Search results for "Third derivative"
showing 3 items of 3 documents
Direct derivative spectrophotometric determination of carbaryl and carbofuran in water samples
1990
Abstract Derivative absorption spectrophotometry has been applied to the direct determination of carbaryl and carbofuran in water samples. The use of the third derivative for carbaryl and the fourth derivative for carbofuran reduces the matrix effect and the seventh derivative provides, in both cases, accurate results for the determination of these pesticides, even working at low dilution levels of the samples. A limit of detection of 4 ppb and a variation coefficient of 0.1% have been obtained for the determination of carbaryl. Carbofuran can be determined with a limit of detection of 5 ppb and a variation coefficient of 0.02%.
Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory
2013
The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections t…
Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order.
2011
A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison …