Search results for "QUANTUM MECHANICS"

Improved embedded molecular cluster model

2002

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the pr…

Experimental evidence for fractional time evolution in glass forming materials

2002

The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless…

Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach.

2013

A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin…

Linear scaling exchange gradients for Hartree–Fock and hybrid density functional theory

2000

Abstract A new method is introduced which allows to form the exchange part of self-consistent field energy gradients in a way which scales linearly with molecular size for molecules with a non-vanishing HOMO–LUMO gap. This is not only important for Hartree–Fock but as well for the popular hybrid density functional theory methods. The method preserves the optimized integral-driven structure of conventional direct methods. Efficiency and scaling behavior of the new method are illustrated for DNA fragments.

A Discussion of Some Problems Associated with the Quantum Mechanical Treatment of Open-Shell Molecules

2003

Extension of Walsh's rules to more general systems

1972

It is demonstrated that location of hydrogen atoms within bonding distance of a simple triatomic molecule can alter the order of energy levels relative to that of the parent system without significantly changing the behavior of the orbital energies under geometrical variation. As a result the ground state electronic configurations of H n AB2 systems often differ from those of triatomics with the same number of electrons and this fact is shown to be directly responsible for the existence of such distinctive geometrical structures as those possessed by cyclopropane, cyclopropyl and allyl cations and cyclopropene. Thus the familiar prescription of Walsh's rules which states that isoelectronic …

Chiral expansion of the nucleon mass to order q^6

2006

We present the results of a complete two-loop calculation at order q^6 of the nucleon mass in manifestly Lorentz-invariant chiral perturbation theory. The renormalization is performed using the reformulated infrared renormalization, which allows for the treatment of two-loop integrals while preserving all relevant symmetries, in particular chiral symmetry.

Form factors of the isovector scalar current and the ηπ scattering phase shifts

2015

33 pages.- 14 figures.- v2: Some clarifications and corrections of typos

Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure…

2020

We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($\chi$PT). The polarized VVCS contains a wealth of information on the spin structure of the nucleon which is relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of the polarized VVCS amplitudes $S_1(\nu, Q^2)$ and $S_2(\nu, Q^2)$, and the corresponding polarized spin structure functions $g_1(x, Q^2)$ and $g_2(x,Q^2)$. Our results for the moments of polarized structure functions, partially related to different spin polarizabilities, are compared to other th…

Process-independent strong running coupling

2016

We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…