result of calculation.

Notes: It is noticed that inclusion of an electrostatic term in the molecular-mechanical treatment of hydrocarbons would compel the nonbonding parameters of different force fields to become more alike than they are at present. Apart from removing the discontinuity in passing from the calculation of an unfunctionalized parent compound to the calculation of its functionalized derivatives, it is expected that the inclusion would improve results for the hydrocarbons themselves.

Notes: We present energy component analysis calculations on alkali atom (Li,Na) hydride (H2O,NH3,H2S) interactions and compare these with corresponding (Li+ … NH3) cation … hydride interactions. In contrast to cation hydride interactions, the neutral atom-hydride interactions are shown to involve considerable contributions from all energy components.

Notes: The values of log10 P (partition coefficient, in octanol/water) were calculated for about 200 organic molecules of diverse structures and functionalities. The method involves a simple procedure and appears accurate enough for semiquantitative applications. Further, this method of calculating log10 P values was shown to be successful in providing a better quantitative structure activity relationship (QSAR) than the Hansch-type approach in the study of inhibitory activity of substituted phenols on Bacillus Subtilis spore germination.

Notes: A computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules. The program requires as input a grid of calculated energies in the vicinity of a stationary point. This grid is fit, in a least squares sense, to a polynomial function of the internal coordinates. This analytic representation of the energy surface is employed in a normal mode analysis, and the energy is reexpanded as a polynominal function of the normal mode coordinates (expressed as vectors in the mass-weighted atomic Cartesian coordinate space). The resulting coefficients are used in a second-order perturbation theory analysis to obtain the vibrational anharmonicity constants. Also reported is an application of this program to formaldehyde employing ab initio, RHF, MP2, MP3, and RHF-CI calculations. The spectroscopic constants obtained for H2CO are in good agreement with experimentally derived values recently reported by Reisner.

Notes: α↑HF and α↓HF are derived for use in spin polarized Hartree-Fock-Slater programs. They are assumed to depend only on the number of up and down spin electrons in the atom. The calculated eigenvalues show a slight improvement only for carbon, nitrogen, and oxygen.

Notes: Conformational energy profiles were calculated for τ1, the C—C—C=O torsion, and τ2, the C—C—C—C torsion, of methyl butanoate, using Pulay's ab initio gradient procedure at the 4-21G level with geometry optimization at each point. In addition, the structures of seven conformations were fully relaxed, including the energy minima (τ1, τ2) = (0, -60), (0, 180), (120, 180), (120, -60), and the maxima (0, 0), (180, 180), and (60, -60). The calculated geometries confirm the previously formulated rule that, in saturated hydrocarbons, a C—H bond trans to a C—C bond (C—Hs) is consistently shorter than a C—H bond (C—Ha) trans to another C—H bond. Specifically, for X—C(α) (= O)—C(β)—C(γ)—C(δ) systems, the following rules can be formulated, incorporating results from previous studies of butanal, butanoic acid, and 2-pentanone: (1) C(δ)—Hs 〈 C(δ)—Ha in all the conformers in which the δ-methyl group is remote from the ester group; whereas, in all the conformers in which nonbonded interactions are possible between the C(δ)-methyl and the ester groups, the bonding pattern is affected by a C—H⃛O=C interaction. (2) In the most stable conformers, (0, 60), C(β)—Ha 〈 C(β)—Hs, and C(γ)—Ha 〈 C(γ)—Hs, regardless of X. (3) The average C—C bonds in the τ2 = 180° conformers are consistently shorter than those with τ2 = 60° (compared at τ1 constant). In the most stable conformations (τ1 = 0°, τ2 = 60° or 180°), the bonding sequence is consistently C(α)—C(β) 〈 C(β)—C(γ) 〈 C(γ)—C(δ); whereas, when τ1 = 120°, C(α)—C(β) 〈 C(β)—C(γ) 〉 C(γ)—C(δ).

Notes: If numerical configuration selection procedures are used in MRDCI calculations, the full MRDCI energy may be estimated by adding energy corrections obtained by perturbation theory. Accurate results may then be obtained by including all selected CFs in the zero-order function instead of only the reference CFs.

