A theoretical study on the first ionic states of vinyl fluoride, vinyl chloride, trifluoroethylene, and trichloroethylene with an analysis of the vibrational structures of the photoelectron spectra

Ab initio calculations have been performed to study the molecular structures and the vibrational levels of the first ionic states of vinyl fluoride, vinyl chloride, trifluoroethylene, and trichloroethylene. The equilibrium molecular structures and vibrational modes of these states are presented. The theoretical ionization intensity curves including the vibrational structures are also presented and compared with the photoelectron spectra. Received: 11 September 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes

A very simple but general index of kinetic stability, T, is proposed for π-electron systems, which is defined as a highest occupied molecular orbital (HOMO)- lowest unoccupied molecular orbital (LUMO) energy separation multiplied by the number of conjugated atoms. This new index can be justified by relating it to the approximate form of the superdelocalizability, an index of chemical reactivity defined by Fukui et al. It is best suited for predicting the kinetic stability of fullerenes. All isolable fullerene isomers have T values larger than 13. Received: 24 June 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

A new technique for the early detection of stiffness in coupled differential equations and application to standard Runge-Kutta algorithms

Higher-order Runge-Kutta (RK) algorithms employing local truncation error (LTE) estimates have had very limited success in solving stiff differential equations. These LTEs do not recognize stiffness until the region of instability has been crossed after which no correction is possible. A new technique has been designed, using the local stiffness function (LSF), which can detect stiffness very early before instability occurs. The LSF is a normalized dimensionless ratio which is essentially based on the product of the step size and the geometric mean of all the slopes. It is exceedingly sensitive to the onset of stiffness. Together, the LSF and the LTE form a complementary pair which can cooperate to help solve some mildly stiff equations which were previously intractable to RK algorithms alone. Examples are given of implementation and LSF performance. Received: 18 September 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (1²Π) and first electronically excited (1²Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 1²Π→1²Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities not well known from experiment. Received: 4 May 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Subduction of Q-conjugacy representations and characteristic monomials for combinatorial enumeration

A new method of combinatorial enumeration is presented. The subduction of Q-conjugacy representations gives a characteristic subduction table and a characteristic monomial table. A cycle index is defined on the basis of such monomials and used for combinatorial enumeration of isomers. Received: 10 October 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Transition states in modern valence-bond theory: application to the Cope rearrangement

Modern valence-bond theory, in its spin-coupled form, is used to study the electronic structure of the transition structures in the Cope rearrangement. It is found that the transition structure described by a “chair” geometry with a “6-in-6” CASSCF/6-31G^* wave function is clearly aromatic while the CASSCF/6-31G^*“boat” transition structure corresponds more closely to two weakly interacting allyl radicals. Moreover, there is a striking resemblance between the CASSCF chair transition structure and the benzene molecule, arising from the modern valence-bond analysis in terms of Rumer spin functions. In agreement with previous works, dynamical correlated wave functions show shorter interallylic distances in the optimized transitions structures. The use of spin-coupled wave functions on the latter geometries results in diradical and aromatic character for the chair and boat transition structures, respectively. Received: 13 October 1998 / Accepted: 30 December 1998 / Published online: 7 June 1999     

Sequence dependence of DNA radioprotection by the thiols WR-1065 and WR-151326

Sequence-dependent variations of DNA structure modulate radiation-induced strand breakage. Thiols reduce breakage by scavenging damaging radiolytic OH ^. and repairing sugar radicals. As shown by sequencing gel electrophoresis, WR-1065 radioprotection is modulated by sequence, whereas that of WR-151326, a larger thiol, is more evenly distributed. Molecular modelling was performed on complexes of a 53 bp oligonucleotide (belonging to a natural restriction fragment) with one molecule of WR-1065 or WR-151326. Energy minimised structures exhibit a broadening of the minor groove of an AAATT motif upon WR-1065 binding, and a narrowing of the groove upon WR-151326 binding. Consequently, the accessibility to OH^˙ of H4′ (whose abstraction leads to strand breakage) increases near WR-1065, whereas it decreases near WR-151326. This modifies locally the otherwise homogeneous radioprotection. The effect of WR-151326 strengthens the protection at all tested binding sites, whereas that of WR-1065 diminishes it in some regions, in good agreement with the observed radioprotection distribution. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

Theoretical investigation of the GaF molecule and its positive ion

Coupled pair approximation and configuration interaction calculations were carried out on the gallium fluoride molecule and its positive ion with flexible basis sets. Spectroscopic constants of these species were examined in detail through step-wise extensions of correlating space. The contribution from correlations of the semi-core 3d electrons in Ga was found to be sizable. The bonding character was revealed to be highly ionic even for the positive ion. Received: 13 June 1998/Accepted: 28 August 1998 / Published online: 7 December 1998     

Pseudopotential study of the ground and excited states of Yb2

The ground state of the van der Waals-type lanthanide dimer Yb₂ has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions. Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like, possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the 4f-shell to the core. Received: 3 April 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998     

Theoretical pKa calculations of proteins; the tyrosine and lysine residues of b-elicitin

Elicitins are small proteins that are secreted by plant pathogenic fungi. In this work we have used a computer program that utilizes the boundary element method for heterogeneous dielectrics with ionic strength to calculate the pK _a of all titrating groups in the 98-residue protein β-cryptogein. Our results are in reasonable agreement with the experimentally determined pK _a values for the Tyr residues in the protein. We find that the functionally important Lys13 residue has a normal pK _a of 10.3. Our work also shows that there is no direct correlation between the exposure of an amino acid sidechain and its pK _a. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package

