Search results for "Numerical differentiation"
showing 7 items of 7 documents
Analytic CCSD(T) second derivatives
1997
A general-purpose implementation of analytic CCSD(T) second derivatives is presented. Its applicability is demonstrated by calculations of vibration-rotation interaction constants for the astrophysically important molecule cyclopropenylidene (C3H2) in which the required cubic force constants have been determined by numerical differentiation of analytically evaluated second derivatives of the energy.
Inverse Problems Light: Numerical Differentiation
2001
(2001). Inverse Problems Light: Numerical Differentiation. The American Mathematical Monthly: Vol. 108, No. 6, pp. 512-521.
Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory.
2011
In this work, we present relativistic corrections to first-order electrical properties obtained using fourth-order direct perturbation theory (DPT4) at the Hartree-Fock level. The considered properties, i.e., dipole moments and electrical-field gradients, have been calculated using numerical differentiation techniques based on a recently reported DPT4 code for energies [S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)]. For the hydrogen halides HX, X=F, Cl, Br, I, and At, we study the convergence of the scalar-relativistic contributions by comparing the computed DPT corrections to results from spin-free Dirac-Hartree-Fock calculations. Furthermore, since in the DPT series spin-…
Grafiska integrēšana un diferencēšana. Neperiodiskas līknes nolīdzinājuma atrašana
1931
Saturs: Funkcionāls sakars, tā attēlošana 3 Empirisks un racionāls nolīdzinājums 3 Pieskares konstrukcijas 6 Grafiska integrēšana 7 Grafiska diferencēšana 9 Līkņu veidi un nolīdzinājumi 10 Līkņu nolīdzinājumi pārveidotā koordinātu sistēmā 11 Deformācija 13 Līkņu pazīmes 13 Atsevišķi nolīdzinājumu veidi 17 Nolīdzinājuma atrašana, ja dots līknes zars 20 Piemēri 21 Nolīdzinājuma atrašana, kad doti līknes visi zari un īpaši punkti 25
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…
COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
2005
We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.
Extension of the Launay Quantum Reactive Scattering Code and Direct Computation of Time Delays.
2019
Scattering computations, particularly within the realm of molecular physics, have seen an increase in study since the development of powerful quantum methods. These dynamical processes can be analyzed via (among other quantities) the duration of the collision process and the lifetime of the intermediate complex. We use the Smith matrix Q = -iℏS†dS/dE calculated from the scattering matrix S and its derivative with respect to the total energy. Its real part contains the state-to-state time delays, and its eigenvalues give the lifetimes of the metastable states [ Smith Phys. Rev. 1960 , 118 , 349 - 356 ]. We propose an extension of the Launay HYP3D code [ Launay and Le Dourneuf Chem. Phys. Let…