Notes: Repulsion and dispersion parameters for alkali-metal halide diatomic molecules were computed by ionic Rittner and truncated Rittner models with radial dependent repulsion terms. Experimental data on the bond energies, the equilibrium interionic distances, and the spectroscopic frequencies were employed for the purpose. The polarizabilities used were also computed from the experimental dipole moments of alkali-metal halides. The potential parameters obtained were compared with parameters from other sources and checked for consistency. The computed potential parameters of alkali-metal halide monomer molecules were used to predict the energetics and geometries for alkali-metal halide dimer molecules. The predicted values are in good agreement with experiment and other calculations indicating the consistency and reliability of the potential employed. Although the magnitude of repulsive and dispersive energy terms varies with potential functions employed, the difference between the two for a molecule is constant. The repulsive term is more sensitive than the attractive term. The uncertainty in the exponential repulsion results in an inaccurate representation of the attractive contribution. Introduction of the radial-dependent repulsion term changes the relative magnitudes of repulsive and dispersive parameters and hence the relative contribution to the total potential with monomers. But this has no significant effect on the energetics and geometries of the dimers.

Notes: Localized molecular orbitals (LMOs) for several octahedral complexes are presented. Wavefunctions are calculated within the PRDDO approximations and localized by the Boys criterion. Complexes of general formula (NH3)x(CO)6-xM, M = Cr0 or Mn+ and x = 1, 2, or 3 illustrate the general trends for carbonyl complexes. Weak to moderate π-bonding results in three equivalent inner shell LMOs dominantly of metal 3s, 3p and 3d character but highly delocalized to the carbonyls. These three LMOs flank the M-CO bond axis. Other π back-bonding situations result in metal-ligand double bonds which are nonequivalent and have σ-π separability [(NH3)5(py)Mn+] and also equivalent double bonds [(NH3)5(NO)Cr+].

Notes: Sets of atom equivalents have been developed which permit the estimation of heats of formation, ΔH°f298(g), from ab initio total energies (3-21G and 6-31G* basis sets). This extends the isodesmic reaction scheme of Pople and the group equivalents of Wiberg. A variety of small inorganic and organic molecules, including fluorocarbons, free radicals, carbocations, and protonated species give excellent agreement with experiment; average errors are less than 1 kcal/mol with unstrained hydrocarbons (both basis sets), and are on the order of 2 kcal/mol for all molecules considered (6-31G*; the 3-21G basis errors, as expected, usually are somewhat higher). The results substantiate Pople's early conclusions that Hartree-Fock theory provides a generally satisfactory description of classical molecules.

Notes: Atomic charges obtained with a previously published charge scheme are given for amino acids and peptides. In order to do this, a method of handling charged species with the basic scheme2,3 has been developed. The charges obtained for alkylammonium ions and carboxylate ions with the scheme are presented and compared with CNDO and ab initio values. The calculated experimental dipole moments of the zwitterionic forms of glycine, alanine and β-alanine are then discussed. Finally, the atomic charges obtained for the naturally occurring amino acids are given, both in the form of the N-acetyl-N′-methyl amino acid amides, used as models for the amino acid residues in enzymes, and as the free zwitterionic amino acids. The charges obtained show a good correlation with n. m. r. chemical shifts of both carbon and hydrogen atoms.

Notes: Ab initio MO calculations have been performed for neutral and cationic C2H2F2 structures. Olefinic and carbene structures are investigated for the neutral isomers, while olefinic, carbene, and fluoronium-type cations are found. Stability orders and rotational barriers are discussed in terms of orbital and Coulomb interaction. Contrary to previous studies, the higher stability of the geminal isomers is interpreted to be caused by Coulomb attraction.

Notes: A method of graphically exhibiting detailed information about a three-dimensional electron distribution function f(x,y,z) is described. Contour lines f = constant are drawn on a set of equidistant parallel planes that intersect the distribution, and a perspective view of all contours on all planes is displayed. Representative examples are given.

Notes: A method is described to analyze observed conformations for molecular fragments with more than three torsional degrees of freedom. The method is an adaption of statistical cluster analysis to multidimensional, symmetric, periodic distributions of data points. Application to the molecular fragment M(PPh3)2 with eight torsional degrees of freedom reveals a model of conformational interconversion. The model implies gearing motion of the two PC3 fragments alternating with stepwise inversions of the helicities of the PPh3-propellers.

