309,055 research outputs found
Semiclassical reaction rate constant calculations: investigation of anharmonicity and quantum effects
Get PDFSemiclassical transition state theory (SCTST) is a relatively simple method for the computation from first principles of reactive rate constants, including quantum effects while accounting for anharmonicity and the coupling between reactive and bound modes.[1-3] In this talk, I will illustrate how we have developed this technique for practical applications[4-7] involving the study of phenomena like kinetic isotope effects, heavy atom tunneling, and elusive conformer lifetimes.[5,6,8]
While many approximate reaction rate theories reduce to the parabolic barrier estimate for the tunneling correction at high temperatures, SCTST, which is based on vibrational perturbation theory (VPT2), gives the exact limit when one considers the leading order term in an expansion of powers of ħ2 of the tunneling transmission coefficient.[9-11] Our investigation of molecular reactive systems assesses the importance of the non-linear corrections to the parabolic barrier estimate of the transmission coefficient. When the reaction barrier is significantly anharmonic, it is mandatory to account for non-linear corrections; otherwise, the transmission coefficient overlooks a high-temperature regime which may be dominated by quantum reflection.[12] These results highlight the importance of having a theory such as SCTST that includes the correct high-temperature limit.
[1] W.H. Miller Faraday Discuss. Chem. Soc. 62, 40 (1977).
[2] W.H. Miller J. Chem. Phys. 62, 1899 (1975)
[3] R. Hernandez et al., Chem. Phys. Lett. 214, 129 (1993).
[4] C. Aieta, F. Gabas, M. Ceotto, J. Phys. Chem. A 120, 4853 (2016).
[5] C. Aieta F. Gabas, M. Ceotto, J. Chem. Theory Comput. 15, 2142 (2019).
[6] G. Mandelli, C. Aieta, M. Ceotto J. Chem. Theory Comput. 18, 623 (2022).
[7] J.R. Barker, MultiWell-2023 software suite; University of Michigan: Ann Arbor, Michigan, USA, 2023; http://clasp-research.engin.umich.edu/multiwell/
[8] G. Mandelli, L. Corneo, C. Aieta J. Phys. Chem. Lett. 14, 9996 (2023).
[9] E. Pollak, J. Cao, Phys. Rev. A, 107, 022203 (2023).
[10] E. Pollak, S Upadhyayula J. Chem. Phys. 160, (2024).
[11] E. Pollak J. Chem. Phys. 160, 150902 (2024).
[12] C. Aieta, M. Ceotto, E. Pollak, in preparation
Comparison between different Gaussian series representations of the imaginary time propagator
No full textA useful approximation for the thermal operator exp (-β Ĥ) is based on its representation in terms of either frozen or thawed Gaussian states. Such approximate representations are leading-order terms in respective series representations of the thermal operator. A numerical study of the convergence properties of the frozen Gaussian series representation has been recently published. In this paper, we extend the previous study to include also the convergence properties of the more expensive thawed Gaussian series representation of the thermal operator. We consider three different formulations for the series representation and apply them to a quartic double-well potential to find that the thawed Gaussian series representation converges faster than the frozen Gaussian one. Further analysis is presented as to the convergence properties and the numerical efficiency of three different thawed Gaussian series representation. The unsymmetrized form converges most rapidly, however, the lower order approximations of the symmetrized forms are more accurate. Comparison with a standard discretized path-integral evaluation demonstrates that the Gaussian based perturbation series representation converges much faster. © 2010 The American Physical Society
Lower Bounds for Coulombic Systems
Get PDFAs of the writing of this paper, lower bounds are not a staple of quantum chemistry computations and for good reason. All previous attempts at applying lower bound theory to Coulombic systems led to lower bounds whose quality was inferior to the Ritz upper bounds so that their added value was minimal. Even our recent improvements upon Temple's lower bound theory were limited to Lanczos basis sets and these are not available to atoms and molecules due to the Coulomb singularity. In the present paper, we overcome these problems by deriving a rather simple eigenvalue equation whose roots, under appropriate conditions, give lower bounds which are competitive with the Ritz upper bounds. The input for the theory is the Ritz eigenvalues and their variances; there is no need to compute the full matrix of the squared Hamiltonian. Along the way, we present a Cauchy-Schwartz inequality which underlies many aspects of lower bound theory. We also show that within the matrix Hamiltonian theory used here, the methods of Lehmann and our recent self-consistent lower bound theory (J. Chem. Phys. 2020, 115, 244110) are identical. Examples include implementation to the hydrogen and helium atoms
Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems
No full textA continuum limit frozen Gaussian approximation is formulated for the reduced thermal density matrix for dissipative systems. The imaginary time dynamics is obtained from a novel generalized Langevin equation for the system coordinates. The method is applied to study the thermal density in a double well potential in the presence of Ohmic-like friction. We find that the approximation describes correctly the delocalization of the density due to quantization of the vibrations in the well. It also accounts for the friction induced reduction of the tunneling density in the barrier region. © 2012 American Institute of Physics
Lower bounds to eigenvalues of the Schrödinger equation by solution of a 90-y challenge
No full textThe Ritz upper bound to eigenvalues of Hermitian operators is essential for many applications in science. It is a staple of quantum chemistry and physics computations. The lower bound devised by Temple in 1928 [G. Temple, Proc. R. Soc. A Math. Phys. Eng. Sci. 119, 276–293 (1928)] is not, since it converges too slowly. The need for a good lower-bound theorem and algorithm cannot be overstated, since an upper bound alone is not sufficient for determining differences between eigenvalues such as tunneling splittings and spectral features. In this paper, after 90 y, we derive a generalization and improvement of Temple’s lower bound. Numerical examples based on implementation of the Lanczos tridiagonalization are provided for nontrivial lattice model Hamiltonians, exemplifying convergence over a range of 13 orders of magnitude. This lower bound is typically at least one order of magnitude better than Temple’s result. Its rate of convergence is comparable to that of the Ritz upper bound. It is not limited to ground states. These results complement Ritz’s upper bound and may turn the computation of lower bounds into a staple of eigenvalue and spectral problems in physics and chemistry
Self-consistent theory of lower bounds for eigenvalues
No full textA rigorous practically applicable theory is presented for obtaining lower bounds to eigenvalues of Hermitian operators, whether the ground state or excited states. Algorithms are presented for computing "residual energies"whose magnitude is essential for the computation of the eigenvalues. Their practical application is possible due to the usage of the Lanczos method for creating a tridiagonal representation of the operator under study. The theory is self-consistent, in the sense that a lower bound for one state may be used to improve the lower bounds for others, and this is then used self-consistently until convergence. The theory is exemplified for a toy model of a quartic oscillator, where with only five states the relative error in the lower bound for the ground state is reduced to 6 · 10-6, which is the same as the relative error of the least upper bound obtained with the same basis functions. The lower bound method presented in this paper suggests that lower bounds may become a staple of eigenvalue computations
Denúncia contra Moisés Pollak e Nielse Fernandes
No full textÉ anexo no relatório produzido pelo GT 2 - Operação Condor presente no Relatório da Comissão Estadual da Verdade do Paraná - Teresa Urban.Denúncia realizada pelo Procurador da Justiça Militar, Alceu Alves dos Santos, contra Moisés Pollak e Nielse Fernandes por compra e venda de armas para o MR-8.Ministério da Justiça MilitarÓtim
Lower Bounds for Nonrelativistic Atomic Energies
Get PDFA recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory
Denúncia contra Moisés Pollak e Nielse Fernandes
No full textÉ anexo no relatório produzido pelo GT 2 - Operação Condor presente no Relatório da Comissão Estadual da Verdade do Paraná - Teresa Urban.Denúncia realizada pelo Procurador da Justiça Militar, Alceu Alves dos Santos, contra Moisés Pollak e Nielse Fernandes por compra e venda de armas para o MR-8.Ministério da Justiça MilitarÓtim
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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