The conductor-like screening model (COSMO) of solvation has been implemented in the Amsterdam density functional program with maximum flexibility in mind. Four cavity definitions have been incorporated. Several iterative schemes have been tested for solving the COSMO equations. The biconjugate gradient method proves to be both robust and memory-conserving. The interaction between the surface charges and the electron density may be calculated by integrating over either the fitted or exact density, or by calculating the molecular potential. A disk-smearing algorithm is applied in the former case to avoid singularities. Several self-consistent field/COSMO coupling schemes were examined in an attempt to reduce computational effort. A gradient-preserving algorithm for removing outlying charge has been implemented. Preliminary optimized radii are given. Applications to the benzene oxide-oxepin valence tautomerization and to glycine conformation are presented. Received: 13 November 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

Grid-free DFT implementation of local and gradient-corrected XC functionals

Following an approach to density functional theory calculations based on the matrix representation of operators, we implemented a scheme as an alternative to traditional grid-based methods. These techniques allow integrals over exchange-correlation operators to be evaluated through matrix manipulations. Both local and gradient-corrected functionals can be treated in a similar way. After deriving all the required expressions, selected examples with various functionals are given. Received: 7 March 1998 / Accepted: 21 May 1998 / Published on line: 6 August 1998     

Peptides in membranes: assessment of environmental effects via simulations using an implicit solvation model

A recently developed implicit solvation model is applied to Monte Carlo simulations of peptides in bilayer-mimetic and polar environments. The model employs the formalism of atomic solvation parameters and reproduces experimental data. Solvent effects on the␣structure of the following peptides were studied: 20-residue poly-Leu and poly-Val, transmembrane helix A of bacteriorhodopsin, magainin2. It was shown that a␣membrane-like environment considerably promotes α-helix formation (all the peptides were found to be α-helical), while simulations in water reveal helix distortion. Consistency of the results with experimental data and further implications of the model are discussed. Received: 24 April 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

Calculation of macroscopic first- and third-order optical susceptibilities for the benzene crystal

Starting from a set of high-level ab initio frequency-dependent molecular first- and third-order polarizabilities, the macroscopic first-order (linear) and third-order (cubic) susceptibilities of the benzene crystal are calculated. Environmental effects are taken into account using a rigorous local-field theory and are compared with the anisotropic Lorentz field factor approach. The experimentally determined first-order susceptibility of crystalline benzene is accurately reproduced. Dispersion curves for the first-order susceptibility and results for electric-field-induced second-harmonic generation and third-harmonic generation experiments are predicted. Comparison with similar calculations conducted in the course of molecular simulations of liquid benzene shows that the theoretical results for the two phases are of comparable accuracy. Overall, the results show that for the fairly compact nonpolar benzene molecules, environmental effects on the effective molecular response are small. Received: 11 February 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Efficient boundary basis functions for time-independent quantum scattering calculations

Novel parametrically energy-dependent boundary functions, F, combined with a finite L ² basis set, permit accurate and efficient calculation of scattering wavefunctions for many energies. Both accuracy and efficiency are achieved simultaneously because all the necessary integrals are energy-independent and also certain functionals, (H−E)|F>, in the Schr?dinger equation are allowed to satisfy desirable boundary conditions. In addition, slight modification of the Schr?dinger equation in the boundary region is shown to be useful for improving the numerical accuracy when a cutoff-radius-truncated basis set is used. The advantages of the present approaches are demonstrated for the one-dimensional Eckart barrier problem. Received: 17 June 1998 / Accepted: 13 July 1998 / Published online: 18 September 1998     

Electric and magnetic multipole integrals in STO basis sets: an analytical approach

A new method for the evaluation of one- and two-centre magnetic and electric multipole integrals for Slater-type functions is presented. The method is strictly analytical in that no approximations of any kind are involved. Two simple functions, ℐ₁ ^aug and ℐ₂ ^aug, are introduced, which employ only functions that are well known in electronic structure theory. With the use of augmentation exponents these functions apply to multipole integrals as well as other one-electron integrals, such as nuclear attraction integrals. The proposed method includes the analytic determination of derivatives of the integrals with respect to atomic displacements. Some illustrative test calculations are presented and compared to results from the literature. Received: 20 April 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Direct subduction of Q-conjugacy representations to give characteristic monomials for combinatorial enumeration

Characteristic monomials for a finite group are obtained by direct subductions of Q-conjugate representations. They are shown to give a generating function that is capable of solving enumeration problems. Received: 1 May 1998 / Accepted: 16 July 1998 / Published online: 18 September 1998     

Information about the biologically relevant properties of Clostridium pasteurianum rubredoxin obtained from modeling and dynamics simulations of molecular variants

Rubredoxins are small electron transfer proteins containing one iron atom at their active site. The rubredoxin from the anaerobic bacterium Clostridium pasteurianum has been subjected to molecular dynamics studies starting from the minimized solvated structure. The results of the simulations have been compared with identical ones carried out with selected mutated forms of the protein obtained by molecular modeling. Surface residues, which are highly conserved among rubredoxins and close to the cysteine ligands, can be replaced by glutamates, i.e. long chain carboxylates. The main structural consequence is a shift of the protein backbone bearing conserved aromatic residues. Reciprocally, substitution of the aromatic residue closest to the iron atom shifts the cysteine-containing peptide fragments. These observations have been related to the changes in electron transfer and redox properties previously measured for this set of rubredoxin molecular variants. Received: 16 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998