Notes: We have carried out a series of molecular mechanics calculations on the alkali ion complexes of valinomycin. For the ions Na+, K+, Rb+, and Cs+ we have found three-fold rotationally symmetric conformations as the lowest energy structures, while for Li+ a markedly asymmetric configuration is preferred. The relative free energies of the complexes show that Li+ is by far the poorest binding partner in solution, followed by Na+, which is in turn far poorer than any of the three larger ions. The binding selectivity derives from the slower variation of the complexation free energy with ionic size than the ionic solvation free energy, so that the ionophore is unable to compete with the solvent for the smaller ions. Our calculated strain energies suggest that valinomycin's failure to form complexes with the smaller ions in solution is due partially to the rigidity of the ionophore structure, which prevents the central cavity from contracting to accommodate them. Certain geometric criteria indicate that K+ provides the best fit to the binding site, although there is some inconsistency between the energetic and geometric criteria of binding ability.

Notes: The protonation energies of alkylated derivatives of NH3 and OH2 are calculated at the Hartree-Fock level with the split-valence 4-31G basis set. The methyl, dimethyl, and ethyl amines are studied; oxygen bases include methanol, dimethylether, and ethanol. The geometries of each molecule and its protonated analog are fully optimized. It is found that protonation leads to significant changes in the molecular structures. In particular, the bonds to the N and O atoms are substantially elongated, especially when the other atom involved is C rather than H. The calculated absolute proton affinities are somewhat larger than the experimental values. However, the differences in protonation energies of the various molecules relative to one another agree quantitatively with experiment. Replacement of one H atom of the base by a methyl group induces an increase in proton affinity of some 10 kcal/mol. If a second methyl group is added to the N or O atom, a further increment of about 70% this amount is noted. On the other hand, placement of the second C atom on the first methyl group (to form an ethyl substituent) leads to a smaller increase (∼30%). The magnitudes of these alkyl substituent effects are somewhat larger for the oxygen bases than for the amines.

Notes: The lowest potential energy surfaces of NO3 have been investigated using CASSCF and contracted CI methods, to determine if NO3 is an intermediate in the oxidation of nitric oxide. This reaction is observed to be termolecular where an intermediate is almost certainly formed. The calculations, which were performed in C2v symmetry, show that the form of NO3 which has a near D3h geometry should not be possible to reach from ground state NO and O2. The energy of this isomer of NO3 is calculated to be 25 kcal/mol higher in energy than separated NO and O2. Furthermore, NO + O2 is separated from NO3 by very high barriers. The C2v constrained barrier is as high as 145 kcal/mol, which makes it very unlikely that NO3 could be formed even along less symmetric pathways. The origin of the barriers are analyzed, and it is shown that a special type of mechanism is involved for the state with the lowest barrier. In this mechanism, which was observed recently also for NiH2, the occupation in each symmetry changes only by one unit in each step of the reaction. The only isomer of NO3 which could be formed is a weak van der Waals complex with a very long bond distance of 6.5 a.u. N2O2 does, however, in this respect seem to be a more likely intermediate with its shorter bond distance of 4.5 a.u. Calculations around the D3h equilibrium further show that 2B2 is the ground state of this isomer of NO3 with 2A2 and 2B1 slightly higher in energy.

Notes: The CGTO integral evaluation, SCF, SCF-gradient, integral transformation, and MR-CI (SD) steps of the COLUMBUS system of programs have been adapted for the CYBER 205. A description is given of our efforts and the partly heavy modifications necessary to exploit the potential of this supercomputer and to avoid its shortcomings. Typical timings are reported, vector and scalar performance are compared.

Notes: A new instrument of exploration can be used to develop unrecognized connections among points in a variety of geometric designs. Operational methods are used to derive the relationships, and a new approach to extremum location is demonstrated. The technique is suitable for interpolation problems which arise in experimental design and the treatment of data.

Notes: The direct interconversion of the two C3-symmetric enantiomeric conformations of triethylamine, via C—N bond rotation, has been studied by molecular mechanics (MM2) calculations. The MM2 calculations have been used to characterize the minima (equilibrium geometries) and first-order saddle points (transition states) for this process. For one interconversion, there are five saddle points and six minima. The highest energy saddle point results from the uncoupled rotation of one ethyl group to eclipse the lone pair. Two of the barriers result from coupled rotation of two ethyl groups in close passage.

