Some analytical properties of the dilated SCF Equations

The self-consistent field (SCF ) equations for many-electron systems, suitable within the complex-coordinate method, are derived. The formulation is based on a general bivariational theorem for non-Hermitian operators, with an emphasis on the analytic structure invoked by the complex dilation of the total Hamiltonian. The dilation structure of the resulting SCF equations is stressed and the concomitant analytical properties are discussed. The solutions are classified with respect to these properties, and interpreted in terms of a general form of the symmetry dilemma. The role of the dilated SCF equations for resonance calculations is discussed.     

Ground states of conjugated molecules—VI Calicene derivatives

Calculations have been carried out for calicene and its various possible benzo derivatives, by the semi-empirical SCF MO procedures described in previous papers. The results imply that calicene is not aromatic, showing strong bond fixation and having a negligible resonance energy.     

Resonance energies of fullerenes with 4-membered rings

We report the resonance energies (REs ) of several fullerenes with 4-membered rings and their isomers with only 5- and 6-membered rings computed using the conjugated-circuit model [RE (CC )] and the topological resonance energy (TRE ) model. Both aromaticity indices were normalized by dividing by the size of the considered fullerene [RE (CC )/e and TRE /e]. The results parallel the predictions by Gao and Herndon using the much more advanced SCF –UHF π-electron approach. A good linear correlation is found between the topologically defined indices [RE (CC )/e and TRE /e] and normalized SCF –UHF π-electron energy. © 1995 John Wiley & Sons, Inc.     

Thermochemical parameters for benzenoid hydrocarbons

The heats of atomization of aromatic hydrocarbons are correlated with an incremental 5-term scheme that includes CH and CC bond energy terms, resonance energies, and two steric parameters. Regression analysis of the experimental data with respect to the proposed parameters gives reasonable values for each term. A simple method for calculating resonance energies is illustrated that agrees with the results of SCFLCAOMO calculations.     

Additivity of resonance energy in benzenoid hydrocarbons

A simple method is described for the calculation of resonance energies (RE ) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A-II, graph-theoretical (GT ), Hess–Schaad (HS ), and Dewar resonance energies (SCF ). These relations apply to 42 hydrocarbons and lead to the following equations: A-II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least-squares analysis of the data leads to the following equation: RE = 0.412(λ)^½ ?15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.     

LFMO和NBO的定域性和作用能解析

为分析苯并分子C12H6的垂直共振能(VRE), 建立了定域片断分子轨道(LFMO)和自然键轨道(NBO)两种基组, 并在两种基组之上进行NBO能量分析和Morokuma能量分解. 在NBO能量分析中, 两种基组的VRE都是稳定的; 而在Morokuma能量分解中, VRE的稳定性取决于基组. 在NBO能量分析中, Fock矩阵的一次性对角化忽视了σ体系和π体系之间的电子耦合作用. 故NBO基组和NBO能量分析方法在计算VRE时似乎都不合理.     

Parameterized valence bond calculations for benzenoid hydrocarbons using clar structure

SCF (Dewar-de Llano) calculations are used to parameterize a valence bond theory with a basis of Clar structures. A precise correlation of calculated resonance energies is found (corr. coeff. 0.9998). Graphtheoretic algorithms for carrying out the calculations are illustrated. It is suggested that this theoretical approach would be useful in considering structure and reactivity problems in very large polycyclic benzenoid aromatic hydrocarbons.     

Elektronenstruktur und Stabilität kondensierter Kohlenwasserstoffe

The theory of significant electron structures is applied to benzenoid, nonbenzenoid and semibenzenoid condensed hydrocarbons. Stabilization energies are obtained in agreement with SCF MO resonance energies. The weights of the structures enabled to calculate benzene characters and other character indices.Clar's postulate of localized benzene-like regions is justified. The structural and energetic properties of semibenzenoid hydrocarbons are derived in a systematic manner.     

