On the “Wolfsberg–Helmholz Conjecture” of “Extended‐Hückel Theory”

After having reviewed some pioneer integral approximations closely related to Rüdenberg's expansions of one‐ and two‐electron orbital products, we apply the previously described “Implicit Multi‐Center Integration” techniques on Roothaan's “restricted” Fock‐matrix components over standard atomic orbital bases. The resulting compact forms are very similar to the well‐known “Wolfsberg–Helmholz Conjecture” of “Extended‐Hückel Theory,” which relates the various off‐diagonal matrix elements of “restricted” Fock‐type to their corresponding diagonal counterparts. In this way, a “nonempirical Extended‐Hückel Theory” can be created. © 2012 Wiley Periodicals, Inc.     

A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.     

Direct minimization of the energy functional in LCAO–MO calculations

In this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO -MO -MC -SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed- and open-shell problems as special cases.     

X–NO2 rotational energy barriers: Local density functional calculations

The X–NO₂ rotational energy barriers of nitromethane, nitroethylene, nitrobenzene, and a group of nitramines have been computed using a local density functional (LDF ) procedure, using ab initio Hartree–Fock (HF )-optimized structures of the ground and rotational transition states. The results have been discussed in relation to HF and some correlated ab initio values and the available experimental data. Our LDF barriers are overall quite reasonable, in generally satisfactory agreement with the experimental and correlated ab initio results. © 1993 John Wiley & Sons, Inc.     

Ab initio calculations on phenol–water

The structures of the three phenol–water minima are optimized with MP2 and the interaction-optimized DZPi basis set. Single point calculations are carried out using the slightly larger ESPB basis set, which contains a set of (s,p) bond functions at the midpoint of the hydrogen-bond. The binding energies and hydrogen-bond distances are corrected for basis set superposition error. For all minima, our binding energies D_e are larger than the previous theoretical estimates. Despite this, our best estimate of the binding energy D₀ for the global minimum, 21.08 kJ/mol, is about 2 kJ/mol smaller than the experimental values (23.45±0.48 and 22.92±0.36 kJ/mol).     

Molecular MC–SCF calculations

A practical method for finding multi-configurational SCF wave functions is proposed. The basic equation is equivalent to the Brillouin theorem; comparison with the usual SCF equations obtained through effective hamiltonians gives an interpretation of the offdiagonal Lagrange multipliers. Numerical applications to Formaldehyde in a minimum Slater-type orbital basis with four different variational wave functions are reported. The molecular orbitals found in these calculations are localized on the chemical bonds. The largest contributions to the energy are obtained from π-π and dispersion-type σ-π correlation.     

Some remarks on the perturbation and variation–perturbation calculations of the free energy for quantum systems

A generalization of the Gibbs–Bogoliubov inequality F ? F₀ + 〈H ? H₀〉₀ for the free energy F is studied which leads to a variation principle for this quantity that may be of importance in certain computational applications to quantum systems. This approach is coupled with a study of the perturbation expansion of the free energy for a canonical ensemble with H = H₀ + λV in the general case when H₀ and V do not commute. The second- and high-order derivatives of the free energy with respect to the perturbation parameter λ are calculated. From the second-order term is finally obtained a second-order correction to the previous variational minimum for the free energy.     

Density functional calculations on CO attached to PtnRu(10−n) (n = 6–10) clusters

B3LYP and SCF‐Xα calculations have been performed on Pt_nRu_(10−n)CO (n = 6–10) clusters. The work aims to simulate the adsorption of CO on the (111) surface of platinum metal and to examine the electronic effects that arise when some Pt atoms are replaced with Ru. Adsorption energies and Pt C and C O stretching frequencies have been calculated for each cluster. Ru does affect the electronic structure of the clusters, the calculated adsorption energies, and frequencies, the Pt C frequency more than the C O. The donation‐backbonding mechanism that accompanies the shift in CO stretching frequency that occurs when CO adsorbs on platinum does not explain the differences in frequency shift observed in CO on various Pt/Ru surfaces. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 589–598, 2000     

A functionally flexible interatomic energy function based on classical potentials

