Search results for " Algebra"

A coupled cluster study of the 1 1A1g and 1 1B2u states of benzene

1998

A theoretical investigation of the equilibrium structures and harmonic frequencies of the 1 1A1g and 1 1B2u states of benzene is presented. The performance of coupled cluster singles (CCS), the recently proposed CC2 model, and coupled cluster singles and doubles (CCSD) is compared. The CC2 ground and excited states frequencies are a significant improvement of the CCS results and are relatively close to the CCSD results. A comparative analysis of the vibrations in the two electronic states of both C6H6 and C6D6 is presented. The reliability of predicted shifts in harmonic frequencies between the two states and isotopic shifts is estimated on the basis of the convergence in the CCS, CC2, and …

Vibrational Spectra of Polyatomic Molecules through an Algebraic Approach

1987

The study of molecular oscillators may be performed with algebraic methods based upon dynamical chains and their realization in terms of boson operators. From the dynamical algebra U(p+1) for p equivalent oscillators, associated with stretching modes, the local, pseudo-normal and normal limits are obtained through appropriate subgroup chains and various realizations of the U(p+1) generators. Similar technics can be applied to bending modes. Application to XY4 molecules will be presented.

Rovibrational interactions in the local-mode limit. The (n000) stretching overtone bands of spherical tops.

1993

Topological virtual screening: a way to find new anticonvulsant drugs from chemical diversity.

2003

A topological virtual screening (tvs) test is presented, which is capable of identifying new drug leaders with anticonvulsant activity. Molecular structures of both anticonvulsant-active and non active compounds, extracted from the Merck Index database, were represented using topological indexes. By means of the application of a linear discriminant analysis to both sets of structures, a topological anticonvulsant model (tam) was obtained, which defines a connectivity function. On the basis of this model, 41 new structures with anticonvulsant activity have been identified by a topological virtual screening.

Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

2021

An individual’s reaction time data to visual stimuli have usually been represented in Experimental Psychology by means of an ex-Gaussian function. In most previous works, researchers have mainly aimed at finding a meaning for the parameters of the ex-Gaussian function which are known to correlate with cognitive disorders. Based on the recent evidence of correlations between the reaction time series to visual stimuli produced by different individuals within a group, we go beyond and propose a Physics-inspired model to represent the reaction time data of a coetaneous group of individuals. In doing so, a Maxwell–Boltzmann-like distribution appeared, the same distribution as for the velocities …

Adaptive Vocabulary Learning Environment for Late Talkers

2016

The main aim of this research is to provide children who have an early language delay with an adaptive way to train their vocabulary taking into account individuality of the learner. The suggested system is a mobile game-based learning environment which provides simple tasks where the learner chooses a picture that corresponds to a played back sound from multiple pictures presented on the screen. Our basic assumption is that the more similar the concepts (in our case, words) are, the harder the recognition task is. The system chooses the pictures to be presented on the screen by calculating the distances between the concepts in different dimensions. The distances are considered to consist o…

Have Fun with Math and Music!

2019

If abstraction makes mathematics strong, it often makes it also hard to learn, if not discouraging. If math pedagogy suffers from the lack of engaging strategies, the pedagogy of mathematical music theory must deal with the additional difficulty of double fields and double vocabulary. However, games and interdisciplinary references in a STEAM framework can help the learner break down complex concepts into essential ideas, and gain interest and motivation to approach advanced topics. Here we present some general considerations, followed by two examples which may be applied in a high-school or early college level course. The first is a musical application of a Rubik’s cube, the CubeHarmonic, …

Accurate molecular geometries of the protonated water dimer

2000

The equilibrium geometry of the protonated water dimer, H5O2+, was studied using Moller–Plesset perturbation theory and coupled-cluster theory. Constrained geometry optimizations were carried out for the C2 and Cs symmetric structures within the counterpoise framework and near the limit of a complete basis set. In the constrained optimization, the degrees of freedom of the complex are reduced to an intrafragmental distortion and an interfragmental coordinate, making the procedure tractable for large basis sets and explicitly correlated linear r12 methods. The energy of the stationary point of C2 symmetry was found to be 1.2 kJ mol−1 below the energy of the Cs structure.

New-stage discharge relationship for weirs of finite crest lenght

2014

AbstractThe flow process of weirs of finite crest length is analyzed on the basis of the dimensional analysis and incomplete self-similarity theory. The crest length is incorporated in the functional stage-discharge relationship for weirs of finite crest length. The theoretically deduced stage-discharge formula was then calibrated using the experimental data compiled in this research. According to the current experimental data it is also concluded that the performance of the proposed stage-discharge formula is better than the previous dimensional stage-discharge formulae. Also, the proposed stage-discharge formula is applicable for all types of the weirs, i.e., long-crested, broad-crested, …

OpenMolcas: From Source Code to Insight

2019

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multico…