D. Van Neck

Vibrational modes in partially optimized molecular systems

In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem. 65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di-n-octyl-ether.

An extended hindered-rotor model with incorporation of Coriolis and vibrational-rotational coupling for calculating partition functions and derived quantities

Large-amplitude motions, particularly internal rotations, are known to affect substantially thermodynamic functions and rate constants of reactions in which flexible molecules are involved. Up to now all methods for computing the partition functions of these motions rely on the Pitzer approximation of more than 50 years ago, in which the large-amplitude motion is treated in complete independence of the other (vibrational) degrees of freedom. In this paper an extended hindered-rotor model (EHR) is developed in which the vibrational modes, treated harmonically, are correctly separated from the large-amplitude motion and in which relaxation effects (the changes in the kinetic-energy matrix and potential curvature) are taken into account as one moves along the large-amplitude path. The model also relies on a specific coordinate system in which the Coriolis terms vanish at all times in the Hamiltonian. In this way an increased level of consistency between the various internal modes is achieved, as compared with the more usual hindered-rotor (HR) description. The method is illustrated by calculating the entropies and heat capacities on 1,3-butadiene and 1-butene (with, respectively, one and two internal rotors) and the rate constant for the addition reaction of a vinyl radical to ethene. We also discuss various variants of the one-dimensional hindered-rotor scheme existing in the literature and its relation with the EHR model. It is argued why in most cases the HR approach is already quite successful.

Nuclear symmetry energy and the neutron skin in neutron-rich nuclei

The symmetry energy for nuclear matter and its relation to the neutron. skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.

Cartesian formulation of the mobile block Hessian approach to vibrational analysis in partially optimized systems

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.

The Significance of Parameters in Charge Equilibration Models

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

Calculating Reaction Rates with Partial Hessians: Validation of the Mobile Block Hessian Approach.

In an earlier paper, the authors have developed a new method, the mobile block Hessian (MBH), to accurately calculate vibrational modes for partially optimized molecular structures [J. Chem. Phys. 2007, 126 (22), 224102]. The proposed procedure remedies the artifact of imaginary frequencies, occurring in standard frequency calculations, when parts of the molecular system are optimized at different levels of theory. Frequencies are an essential ingredient in predicting reaction rate coefficients due to their input in the vibrational partition functions. The question arises whether the MBH method is able to describe the chemical reaction kinetics in an accurate way in large molecular systems where a full quantum chemical treatment at a reasonably high level of theory is unfeasible due to computational constraints. In this work, such a validation is tested in depth. The MBH method opens a lot of perspectives in predicting accurate kinetic parameters in chemical reactions where the standard full Hessian procedure fails.

Self-consistent solution of the second-order Dyson equation for single-particle propagators, with application to the spectral functions of 48Ca

Abstract We present a new method to describe the fragmentation of single-particle strength in the framework of the Green function formalism. By means of an iterative scheme, we are able to construct a self-consistent solution of the Dyson equation up to second order in the interaction. Damping effects, such as the broadening of the spectral function for deep-lying hole states, show up in a natural way. We apply the formalism to a schematic model and to the case of the doubly-closed shell nucleus 48Ca.

Solving the Richardson equations for fermions

Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain(Dated: February 4, 2008)Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constantinteraction strength can be calculated by solving a set of non-linear coupled equations. However,in the case of Fermions these equations lead to singularities which made them very hard to solve.This letter explains how these singularities can be avoided through a change of variables makingthe Fermionic pairing problem numerically solvable for arbitrary single particle energies and degen-eracies.

Pion and photon induced reactions on the nucleon in a unitary model

Abstract We present a relativistic calculation of pion scattering, pion photoproduction and Compton scattering on the nucleon in the energy region of the Δ-resonance (upto 450 MeV photon lab energy), in a unified framework which obeys the unitarity constraint. It is found that the recent data on the cross section for nucleon Compton scattering determine accurately the parameters of the electromagnetic nucleon-Δ coupling. The pion-photoproduction partial-wave amplitudes, calculated with parameters fitted to the pion-nucleon and Compton scattering, agree well with the recent Arndt analysis.

Dislocation mechanism of deuterium retention in tungsten under plasma implantation.

We have developed a new theoretical model for deuterium (D) retention in tungsten-based alloys on the basis of its being trapped at dislocations and transported to the surface via the dislocation network with parameters determined by ab initio calculations. The model is used to explain experimentally observed trends of D retention under sub-threshold implantation, which does not produce stable lattice defects to act as traps for D in conventional models. Saturation of D retention with implantation dose and effects due to alloying of tungsten with, e.g. tantalum, are evaluated, and comparison of the model predictions with experimental observations under high-flux plasma implantation conditions is presented.