Theoretical studies on pteridines. 2. Geometries,tautomer, ionization and reduction energies of substrates and inhibitors of dihydrofolate reductase

Ab initio SCF calculations with STO-3G and 3-21G basis sets are reported for approximately 85 pteridines of interest to the study of the reaction and inhibition mechanisms of dihydrofolate reductase. These include tautomeric, protonated, deprotonated, reduced and 6-substituted forms of the 2-amino-4-oxo- and 2,4-diamino-pteridines, many of which are not easily amenable to experimental investigation. Full geometry optimizations at the SCF/STO-3G level for 30 such pteridines have been performed. A step-wise computational protocol designed to identify the minimum level of theory necessary for reliable prediction of relative tautomer, reduction and ionization energies has been developed in an effort to minimize the cost of calculations for this reasonably large N-heterobicylic system. In general, SCF/STO-3G results were found to be inadequate while SCF/3-21G results obtained with STO-3G optimized geometries agreed with all available experimental evidence with the exception of the relative acidity of 6-methyl-7,8-dihydropterin. Correlation graphs relating experimental pK_a's to the calculated ionization energies are presented: these are of potential predictive value. An analysis is given of the importance of resonance substructures, such as the guanidinium and extended-guanidinium groups, in stabilizing some preferred tautomeric and ionized forms, and in explaining the observed geometry changes.     

Conjugated circuits and resonance energies of benzenoid hydrocarbons

A concept of conjugated circuits contained in Kekulé forms of benzenoid hydrocarbons is considered. Circuits of size (4n + 2) in which CC single and double bonds formally alternate are enumerated and serve as the basis for the characterization of a given system. Resonance energies of benzenoid systems are given by contributions of conjugated circuits of different size. The scheme permits the expression of resonance energies of different molecules in terms of selected reference compounds, such as linear acenes. The approach is illustrated on a dozen benzenoid hydrocarbons and the calculated resonance energies are on average within 0.05 eV of the values obtained by SCF MO calculations.     

Use of VN−1 potentials in Green's function calculations

An analysis of the leading effects of a propagator approach to the calculation of resonance energies is presented. By comparison with ΔSCF results, a simple approximation formula has been developed which contains the main features of the V^N?1 potential option and the diagonal Tamm–Dancoff approximation. This result is expected to be a useful guide for further refinements of the many-body aspects of the theory.     

The nuclear quadrupole double resonance spectrum of decaborane

The boron nuclear quadrupole double resonance spectrum of decaborane, B₁₀H₁₄, was taken at 77 K. The assignment of its ¹¹B lines to the various boron atoms of the molecule is based on the spectrum of μ,1,2,3,4,5,7,8,10-B₁₀H₂D₁₂, the theoretically verified intensity relations, and the transition frequencies calculated from a SCF study.     

Thermomechanical and shape memory properties of SCF/SBS/LLDPE composites

A thermally triggered shape memory polymer composite was prepared by blending short carbon fiber (SCF) into a blend of poly(styrene-b-butadiene-b-styrene) triblock copolymer (SBS)/linear low density polyethylene (LLDPE) prior to curing. These composites have excellent processability compared with other thermosets. The dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC) were investigated to assess the thermomechanical properties of the SCF/SBS/LLDPE composite. Scanning electron microscope (SEM) imaging of the samples was performed to show the distribution of the SCF in the composite. The study specifically focused on the effect of SCF on the shape memory behavior of the SCF/SBS/LLDPE composite. The results indicated that the large amount of SCF significantly improved the mechanical property of the polymer composites while not damaging the shape memory performance. The SCF/SBS/LLDPE composites exhibited excellent shape memory behavior when the SCF content was less than 15.0 wt%. Moreover, the shape fixity ratio and shape recovery time of the SCF/SBS/LLDPE composites increased with the SCF content.     

Perturbative virtual SCF CI treatment for energy levels of coupled oscillator systems

A perturbative SCF CI treatment to obtain energy levels of coupled oscillator systems is proposed. The method uses the virtual SCF basis set, and the SCF equations are solved by means of a perturbative treatment that provides the diagonal matrix elements involved in the CI calculation. The off-diagonal matrix elements are calculated using a commutation relationship derived from exact quantum theorems. Numerical results for several systems are obtained and compared with those from others SCF, SCF CI , and variational treatments.     