Notes: The new contracted Gaussian-type orbitals (CGTOs) for molecular calculations have been developed from Li to Ne. The CGTOs are minimal type, i.e. composed of two s-type CGTOs, s1, s2, and one p-type CGTO, p1. They are new family of CGTOs given by Tatewaki and Huzinaga, and others. In the previous works three primitive GTOs are used for s2, which is the main part of the 2s orbital, whereas four primitive GTOs are employed in the present work. The sets generated are [54/5], [64/5], [64/6], [74/6], and [74/7]. In almost all the cases the errors in the 2s and 2p orbital energies are smaller than those of DZ. The resulting 2s orbitals are close to the orbitals of the uncontracted GTO sets, (13/n) and (14/n) of Duijneveldt. It is found that the 2s and 2p orbitals given by [64/6], [74/6], and [74/7] are satisfactorily near to those of Hartree-Fock. The basis sets [54/5], [64/6], and [74/7] are applied to the N2 molecule in the split valence forms of [5211/311], [6211/3111], and [7211/4111]. Adding the d-type polarization functions from one through three, the quality of the basis sets has been examined. All of the three sets show good behavior and the sets augmented with three d-type polarization functions give almost entirely the same results as the very extended basis set.

Notes: The orbital behavior of both the singlet and triplet Rydberg series for 1sns configurations of the He atom has been investigated using one- and two-configuration Hartree-Fock wave functions. The core orbital within the triplet series changes negligibly; however, a contract trend is noticeable as the Rydberg orbital penetrates more into the core region, which is in contrast to that found in the 1s2ns 2S Rydberg series of Li atom. Although some properties of the whole atom can be calculated, the core relaxation of the singlet series can not be drawn without ambiguity because a two-configuration correlated wave function has to be used, and thus the orbital picture is lost.

Notes: Relativistic effective potentials (REP) are now widely used in molecular electronic structure calculations. Tests of these REP are needed to assess their accuracy. This can now be done for AgH and AuH since Lee and McLean have published Dirac-Fock calculations for these molecules. Comparative SCF calculations have been performed for two types of effective potential. Satisfactory agreement between the effective potential results and Dirac-Fock values is found for spectroscopic constants and dipole moments, which supports the use of these potentials for heavy atom containing molecules.

Notes: Molecular mechanics calculations (MM2) are used to elucidate energies and structures of possible reaction products in olefin metathesis of 2,3-dimethylnorbornadiene. The comparison of experimental and calculational results concerning norbornadiene itself shows excellent agreement both in energy and structure. The predicted isomers of lowest energy in a series of three different reaction products seem highly reliable and will lead to a more precise interpretation of the olefin metathesis reaction and the resulting product distribution. Some sixty different isomers have been considered and structures and energies are given. Nonplanarity of double bonds and van der Waals repulsions of closely related hydrogen atoms in polycyclic cycloolefins are considered in some detail. In order to reduce computing time and efforts in obtaining starting coordinates, a computer program for some dimeric structures was devised, which can combine minimized structures stemming from MM2 calculations.

Notes: A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.

Notes: General expressions for monocenter electron repulsion integrals in a basis of real atomic orbitals are derived in terms of the radial integrals Rabcdk. The final expressions for these integrals can be classified into five main classes which are characterized by the angular part of the real atomic orbitals. For a basis of real s, p, d, and f AO's the total number of monocenter repulsion integrals is 65536, from which 6652 are different from zero. The nonzero integrals can be classified into 430 groups which contain integrals of equal value.

Notes: Reequilibration processes are often encountered within solids and they have long been described mathematically. However, computation of reequilibration data over entire processes is often difficult. An algorithm has been developed specifically for this purpose. It allows a fast and efficient computation of reequilibration parameters. Anisotropic diffusion can, moreover, be taken into account.

Notes: We describe a real-time docking method using molecular graphics and high-speed calculation of the energy of interaction between a drug and a receptor. A three-dimensional tabulation of the potential is computed prior to the docking experiment, and the total interaction energy is calculated and updated on the display screen in real-time to provide immediate visual feedback to the user as the drug molecule is moved inside the receptor pocket. The “Simplex” method is then used to minimize the energy of interactions after each docking. Using this real-time method, it is now possible to examine rapidly the interactions of a large number of drugs and their analogues with receptor molecules. As an application, the interaction of thyroid hormone and its analogues with prealbumin is considered. The final interaction energies of this very rapid method compare well with those calculated by more orthodox means, while also providing visual feedback on both molecular geometry and energy.

