1,377 research outputs found
Sum rules related to third-order properties: a numerical check
No full textAlthough electrodynamics is formally invariant in a gauge transformation, the values of some physical quantities, e.g., magnetic properties, depend on the approximation employed to calculate them. The conditions for gauge independence of third-rank tensor properties that describe the response of a molecule in the presence of three perturbations, that is, external electric and magnetic field, and intramolecular nuclear magnetic dipoles, are discussed. The relationships for invariance of the physical properties to a gauge translation are exactly the same as the constraints for charge conservation. They are expressed in terms of second-rank response properties, namely electric polarizabilities and electric shielding at the nuclei. An extended numerical test has been carried out to determine the Hartree-Fock limit for a series of quantities entering the gauge-invariance sum rules
Calculation of third-rank molecular hypermagnetizabilities by continuous transformation of the origin of the current density
No full textThe third-rank hypermagnetizabilities of three small molecules have been evaluated at the Hartree-Fock level of accuracy within the conventional common-origin approach as well as alternative procedures formally based on continuous transformation of the origin of the electronic current density induced by a perturbing electromagnetic field. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test (i) to assess the practicality of distributed origin methods whereby the diamagnetic contribution to the current density is formally annihilated, and (ii) to estimate the degree of convergence of diamagnetic and paramagnetic contributions to tensor components. It is shown that two nice features characterize the computational scheme adopted in this study: (i) the results depend only linearly on a shift of origin; (ii) a permutational symmetry condition of tensor indices yields a natural criterion for the near-Hartree-Fock quality of computed values
High Order Approximation to Caputo Derivative On Graded Mesh and Time-Fractional Diffusion Equation for Non-smooth Solutions
No full textIn this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed. At first, we employ a numerical algorithm based on the Lagrange polynomial interpolation to approximate the Caputo derivative on the non-uniform mesh. Then truncation error rate and the optimal grading constant of the approximation on a graded mesh are obtained as min{4 - a, ra} and 4-a/a , respectively, where α ∈ (0, 1) is the order of fractional derivative and r ≥ 1 is the mesh grading parameter. Using this new approximation, a difference scheme for the Caputo-type time-fractional diffusion equation on the graded temporal mesh is formulated. The scheme proves to be uniquely solvable for general r. Then we derive the unconditional stability of the scheme on uniform mesh. The convergence of the scheme, in particular for r = 1, is analyzed for non-smooth solutions and concluded for smooth solutions. Finally, the accuracy of the scheme is verified by analyzing the error through a few numerical examples.The first author acknowledges the support provided by the Council of Scientific and Industrial Research, India, under grant number
09/086(1483)/2020-EMR-I. The fourth author acknowledges the support provided by the SERB, a statutory body of DST,
India, under the award SERB–POWER fellowship (grant
number SPF/2021/000103)
Thomas-Reiche-Kuhn populations in alkanes
No full textAtomic populations in a molecule have been defined via the 'Thomas-Reiche-Kuhn sum rule for oscillator strengths written within the acceleration gauge. These atomic populations are related to nuclear electric shieldings, i.e., to geometrical derivatives of electric dipole moment, and can therefore be connected with observable infrared intensities. A number of relationships can be considered to test a priori the quality of calculated electronic charges and to assess their physical meaning. It is shown via extended numerical tests on the first members of the alkane series that the Thomas-Reiche-Kuhn populations are consistent with a (small) polarity C+-H- of carbon-hydrogen bond in methane, for which a bond dipole moment can be exactly defined. Although the idea of bond dipole cannot be extended to the C-H fragments belonging to other alkane molecules in the absence of local C-3v symmetry, the calculations prove that the same electron charge polarization should characterize the whole homologous series. (C) 1999 Elsevier Science B.V. All rights reserved
Theoretical study of magnetic properties of ammonia molecule in nonuniform magnetic field
No full textThe interaction Hamiltonian within the Bloch gauge for the potentials of the electromagnetic field has been used to define magnetic multipole moment operators and operators for the magnetic field of electrons acting on the nuclei of a molecule in the presence of nonhomogeneous external magnetic field. Perturbation theory has been applied to evaluate the induced electronic moments and magnetic field at the nuclei. Multipole magnetic susceptibility and nuclear magnetic shielding tensors have been introduced to describe the contributions arising in nonuniform fields, and their origin dependence has been analyzed. Extended numerical tests on the ammonia molecule in a static, nonuniform magnetic field have been carried out, using the random-phase approximation within the framework of accurate Hartree-Fock zero-order wavefunctions, and allowing for both angular momentum and torque formalisms in the calculation of paramagnetic contributions
Canadian English-Language Children's Songs in Toronto Schools: A Comparison of 1959-64 and 1988 Collections
