16 research outputs found

    Fast hybrid density-functional computations using plane-wave basis sets

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    A new, very fast, implementation of the exact (Fock) exchange operator for electronic-structure calculations within the plane-wave pseudopotential method is described and carefully validated. Our method combines the recently proposed adaptively compressed exchange approach, to reduce the number of times the exchange is evaluated in the self-consistent loop, with an orbital localization procedure that reduces the number of exchange integrals to be computed at each evaluation. The new implementation, already available in the Quantum ESPRESSO distribution, results in a speedup that is never smaller than 3\u20134 and that increases with the size of the system, according to various realistic benchmark calculations

    Mathematical Methods in Quantum Chemistry

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    The field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for N electrons being a partial differential equation on R3N ), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of densityfunctional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations

    Light-triggered unidirectional molecular rotors: theoretical investigations on conformational dynamics and laser control

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    Two light-triggered molecular motors based on chiral overcrowded alkenes have been studied in the electronic ground state: a second-generation motor (2) and a redesigned motor (3). A semiempirical Monte-Carlo-type of conformational search has been implemented to find local minima in the ground state PESs of 2 and 3, which then have been reoptimized by ab-initio calculations. While in 3 only the four isomers of the rotary cycle are found, new isomers have been found in the case of 2, leading to different reaction pathways for the thermal helix-inversion. TSs for all the possible thermal conversions have been also computed. The obtained E_a values are in excellent agreement with those reported in the literature. The simple model BCH (core unit of many motors) has been studied from a quantum chemical and quantum dynamical point of view. The controversial nature of BCH's electronic transitions has been investigated using high-level ab-initio multiconfigurational and perturbational methods, including the development of a basis set specific to the problem at hand. The first two excited states of Bu-symmetry ((pi,3s)-Rydberg and (pi,pi*), respectively) are resolved at the MS-CASPT2-level of theory, providing vertical transition energies and oscillator strengths matching the experimental values. In addition, the origin of the (p,p*)-band is computed, yielding an energy value well below the FC-value of the (pi,3s_R)-maximum, explaining this band's unexpected intensity. Finally, a one-dimensional PES along BCH's torsional coordinate has been computed at the MS-CASPT2-level of theory, and quantum dynamical simulations have been carried out. These have focused on the obtainment of control laser fields that are able to trigger unidirectionality even in the symmetric PES (as opposed to 2 and 3 system). Optimal control strategies as well as the intuitive IR+UV-scheme both succeeded in achieving sustained, unidirectional torsional motion of BCH in the excited state

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
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