Notes: The thermal limiting high-pressure unimolecular rate constant k∞ represents, operationally, the Laplace transform of the product of microcanonical rate constant for decomposition of molecules having specified energy E [k(E)] and the density of states [N(E)]. By inversion, it is possible to recover k(E)N(E), from which one can obtain the energy dependence of k(E) and the pressure dependence of kuni, the thermal general-pressure unimolecular rate constant. This article examines numerical aspects of three methods of inversion, their reliability and dependence on sampling, i.e., on the number of available experimental data points, by comparing exact k(E) and kuni with those obtained by inversion. It turns out that the method of steepest descents is the best all-round performer.

Notes: The molecular mechanics (MMP2) description of the torsion of a methyl group attached to a conjugated system has been improved by using bond order dependent torsional force constants.

Notes: A corrected Born equation, which describes the solute-dipolar solvent interaction by placing the charges of the atoms of the solute at their position in space inside a spherical cavity of the solvent, is used to calculate the solvent effect on three systems: the hydrated OH- ion, the lithiated aziridine, and the lithiated oxirane. It is found that the solvent effect stabilizes the addition of a water molecule to the OH-(H2O)3 system with the additional water acting as a proton donor. It is also found that the lithiation energy of aziridine and oxirane which are found to be 47 and 43 kcal/mol in gas-phase, respectively, decrease to 32 and 23 kcal/mol in water solution.

Notes: The problem of chance correlations in studies of structure - activity relationships using multivariate linear regression techniques is addressed. Random correlations are simulated by scrambling real potency values in data bases consisting of molecules possessing various biological properties. The statistical parameters of these correlations are compared to those obtained using the actual potency/compound data pairs and it is noted that the most noticeable differences are in the magnitude of the F values for the overall regression. Cutoff points for this parameter are suggested, which, when implemented in the recently introduced CASE method that correlates biological activity with substructural descriptors, can serve to weed out effectively the majority of meaningless correlations.

Notes: SINDO1 calculations were performed to study the reactivity of molecules with a valence number derived from the density matrix. A comparison of valence numbers was made for selected examples of rotation barriers, substituted strained molecules, radical gas phase reactions, and acid-base reactions. Relations between valence, geometry, and energy changes are discussed.

Notes: A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3dn-14s1 and 3dn-24s2 configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.

Notes: An iterative algorithm is described for finding topological equivalence, ordering, and canonical numbering of vertexes (atoms) in molecular graphs. Like the Morgan algorithm, it is based on extended connectivities but: (i) the latter are used hierarchically, i. e., the discrimination in the next iteration is carried out only for the vertices having the same extended connectivities (ranks) at the previous iteration; (ii) at equal extended connectivities, additional discrimination is introduced by the ranks of adjacent vertices; (iii) there is no “best name” search; (iv) three levels of complexity of chemical structures are distinguished and handled by different procedures.Two schemes of application of HOC procedures are presented: one directed towards a fast canonical numbering for coding systems, and another one yielding levels of topological equivalence allowing a unique topological representation of the molecule with possible applications to similarity search, structure-activity correlations, etc.

Notes: A topological code is devised on the basis of the unique topological representation of the molecule described in the preceding two parts of this series.1 By adding to the topological code additional chemical information on atoms and/or bonds, as well as stereochemical information, a chemical and respectively stereochemical code (SHOC) are also constructed. The advantages of the new linear codes are that they are convention-free codes, preserving the symmetry of molecular graph, and easily implemented either manually or by means of computer programs. By concentrating all topological, chemical, and stereochemical information, our code (SHOC) is more compact and more general than the codes based on several separate lists.

Notes: Different schemes are explored for the calculation of the proton transfer process in the hydrogen bonded cation [CH3OH · H · NH3]+. Results from ab-initio calculations with the STO-3G, 3-21G and 4-31G basis sets, are compared in search for an efficient reliable scheme to study the potential energy curves for the proton transfer. The curve constructed from the lowest energies calculated with the frozen optimized geometries of the two possible pairs of proton donor and acceptor fragments, (i.e., CH3OH2+/NH3 and CH3OH/NH4+) is in good agreement with that obtained when all the fragments of the hydrogen bonded complex are completely optimized simultaneously.

Notes: The computer implementation of the HOC procedures presented in Parts I, II and III of this series is based on the module principle. It contains a main program and seventeen subroutines in Fortran IV. The system is able to provide unique atom numbering and code for all kinds of chemical compounds in their tremendous variety of structures.

