The riboflavin—dihydroriboflavin system in acidic medium on mercury: Part II. A polarographic investigation

Polarographic current—potential characteristics and current—time curves for the reduction of riboflavin (RF) to dihydroriboflavin (DRF) in 0.01 M HClO₄ + 0.09 M NaClO₄ have been examined in detail. It has thus been shown that the RF adsorption prewave is due to the formation of two overlapping adsorbed monolayers of DRF molecules. Lateral interactions of RF molecules between themselves, of DRF molecules between themselves and of RF with DRF molecules in the first adsorbed monolayer are weak, whereas vertical interactions between overlapping DRF molecules are relatively strong. This explains the abrupt increase in the slope of the RF adsorption prewave and its shift towards more positive potentials as soon as the second adsorbed monolayer of DRF starts to form. The so-called “normal” wave for RF reduction has a half-wave potential E^II_{$\text{1}\text{2}$} = ?0.180 V/SCE, practically coinciding with the formal potential of the RF/DRF couple, and a slope corresponding to a reversible two-electron reduction unaffected by semiquinone formation. The shape of polarographic mean current vs. potential curves has been accounted for through an approximate solution of the corresponding diffusional problem.     

The riboflavin—dihydroriboflavin system in acidic medium on mercury: Part I. A chronocoulometric investigation

The riboflavin (RF)—dihydroriboflavin (DRF) system in 0.01 M HClO₄ + 0.09 M NaClO₄ has been studied on mercury by the single-step chronocoulometric technique. At ?0.040 V/SCE, where RF is still electro-inactive, this substance is adsorbed according to a Langmuir isotherm with an adsorption coefficient K_O = 5.2 × 10⁶ 1 mol^?1, giving rise to a single adsorbed monolayer. At potentials along the plateau of the RF polarographic adsorption prewave, as well as at more negative potentials, DRF is adsorbed with formation of two overlapping monolayers. This behaviour denotes strong attractive vertical interactions between overlapping adsorbed DRF molecules. The progressive shift in the chronocoulometric Q vs. E curve for electro-oxidation of adsorbed DRF towards more positive potentials with an increase in the surface concentration of DRF confirms the strength of these vertical interactions. The simultaneous presence, with formation of a charge-transfer complex, of adsorbed RF and DRF molecules along the plateau of the polarographic RF prewave, as postulated by Tedoradze and co-workers [21,22] is excluded.     

Uniform semiclassical self-consistent-field calculations of vibrational resonance energies and widths

Using the Breit—Wigner definition of a resonance, we calculate both resonance positions and widths for a model non-separable hamiltonian, using a uniform semiclassical self-consistent-field (SCF) method. Excellent agreement with recent complex-coordinate quantum SCF calculations is obtained.     

Electric dipole polarity of diatomic molecules

The restricted SCF (single-configuration SCF) and MCSCF (multiconfiguration SCF) calculations are performed to compute the ground-state electric dipole moments of four pairs of diatomic molecules—(1) CO and BF; (2) SiO and AlF; (3) CS and BCl; and (4) SiS and AlCl—at a number of internuclear distances on both sides of the equilibrium position. Near Hartree–Fock accuracy is obtained in the SCF calculations. All eight molecules have a range of internuclear distance in which electric dipole moments are of the polarity of A^?B⁺. The shapes of computed electric dipole moment functions are discussed in the language of the molecular orbital method and in relationship to electronegativities of atoms. The present study gives us deeper understanding of electron transfer inside molecules and consequently of the apparent contradiction between electronegativity and the dipole polarity of some molecules. © John Wiley & Sons, Inc.     

Hartree—Fock—Slater functions as basis for one-electron perturbation calculations for molecules: I. Calculation of ground state electric dipole polarizabilities

The analysis of the decoupling of Hartree—Fock—Slater SCF perturbation equations for an external field is undertaken. The points of departure from the corresponding Hartree—Fock perturbation equations are stressed. Both formal and numerical results suggest that the fully uncoupled Hartree—Fock—Slater expression is a less drastic approximation than the same Hartree—Fock one. The uncoupled expression for the ground state electric dipole polarizability is calculated for CO, N₂, ethylene, acethylene and trans-butadiene in the dipole length—dipole length, dipole velocity—dipole length and dipole velocity—dipole velocity alternative formulations with an ab initio Hartree—Fock—Slater SCF basis set. The results compare well with other non-empirical results and the dipole velocity-dipole length results are in remarkably good agreement with experiments.     