A flexible potential energy function is proposed herein on the basis of classical potential functions of Lennard-Jones, Morse, Buckingham and Linnett. By introducing two indices, which range from 0 to 1, the proposed function can either be reduced to the classical potentials by fixing the indices at their extremes or be used as a flexible function for curve-fitting interatomic energy data over a broad range of interatomic distance. In a departure from previous effort that give exact parametric relationships only at the minimum well-depth, the present paper quantitatively accounts for the discrepancies at very large interatomic compression and stretching.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Bond polarization in the FeCO system: Semiempirical MO–SCF (BMV) calculations

Charge distributions in FeCO for different Fe–C distances and the Fe–C–O angle equal to 180° and 90° have been computed by the BMV method, a semiempirical SCF scheme including overlap and especially suited for transition-metal atoms. A comparison with available EHT and ab initio calculations suggests that the BMV method is a useful complement to ab initio calculations. The information obtained on the dependence of the binding in FeCO on the Fe–C distance is also briefly discussed in connection with the views of experimentalists of the state of CO absorbed on iron.     

Potential energy calculations for argon and methane adsorbed on MgO(001) substrate

A semi-empirical potential model is used to calculate the interaction energy of a rare gas atom or a methane molecule adsorbed on a MgO substrate with square symmetry. The potential surfaces are drawn and compared with the results obtained on the hexagonal (0001) face of graphite. MgO appears as a corrugated surface for both argon and methane whereas graphite is a nearly perfect planar surface. The calculated holding and corrugation energies are in agreement with experimental data.     

Study of the carbon fiber–poly(ether–ether–ketone) (PEEK) interfaces, 2: relationship between interfacial shear strength and adhesion energy

In the second part of this general study, the carbon fiber–PEEK interfacial shear strength is measured by means of a fragmentation test on single-fiber composites. Different thermal treatments (continuous cooling from the melt, isothermal treatments and long melting temperature time) are applied to these model composites prior to testing. The results are systematically compared with the previously determined reversible work of adhesion between carbon fiber and PEEK. It is shown that physical interactions at the interface determine, to a large extent, the magnitude of the interfacial shear strength between both materials. However, it appears that the magnitude of the stress transfer from the matrix to the fiber is affected either by the existence of an interfacial layer or by a preferential orientation of the polymer chains near the fiber surface. The results obtained on systems that have been subjected to isothermal treatments (isothermal crystallization of PEEK) seem to confirm the existence of a transcrystalline interphase, the properties of which are dependent upon the crystallization rate of the matrix and the interfacial adhesion energy.     

Electrostatic energy calculations by a Finite-difference method: Rapid calculation of charge–solvent interaction energies

Finite-difference Poisson–Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge–solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self-energies and the finite-difference approximation to the Coulombic energies as well as the reaction field energy. A second finite-difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite-difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite-difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 10³ for small molecules. © 1992 by John Wiley & Sons, Inc.     

Ab initio Hartree–Fock–Slater calculations of polysulfanes H2Sn (n = 1–4) and the ions HS and S

An ab initio Hartree–Fock–Slater procedure was applied to the calculation of the electronic structure of polysulfanes, H₂S_n (n = 1–4) and the ions HS and S. Charge densities, overlap populations, and deprotonation energies are calculated; the latter appear well correlated with the first and second acidity constants.     

Förster energy transfer from poly(arylene–ethynylene)s to an erbium–porphyrin complex

We study the infrared emission at 1.54 μm of an organolanthanide complex, Er(III)-tetraphenylporphyrin [Er(TPP)acac], both as a result of direct optical excitation and via energy transfer from host π-conjugate polymers of type poly(arylene–ethynylene) [PAE]. In the first case, the emission of the neat complex is characterized in inert transparent materials and a value of the quantum yield at 1.54 μm φ_IR=4×10⁻⁴ is measured. Then, fluorescence resonance transfer is investigated in blends of Er(TPP)acac with PAEs by monitoring the quenching of the polymer fluorescence along with the enhancement of both the visible emission of the ligand and the near-infrared band of Er³⁺. These different procedures allow a detailed analysis of the transfer efficiency within a specific implementation of the Förster model for polymeric donors. The experimental values of the critical radius R₀, ranging from 1.3 to 2.5 nm for the different blends, are in good agreement with theory for a wide interval of the physical and spectroscopic parameters. This suggests that other mechanisms for excitation transfer do not play a significant role in these materials.