Notes: The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the form of a tree. This formula, which represents the first general recursion formula for trees of any kind, is valid irrespective of the valence of the vertices of G or of the degree of branching in G. Several closed expressions giving W(G) for special classes of tree molecules are derived from the general formula. One illustrative worked example is also presented. Finally, it is shown how the presence of an arbitrary number of heteroatoms in tree-like molecules can readily be accommodated within our general formula by appropriately weighting the vertices and edges of G.

Notes: The cellular species formed in the hydrolysis of cis-Pt(NH3)2Cl2 (DDP), namely, cis-[Pt(NH3)2XY]n+ (X, Y = Cl-, H2O, OH-; n = 0, 1, 2) have been investigated theoretically using the relativistic and nonrelativistic extended Huckel molecular orbital method. Molecular orbital (MO) results for trans-DDP and its hydrolysis products are also reported for comparison. Transition energies, molar absorption coefficients (∊), and B terms from magnetic circular dichroism (MCD) derived from theory are presented for each of the species studied. The electronic absorption and MCD spectra of all the complexes are predicted to exhibit ligand field transitions arising primarily from excitations between the occupied Pt 5d orbitals and the unoccupied Pt 5d and 6pz orbitals, respectively. The 5d → 6pz transitions are expected to yield intense absorptions in the UV spectral region. Some intensity is generated in the d → d transitions as a result of the low symmetry of these complexes. Correlation of available experimental data with theory allows spectral assignments to be made and predicted. Substituent effects in the cis- and trans-isomeric species are discussed. Finally, the applicability of the EHMO method to these systems is examined.

Notes: This article presents a strategy to perform molecular dynamics simulations using parallel processing techniques on a parallel-distributed loosely coupled system consisting of IBM host computers (4341 and 4381) with attached scientific processors (FPS-164). This substantially enhances our ability to perform fast and more realistic large scale many-body trajectory simulations. A powerful extention of the computational range of molecular dynamics the parallel approach offers the opportunity to substantially reduce the simulation time to allow a longer simulation period to study more realistic models and larger systems. It is flexible and uses, for the most part, standard products and straightforward implementation with a broad range of applicability. The implementation of a simulation of water molecules with the inclusion of two- and three-body interactions is discussed. Some considerations in the design and implementation of parallel programs on a loosely coupled system are also presented.

Notes: We compare calculated total energies for 150 open-chain molecules using ab initio methodology and the PRDDO approximations. The bulk of the errors implicit in the PRDDO approximations are apparently of a one-center nature, i.e., they are due to the number and type of atoms in the molecule, and not the details of the molecular geometry. Atomic correction factors are developed which reduce the errors in the calculated total energy of PRDDO wave functions by a factor of eight relative to the ab initio reference calculations. PRDDO calculations on ring and cage compounds are shown to have additional systematic errors in the total energy.

Notes: Benzylic anions were studied with the semiempirical MNDO molecular orbital method. Structural changes were analyzed as metal counterions and solvents were allowed to interact with the benzylic carbon. Generally, benzylic carbanions were found to be trigonal planar but became pyramidal or bent when metals were included in the calculation.

Notes: Using the previously reported ab initio interaction energies among K+, Na+, water, and Gramicidin A (GA), this report presents Monte Carlo simulations for the microscopic effect of an applied voltage (0.5 V/32 Å) on a solvated gramicidin. The reorientation of water molecules due to the applied voltage is found to be marginal for both cations. The energy contribution due to water dipoles was within 10% of the total energy contribution due to the applied voltage. Inside the channel the total energy contribution varied almost linearly along the channel axis; outside the channel the slope of the total energy contribution with respect to the channel axis decreased.

Notes: Optimized monopole expansions for the peptide subunits of proteins are developed by a reparameterization of the Hückel-Del Re procedure designed to reproduce closely the electrostatic properties obtained with ab initio OMTP multipole expansions. It is shown that satisfactory values of both potential and field may be obtained for different conformations of the peptide backbone as well as for the common side chains. A comparison is presented for the pentadecapeptide Gramicidin A.