Principles for a direct SCF approach to LICAO–MOab-initio calculations

The principles and structure of an LCAO -MO ab-initio computer program which recalculates all two-electron integrals needed in each SCF iteration are formulated and discussed. This approach—termed “direct SCF ”—is found to be particularly efficient for calculations on very large systems, and also for calcuations on small and medium-sized molecules with modern minicomputers. The time requirements for a number of sample calculations are listed, and the distribution of two-electron integrals according to magnitude is investigated for model systems.     

Beiträge zur chemie der Pyrrolpigmente, 10. Mitt.: Elektronenspektrometrische Untersuchungen über die Struktur von Quadratsäurederivaten

The structure of squaric acid derivatives was investigated on the basis of the PPP—SCF—LCAO—MO—CI method utilizing the π-electron densities and bond orders. The parameters used in the calculations were modified to fit the experimental data for representative compounds. The data were obtained by X-ray photoelectron spectrometry and electron absorption spectroscopy (including the polarization of the bands as determined by liquid crystal induced circular dichroism measurements).     

Etude theorique des proprietes thermodynamiques du radical CN et de ses dimeres

Using the ab initio LCAO—SCF—MO method and the 6–31G extended basis set, the CN radical and its possible dimers (NCCN, CNNC or CNCN) have been studied in terms of nuclear equilibrium geometries, normal modes of vibration, IR spectrum and thermodynamic properties. The results show that quantum chemical calculations enable these parameters to be obtained with adequate accuracy. Working properly, one can build a local potential energy surface on which to perform a harmonic vibrational analysis. Hence all the required information to apply the principles of statistical thermodynamical analysis is available.     

Convergence of a multireference second-order mbpt method (CIPSI) using a zero-order wavefunction derived from an MS SCF calculation

The convergence properties of a multireference second-order MBPT method (CIPSI algorithm) which uses a zero-order wavefunction derived from a preliminary MC SCF calculation are analyzed. It is found that by using the MO set obtained from an initial pairwise MC SCF calculation the results are comparable to those of an iterative MC SCF + CIPSI (MC PSI) calculation. In both cases the resulting zero-order wavefunction is largely improved in comparison with the standard CIPSI method.     

Dipole moment derivatives of H2O and H2S

The dipole and quadrupole derivatives of H₂O and H₂S are calculated analytically, using the coupled Hartree—Fock method first proposed by Gerratt and Mills. The greater efficiency, of this method allows SCF wave functions very, close to the Hartree—Fock limit to be used. Agreement, with experimental data is good.     

A direct,restricted-step,second-order MC SCF program for large scale ab initio calculations

A general purpose MC SCF program with a direct, fully second-order and step-restricted algorithm is presented. The direct character refers to the solution of an MC SCF eigenvalue equation by means of successive linear transformations where the norm-extended hessian matrix is multiplied onto a trial vector without explicitly constructing the hessian. This allows for applications to large wavefunctions. In the iterative solution of the eigenvalue equation a norm-extended optimization algorithm is utilized in which the number of negative eigenvalues of the hessian is monitored. The step control is based on the trust region concept and is accomplished by means of a simple modification of the Davidson—Liu simultaneous expansion method for iterative calculation of an eigenvector. Convergence to the lowest state of a symmetry is thereby guaranteed, and test calculations also show reliable convergence for excited states. We outline the theory and describe in detail an efficient implementation, illustrated with sample calculations.     

Ring opening of the molecular ion of 5(4H)-oxazolone

Quantum chemical calculations were carried out at several theoretical levels (semi-empirical, MNDO; ab initio, 3–21G SCF, 6–311G** SCF and DZP CISD) to investigate the ring-opening process of and the loss of CO from the molecular ion of 5(4H)-oxazolone. The ring-opening process is predicted to be slightly endothermic and the loss of CO from the open-ring molecular ion to be slightly exothermic. Detailed population analysis calculations suggest the weakening of the lactonic C? O bond in the closed-ring molecular ion and weak carbon—carbon and nitrogen—(formy)—carbon bonds in the open form. Both the open-ring molecular ion and the [M–CO]^+· ion are suggested to be of distonic type.     

Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions

A quasi-Newton method involving a diagonal guess orbital hessian with iterative updates has been proposed recently by Almlof for the optimization of closed shell self-consistent field (SCF) wavefunctions. The technique is extended in the present work to more general wavefunctions, ranging from open shell SCF through multiconfigurational SCF. A number of examples are presented to show that convergence for closed and open shell SCF rivals conventional direct inversion in the iterative subspace (DIIS). For multiconfigurational SCF wavefunctions, the method presented here requires more iterations than an exact second order program, but since each iteration is substantially faster, leads to a more efficient overall program. Received: 15 August 1996 / Accepted: 22 January 1997     

Ab initio studies on the thermolysis of azetidine

The reaction mechanism of the thermolysis of azetidine to form ethylene and methylen-imine has been studied by ab initio SCF MO method at STO--3G and 3-21G levels. Two possible step-wise pathways are explored. One is the breaking of C--C bond as the first step, while the other is thebreaking of C--N bond. All the stationary points on the potential energy surface (PES) are fully optimiz-ed. MP2 / 3-21G single point calculations on all stationary points and MCSCF / STO-3G computationsfor some stationary points are also carried out. The calculations indicate that azetidine decomposesvia biradicaloid intermediates and the cleavage of C--N bond is preferable to that of C--C bond.     