Design of Recombinant Stem Cell Factor–macrophage Colony Stimulating Factor Fusion Proteins and their Biological Activity <Emphasis Type="BoldItalic">In Vitro</Emphasis>

Summary Stem cell factor (SCF) and macrophage colony stimulating factor (M-CSF) can act in synergistic way to promote the growth of mononuclear phagocytes. SCF–M-CSF fusion proteins were designed on the computer using the Homology and Biopolymer modules of the software packages InsightII. Several existing crystal structures were used as templates to generate models of the complexes of receptor with fusion protein. The structure rationality of the fusion protein incorporated a series of flexible linker peptide was analyzed on InsightII system. Then, a suitable peptide GGGGSGGGGSGG was chosen for the fusion protein. Two recombinant SCF–M-CSF fusion proteins were generated by construction of a plasmid in which the coding regions of human SCF (1–165aa) and M-CSF (1–149aa) cDNA were connected by this linker peptide coding sequence followed by subsequent expression in insect cell. The results of Western blot and activity analysis showed that these two recombinant fusion proteins existed as a dimer with a molecular weight of ~84 KD under non-reducing conditions and a monomer of ~42 KD at reducing condition. The results of cell proliferation assays showed that each fusion protein induced a dose-dependent proliferative response. At equimolar concentration, SCF/M-CSF was about 20 times more potent than the standard monomeric SCF in stimulating TF-1 cell line growth, while M-CSF/SCF was 10 times of monomeric SCF. No activity difference of M-CSF/SCF or SCF/M-CSF to M-CSF (at same molar) was found in stimulating the HL-60 cell linear growth. The synergistic effect of SCF and M-CSF moieties in the fusion proteins was demonstrated by the result of clonogenic assay performed with human bone mononuclear, in which both SCF/M-CSF and M-CSF/SCF induced much higher number of CFU-M than equimolar amount of SCF or M-CSF or that of two cytokines mixture.     

Relative proton transfer abilities of acids and alcohols in gas phase and solutions

The present paper applies a method, based on SCF CNDO MO charge densities and assumption of the validity of the virial theorem, for calculation of relative proton affinities of alcohols, and substituted and unsubstituted carboxylic acids in the gas phase. The paper also chalks out a path for calculation of their relative acidities in solution phase by utilising a solvation energy equation and binding energy data in the gas phase. The results obtained by the present method are mostly in agreement with ion cyclotron resonance mass spectrometric experimental studies. The method has also been applied to cover the cases of amines in the gas phase.     

Direct determination of localized SCF orbitals

The determination of SCF molecular orbitals by a perturbation method proposed by Lefebvre and Moser is used for the direct determination of localized SCF orbitals. Comparisons are made with the canonical SCF procedure. Advantages of the present method for conformational studies and for the determination of “local SCF orbitals” are also examined.     

On the ordering of the ionization energies in N2: A MC SCF study of near-degeneracy effects

Single configuration SCF wavefunctions yield poor results for the order and relative energies of low-lying icnic states of N₂. A multi-configurational SCF (MC SCF) model which takes account of the near degeneracy of a small number of strongly and weakly occupied orbitals corrects the errors of the SCF approach. MC SCF results for N₂ predict the correct ordering and give reasonably accurate results for the three lowest ionization potentials.     

Coupled multiconfiguration self-consistent field (MC SCF) perturbation theory

The analytical form of the perturbation theory for the MC SCF method of Veillard and Clementi is presented. The appropriate second-order energy functional which takes into account the self-consistency requirements, leads to a set of coupled first-order perturbed equations determining the perturbed configuration coefficients and orbitals. The second-order energy formula derived from this functional can be given a clear physical interpretation. The present analytical approach is compared with the finite perturbation MC SCF scheme. The possibility of the approximate solution of the coupled MC SCF perturbation equations is also discussed and the so-called uncoupled procedures are devised. In the limit of the single determinant wave function the present formulae are shown to be equivalent to the appropriate Hartree-Fock perturbation results. The differences between the one-configuration SCF and the MC SCF approach are illustrated by the calculation of the electric dipole polarizability of. HZ in the CNDO/2 approximation. It is shown that the one-configuration SCF approaches cannot account for the correct asymptotic properties of the second-order energy for large internuclear distances. This feature of the SCF perturbation theories does not depend on the specific approximations of the CNDO/2 scheme and is corrected by using the MC SCF perturbation theory.