Notes: The structures of α-X-cyclopropyl and α-X-isopropyl radicals (X = H, CH3, NH2, OH, F, CN, and NC) are reported at the RHF 3-21G level of theory. The isopropyl radicals are pyramidal with out-of-plane angles varying from 12° (X = CN) to 39° (X = NH2), and barriers to inversion ranging from 0.4 kcal/mol (X = H) to 4.0 kcal/mol (X = NH2). The cyclopropyl radicals have larger out-of-plane angles, from 39.9° (X = CN) to 49.4° (X = NH2), and their barriers to inversion, which increase with the inclusion of polarization functions, vary from 5.5 kcal/mol (X = H) to 16.7 kcal/mol (X = F). In both types of radicals the amino group is the most stabilizing substituent, while the α-fluoro has little effect. The β-fluoro group is weakly destabilizing in the cyclopropyl radical. The strain energies of the cyclopropyl radicals (36-43 kcal/mol) are compared with those of similarly substituted anions, cations, and cyclopropanes.

Notes: Basis set expansion and correlation effects on the computed proton affinities of the oxygen and nitrogen bases CH3OH, H2CO, CO, CH3NH2, CH2NH, and HCN have been evaluated. Basis set enhancements lead to systematic changes in computed proton affinities. These effects appear to be additive, and are greater for correlated proton affinities than for Hartree-Fock energies. Inclusion of correlation decreases proton affinities, with fourth-order Møller-Plesset energies bracketed by second and third order energies.

Notes: A basis set with bond functions (6-31G + BF) has been tested for its applicability to calculation of dissociation energies of single and multiple bonds by Moeller-Plesset perturbation theory at the second and third orders. Results have been compared with those calculated in the 6-31G* basis set. The 6-31G + BF basis at the MP2 and MP3 levels yields better results than 6-31G* basis and the time consumption is less as well. Consideration of the bond functions on the bonds neighboring the bond being broken has no significant influence on the dissociation energies either at the SCF or at the MP2 levels. If both reactants and products can be characterized by two-center bonds, the 6-31G + BF basis and UMP2 variant of perturbation theory can be recommended for practical calculation of De values, especially for the systems where the use of more exact bases is rather difficult.

Notes: A new approach is presented for identifying all possible cycles in graphs. Input data are the total numbers of vertices and edges, as well as the vertex adjacencies using arbitrary vertex numbering. A homeomorphically reduced graph (HRG) is constructed by ignoring vertices of degree less than three. The algorithm is based on successive generation of possible edge-combinations in the HRG. If a combination yields a cycle, it is either printed or stored and then finally printed in a list of all possible cycles arranged in the order of increasing ring size. A unique numbering of the cycle is used. The computer program is listed and exemplified. Computing times are given.

Notes: Highly accurate vibration-rotation Franck-Condon factors qab, for a transition between two diatomic electronic states (a) and (b), are sought. When the potentials of states (a) and (b) are of the RKR type, the computation of qab is reduced to that of Franck-Condon integral Iab(i) = ∫riri+1 ψa(r)ψb(r) dr in an interval ri, ri+1. By using convenient interpolations for the potentials Ua and Ub in the considered interval, this integral becomes Iab(i) = ∑n=ON δnab (ri+1 - ri)n+1/(n + 1), where the “coupling constants” δnab depend uniquely on the eigenvalues Ea and Eb of the considered transition and on the potentials Ua and Ub (the number N of terms depends on the desired accuracy). The method used computes the Franck-Condon factors qab without the explicit use of the wave function and by replacing the integrals by simple summations. To test the values of qab obtained by this method, the orthogonality rule ∫0∞ ψv′ψv″ dr = 0 (for v′ ≠ v″) is used for one state or the other. This test, along with other tests, show that the Franck-Condon factors computed by the present method are accurate to nine significant figures for high and low levels.

Notes: A series of ab initio calculations have been carried out, using the 4-21G basis set. Ethane and propane were first studied to obtain reference points. The effect of adding an electronegative atom (fluorine, or carbonyl oxygen) onto the framework was then studied as a function of the torsional angle about the single bond. Some pronounced trends in structural changes were observed, and these can in part be correlated with hyperconjugative effects. For example, fluoroethane has bond lengths which are shorter than those in ethane itself, by 0.024 Åin the C—C bond, and 0.003 Åin the α C—H bonds. These changes are essentially torsionally independent. On the other hand, in propionaldehyde, the C—C bond length of the methyl group and the C—H bond lengths of the hydrogens attached to the alpha carbon vary as a function of the torsion angle. If the methyl C—C bond in the carbonyl plane is taken as a reference, the bond stretches .016 Åwhen the torsion angle is increased to 90°, an α C—H bond similarly stretches up to .007 Å. Many of these geometric changes are large, well beyond the experimental errors in modern measurements.

