Search results for "Quantum Mechanic"
showing 10 items of 2483 documents
(H, ρ)-induced dynamics and the quantum game of life
2017
Abstract We propose an extended version of quantum dynamics for a certain system S , whose evolution is ruled by a Hamiltonian H, its initial conditions, and a suitable set ρ of rules, acting repeatedly on S . The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of H, ρ as well as on the initial conditions. After a general discussion on this (H, ρ)-induced dynamics, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.
On groups having a p-constant character
2020
Let G G be a finite group, and p p a prime number; a character of G G is called p p -constant if it takes a constant value on all the elements of G G whose order is divisible by p p . This is a generalization of the very important concept of characters of p p -defect zero. In this paper, we characterize the finite p p -solvable groups having a faithful irreducible character that is p p -constant and not of p p -defect zero, and we will show that a non- p p -solvable group with this property is an almost-simple group.
Getting discriminant functions of antibacterial activity from physicochemical and topological parameters.
2001
Linear discriminant analysis has been demonstrated to be a very useful tool in the selection and design of new drugs. Up to now we have used it through the search of a topological pattern of activity. In this work our goal is to calculate a complete set of physicochemical parameters using semiempirical (quantum chemical) calculations as well as topological indices (TIs) and try to find out any discriminant function for antibacterial activity through the combined use of both types of descriptors. The physicochemical parameters, such as heat of formation, HOMO, LUMO, dipole moment, polarizability, hyperpolarizability, PM3 generated IR vibrational frequencies, etc., were calculated using PM3 H…
Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
2009
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.
Coupled-cluster theory for atoms and molecules in strong magnetic fields
2015
An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the depende…
NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-…
2021
We report on a formulation and implementation of a scheme to compute NMR shieldings at second-order Moller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed as well as perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field as well as for the computed NMR shieldings, before we illustrate the applicability of our CD based GIAO-MP2 scheme in calculations involving up to about one hundred atoms and more than one thousand basis functions.
Nuclear quantum effects in liquid water from path-integral simulations using anab initioforce-matching approach
2014
We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterized by force-matching to density functional theory-based molecular dynamics simulations. The resulting effective potentials provide an inexpensive replacement for direct ab inito molecular dynamics simulations and allow efficient simulation of nuclear quantum effects. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals…
An ab initio CI study on the rotational barrier of the allyl anion
1986
All-electron and pseudopotential non-empirical calculations have been performed on C 2v and C s (syn, anti) allyl anion conformations. Using a double-zeta valence-shell basis set within the Epstein-Nesbet definition of the unperturbed Hamiltonian, a value about 19 kcal/mol is found for the barrier to rotation of the allyl anion. This value is the theoretical value obtained with greater accuracy, and the lowest one for the rotational barrier.
High-Resolution Spectroscopy and Structure of Osmium Tetroxide. A Benchmark Study on 192OsO4
2012
Osmium tetroxide (OsO(4)) is a heavy tetrahedral molecule that constitutes a benchmark for quantum chemistry calculations. Its favorable spin statistics (due to the zero nuclear spin of oxygen atoms) is such that only A(1) and A(2) (T(d) symmetry) rovibrational levels are allowed, leading to a dense but quite easily resolvable spectrum. We reinvestigate here the ν(1)/ν(3) stretching fundamental (940-980 cm(-1)) dyad region and perform new assignments and effective Hamiltonian parameter fits for the main isotopologue ((192)OsO(4)). We also investigate the ν(2)/ν(4) bending fundamental dyad (300-360 cm(-1)) for the first time and perform a preliminary analysis. New experimental data have been…
On the approximation of the similarity-transformed Hamiltonian in single-reference and multireference coupled cluster theory
2012
Abstract We consider the recursive single commutator (RSC) approximation of the Baker–Campbell–Hausdorff expansion introduced by Yanai and Chan [T. Yanai, G.K.-L. Chan, J. Chem. Phys. 124 (2006) 194106] and apply it in order to approximate the similarity transformation of the Hamiltonian in both traditional and unitary coupled cluster theory. The equilibrium bond distance, harmonic vibrational frequency, and anharmonic constant of H2, HF, N2, CuH, and Cu2 were computed using the coupled cluster approach with single and double excitations (CCSD) and CCSD with the RSC approximation of the similarity-transformed Hamiltonian (CCSD-RSC). Our results demonstrate that the RSC approximation introdu…