Eine Rechenzeitsparende Programmierung des Wellenmechanischen Self-Consistent-Field Verfahrens für Moleküle (SCF?MO?LCGO–Verfahren)

A time-saving way of programming an SCF method for molecules (SCF ? MO ? LCGO method) is proposed, which is based on an economic way of handling the two-electron-multicenter integrals.     

β-丙醇酸内酯气相热分解反应的过渡态——从头计算法研究

本文用量子化学从头计算法研究了β-丙醇酸内酯热分解反应的机理。对均相热分解的两种可能方式进行了自洽场分子轨道法研究(3-21G基组):C_2H_4+CO_2(1)←CH_2—C—O—CH_2→(2)CH_2=C=O+H_2CO反应物、产物和过渡态的几何构型分别用能量梯度法进行了优化, 并对能量做了二级微扰能(MP2)的校正。用这种方法得出反应(1)的活化势垒为166.0 kJ mol~(-1), 反应(2)的话化势垒为302.0 kJ mol~(-1)。计算结果表明: 在一般温度下, 热分解反应主要以反应(1)的机理进行。这个结论与动力学的实验结果是一致的。     

SCF-SW-Xα Calculations on molybdenum—halogen cluster compounds

The electronic structures of the cluster cations Mo₆ X⁴⁺₈ (X = F, Cl, Br, I) have been calculated using the SCF—SW—Xα method. The eigenvalue spectra obtained are discussed and compared with results of other quantum-chemical studies of such systems. The results of population analysis are used to discuss the charge distribution in the clusters studied. A qualitative discussion of the Mo-Mo and Mo-X bond strengths is also presented. Finally, calculated bond energies are compared with adsorption energies.     

Preparative solution crystallization fractionation: a simple and rapid fractionation method for the chemical composition separation of complex ethylene-propylene copolymers

The molecular structure elucidation of complex ethylene-propylene copolymers (EPCs) has benefited tremendously from the ability to combine preparative temperature rising elution fractionation (prep TREF) with various conventional analytical techniques. Recently reported, prep TREF-high-temperature solvent gradient interaction chromatography (HT-SGIC) (Cheruthazhekatt et. al, Macromolecules 45:2025–2034, 2012) is one of the most effective and highly useful coupled methods that allow for the exact measurement of the chemical composition distribution (CCD) present in various components of EPCs. The major drawback of prep TREF involving slow crystallization and elution steps is the long time per experiment. Here, we present a new and by far the simplest and fastest preparative fractionation method for complex polyolefins—preparative solution crystallization fractionation (prep SCF). The scope of the present study was to achieve a fast fractionation of complex bulk samples into an amorphous, semicrystalline and highly crystalline fraction, in sufficient amounts for the subsequent detailed compositional analysis. The effects of two different solvents, xylene and trichlorobenzene (TCB), and their influence on the solution crystallization of chemically different components of EPC were systematically investigated by combining prep SCF with crystallization analysis fractionation (CRYSTAF), FTIR, differential scanning calorimetry (DSC) and HT-SGIC analyses. Significant differences in the chemical composition of similar SCF fractions obtained from xylene and TCB were observed indicating the strong influence of the solvent on solution crystallization. Prep SCF-HT-SGIC results showed that, under similar experimental conditions, TCB as the fractionation solvent provides superior separation of complex semicrystalline ethylene-propylene (EP) components. Very interestingly, for the first time, separation of soluble fractions (30 °C) of iPP, EPC and PE homopolymer components in complex EPC was achieved by prep SCF in TCB. On the other hand, SCF fractionation in xylene provides a soluble fraction that is perfectly amorphous as has been shown by DSC and CRYSTAF. Based on these results, the present SCF approach and an updated method of the combination of prep SCF-HT-SGIC hold significant promise for the fractionation and characterization of similar complex EPCs in a simple way within a short analysis time, by using significantly smaller amounts of solvent compared to the previously reported, rather time-consuming, prep TREF-HT-SGIC combination. No similarly selective solution crystallization fractionations in preparative scale have been reported before.

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.