Notes: Timings are reported for 6-31G*/UMP2 calculations on planar allene, twisted ethylene, cyclopropenyl anion, allyl, ethyl, isopropyl and CF3 radicals performed by means of the programs GAUSSIAN 80 and HONDO UMP2. The comparison of the two programs is used for pointing out several factors affecting the speed of MP2 calculations.

Notes: The Hammett σ and Taft σ0 constants have been examined using the MNDO computational procedure. They are both best explained by using computed properties based upon the benzoate ion, especially the reciprocal of the energy of the highest occupied molecular orbital.

Notes: The conformational properties of the recently synthesized highly strained permethylcyclohexane molecule 2 have been studied by empirical force field calculations using three different potentials (CFF, MM2, MM2′) and second-derivative optimization methods. A comparison of the results with the conformational behavior of parent cyclohexane 1 leads to the following conclusions: The best conformation of 2 is a chair minimum whose six-membered ring is flatter than that of 1, due to the strong H…H repulsions introduced by the methyl groups. The twist minimum of 2 is energetically less favorable than the chair by an amount similar to 1. A potential energy barrier Δ V# for the chair inversion of 2 of 15.32 kcal/mol results with the CFF, only about three kcal/mol higher than for 1. The free energy of activation ΔG# for this process obtained with the CFF is 16.96 kcal/mol (at 333 K) and agrees well with the experimental value of 16.7(2) kcal/mol.1 MM2 and MM2′ give substantially lower and higher potential energy inversion barriers Δ V# of 9.03 and 20.29 kcal/mol, respectively, which is attributed to inappropriate torsional energy terms in these force fields. The characteristic difference in the conformational behavior of 2 and 1 concerns the boat forms which are substantially less favorable in the per-methyl compound than in 1. Expectedly, strong H…H repulsions between the 1,4 diaxial flagpole-bowsprit methyl groups in 2 are responsible for this difference. The particularly high strain of the boat forms of 2 leads to flexibility differences as compared to 1 which in turn affect the relative entropies of the various statiomers (stationary point conformations); e.g., the chair ring inversion activation entropies of 2 and 1 are predicted by the CFF calculations to have opposite signs (-4.82 and 3.41 cal/mol K, respectively, at 298 K). The twist and half-twist statiomers of 2 are much more rigid than those of 1, which is a consequence of the substantially larger boat barriers along their pseudorotational interconversion paths. The boat transition state separating two enantiomeric twist minima represents a barrier calculated to be more than tenfold higher for 2 than for 1 (CFF Δ V# values 11.14 and 0.92 kcal/mol, respectively); likewise the half-boat chair inversion barrier of 2 is calculated 5.07 kcal/mol less favorable than the respective half-twist barrier. These statiomers are practically equienergetic in the case of 1. Except for the axial flagpole-bowsprit CH3 substituents of the boat forms, the methyl groups of all the relevant calculated statiomers of 2 are more or less staggered. The rotational barrier of the equatorial methyl groups of the chair minimum of 2 is computationally predicted to be 5.78 kcal/mol (ΔG#), i.e., unusually high. Interesting vibrational effects are brought about by the strong H…H repulsions in 2; thus the chair minimum has a largest C—H stretching frequency estimated to be 3050 cm-1 and involves several particularly low frequencies which have a substantial influence on its entropy. CFF calculations for the lower homologue permethylcyclopentane 5 indicate that its pseudorotational properties are similar to those of cyclopentane 4, in contradistinction to the pair 2/1.

Notes: The molecular association between some substituted β-carbolines and a model flavin, lumiflavin, has been studied by means of a semiempirical approach proposed by Fraga based on a 1/R expansion of atom-atom pair potentials. Only stacked minima have been considered because of their possible biological interest. The calculations characterize 15 different minimum stacked conformations, most of them occurring in the complexes considered. The structural and energetic effects of 1-Me, 6-OH and 7-OH substituents of β-carboline are discussed. An equilibrium conformation involving geometric overlap between the pteridinic portion of flavin and the indole group of β-carboline is predicted to be the most characteristic structure of the complexes. The recognition of this feature can serve to check the effect of substituents and substitution sites of β-carboline in its association complexes.