No full textVirginia Caputo examine la transmission orale des chansons enfantines. Par une comparaison des chansons enregistrées pendant la période 1959-64 et un corpus enregistré aux mêmes écoles en 1988, elle analyse la stabilité et l’évolution caractérisant cette tradition musicale à travers le temps. Elle détermine que ces chansons reflètent les attitudes des enfants envers la classe sociale, le genre, le pouvoir, et l’ethnicité
The contribution of psychology to research on congenital anomalies (CAs): computer-aided thematic analysis of international scientific literature
No full textThe paper aims at exploring the contribution of psychology-related research on Congenital Anomalies (CAs) from the analysis of international scientific literature. This could provide further knowledge to be integrated with biomedical evidence and contribute to the understanding of the risk and the protective factors which, according to a biopsychosocial perspective, may improve prevention strategies. A comprehensive search of academic literature was conducted on PsychINFO database resulting in 116 scientific publications published from 1931 to 2013. A qualitative software-based thematic analysis was carried out on the publications’ abstracts to explore the main themes relating to CAs as provided by psychology-related research. Overall, * Corresponding Author E-mail: [email protected]. Complimentary Contributor Copy 92 Andrea Caputo results highlighted a rapid increase of scientific psychology-related research on CAs after 2000, thus confirming the relevant attention to these diseases in healthcare policies over the last years. Five different thematic domains emerged which respectively refer to: schizophrenia (23.62%), psychiatric drugs (16.2%), parenting (25%), developmental neuropsychology (17.36%), and relationship with healthcare workers (17.82%). In sum, with regard to the prenatal/perinatal period, psychology-related research focuses on pregnancy-related factors such as maternal risk due to psychopathological conditions, prenatal consultation and more widely healthcare workers’ diagnosis/communication skills about CAs. Instead, the postnatal period deals with cognitive and emotional development of children with CAs by promoting parental skills and detecting rehabilitation strategies for improving residual cognitive abilities. Then, the analysis on the main trends of psychology-related research on CAs highlighted two issues. The first one concerns the shift of psychological science between psychopathology and disability as research objects. The second issue pertains to the different social impacts of CAs and the relevance of both health and family care
Shielding polarizabilities via continuous transformation of the origin of the current density in the set of small molecules: H2O2, F-2, H2C2, H2CO, NH3, HCN, and HNC
No full textA procedure, based on a continuous transformation of the origin of the (quantum mechanical) current density that sets the diamagnetic contribution to zero (CTOCD-DZ ) all over the molecular domain, is applied to determine shielding polarizabilities to first order in a perturbing electric field. In any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the CTOCD-DZ magnetic shielding polarizability are origin independent, and the constraints for charge and current conservation are exactly satisfied. The effects of a static uniform electric field on the nuclear magnetic resonance (NMR) shielding of H2O2, F-2, H2C2, H2CO, NH3, HCN, and HNC molecules have been investigated within the CTOCD-DZ method, and compared with the conventional results evaluated via the same basis sets, and with theoretical results taken from the literature. (C) 2000 American Institute of Physics. [S0021- 9606(00)30714-0]
Calculation of magnetic properties of HF, H2O, NH3, and CH4 molecules using a longitudinal gauge for the vector potential
No full textA transformation of the transverse Coulomb vector potential was implemented to calculate molecular magnetic properties via the random-phase approximation (RPA) within the framework of a ́ ́longitudinal gauge. ́ ́ In this gauge, the diamagnetic contribution to magnetic susceptibility is a tensor with equal diagonal components as in atoms, irrespective of molecular symmetry, whereas diagonal and average diamagnetic contributions to the nuclear magnetic shielding are the same as in the Coulomb gauge. Near-Hartree-Fock magnetic susceptibility and nuclear magnetic shielding tensors were evaluated for a set of small molecules, HF, H2O, NH3, and CH4, employing extended Gaussian basis sets. The peculiar features of the longitudinal gauge, and the fulfillment of a series of sum rules involving the virial operator, which must be satisfied to guarantee gauge invariance of total magnetic tensors, were exploited to check the degree of convergence of theoretical values and to estimate the corresponding Hartree-Fock limit for the properties
Some mathematical properties of gauge transformations with respect to the Coulomb gauge: Variational analysis of an energy functional
No full textAs gauge invariance of computed magnetic properties, usually partitioned into diamagnetic and paramagnetic terms, is not achieved within the algebraic approximation, unless ad hoc techniques are adopted, a general variational treatment is analyzed, attempting to minimize the term more difficult to evaluate accurately, i.e., the paramagnetic contribution to magnetic susceptibility, by means of a gauge transformation. It is shown that an absolute minimum in a variational sense cannot be determined a priori. However, a local minimum of the paramagnetic contribution to magnetic susceptibility can be arrived at by employing general gauge transformations of polynomial form
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