Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Interaccions moleculars: correcció de l'error de superposició de base i propietat de les funcions flotants

A primary interest of this thesis is to obtain a powerful tool for determining structural properties, electrical and reactivity of molecules. A second interest is the study of fundamental error based on complex overlay of bridge hydrogen. One way to correct this error, using Counterpoise correction proposed by Boys and Bernardi. Usually the Counterpoise correction is applied promptly on the geometries previously optimized. Our goal was to find areas of potential which had all the points fixed with CP. These surfaces have a minimum corresponding to a surface other than corrected, ie, the geometric parameters will be different. The curvature of this minimum will also be different, therefore the vibrational frequency will also change when they are corrected with BSSE. Once constructed these surfaces have been studied various complex. It has also been investigated as the method for calculating the error influenced on the basis superposition.

Estimation of systematic error in an equatorial ocean model using data assimilation

Assimilation of temperature observations into an ocean model near the equator often results in a dynamically unbalanced state with unrealistic overturning circulations. The way in which these circulations arise from systematic errors in the model or its forcing is discussed. A scheme is proposed, based on the theory of state augmentation, which uses the departures of the model state from the observations to update slowly evolving bias fields. Results are summarized from an experiment applying this bias correction scheme to an ocean general circulation model. They show that the method produces more balanced analyses and a better fit to the temperature observations.

Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Power allocation strategies for distributed space-time codes in two-way relay networks

We study a two-way relay network (TWRN), where distributed space-time codes are constructed across multiple relay terminals in an amplify-and-forward mode. Each relay transmits a scaled linear combination of its received symbols and their conjugates,with the scaling factor chosen based on automatic gain control. We consider equal power allocation (EPA) across the relays, as well as the optimal power allocation (OPA) strategy given access to instantaneous channel state information (CSI). For EPA, we derive an upper bound on the pairwise-error-probability (PEP), from which we prove that full diversity is achieved in TWRNs. This result is in contrast to one-way relay networks, in which case a maximum diversity order of only unity can be obtained. When instantaneous CSI is available at the relays, we show that the OPA which minimizes the conditional PEP of the worse link can be cast as a generalized linear fractional program, which can be solved efficiently using the Dinkelback-type procedure.We also prove that, if the sum-power of the relay terminals is constrained, then the OPA will activate at most two relays.

On the Nusselt number for frazil ice growth—a correction to ”Frazil evolution in channels“ by Lars Hammar and Hung-Tao Shen

The growth (melt) rate of frazil ice is governed by heat transfer away from (towards) the ice crystal, which can be represented by the Nusselt number. We discuss choices for the Nusselt number and turbulent length scale appropriate for frazil ice and note an inaccuracy in the study ”Frazil evolution in channels“ by Lars Hammar and Hung-Tao Shen, which has also led to potentially significant errors in several other papers. We correct this error and suggest an appropriate strategy for determining the Nusselt number applicable to frazil ice growth and melting.

Design of delay-tolerant space–time codes with limited feedback

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. Such a timing mismatch may cause rank deficiency of the conventional space-time codes and, thus, performance degradation. One efficient way to overcome such an issue is the delay-tolerant space-time codes (DT-STCs). The existing DT-STCs are designed assuming that the transmitter has no knowledge about the channels. In this paper, we show how the performance of DT-STCs can be improved by utilizing some feedback information. A general framework for designing DT-STC with limited feedback is first proposed, allowing for flexible system parameters such as the number of transmit/receive antennas, modulated symbols, and the length of codewords. Then, a new design method is proposed by combining Lloyd's algorithm and the stochastic gradient-descent algorithm to obtain optimal codebook of STCs, particularly for systems with linear minimum-mean-square-error receiver. Finally, simulation results confirm the performance of the newly designed DT-STCs with limited feedback.

Hamming and Reed-Solomon codes over certain rings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Step by step analyses of Clarke's matrix correction procedure for untransposed three-phase transmission line cases

The correction procedure for Clarke's matrix, considering three-phase transmission line analyzes, is analyzed step by step in this paper, searching to improve the application of this procedure. Changing the eigenvectors as modal transformation matrices, Clarke's matrix has been applied to analyses for transposed and untransposed three-phase transmission line cases. It is based on the fact that Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines considering symmetrical and asymmetrical cases. Because of this, the application of this matrix has been analyzed considering untransposed three-phase transmission lines. In most of these cases, the errors related to the eigenvalues can be considered negligible. It is not true when it is analyzed the elements that are not in main diagonal of the quasi-mode matrix. This matrix is obtained from the application of Clarke's matrix. The quasi-mode matrix is correspondent to the eigenvalue matrix. Their off-diagonal elements represent couplings among the quasi-modes. So, the off-diagonal quasi-mode element relative values are not negligible when compared to the eigenvalues that correspond to the coupled quasi-modes. Minimizing these relative values, the correction procedure is analyzed in detail, checking some alternatives for the correction procedure application.

Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.