Search results for "Linear Algebra."
showing 10 items of 552 documents
Towards the Hartree-Fock and coupled-cluster singles and doubles basis set limit: A study of various models that employ single excitations into a com…
2010
In explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] calculations, the basis set incompleteness error in the double excitations is reduced to such an extent that the error in the Hartree–Fock energy and the error in the single excitations become important. Using arguments from perturbation theory to systematically truncate the coupled-cluster singles and CCSD(F12) Lagrangians, a series of coupled-cluster models are proposed and studied that reduce these basis set incompleteness errors through additional single excitations into a complementary auxiliary basis. Convergence with model and size of complementary basis is rapid and there appears to be no need to go beyond seco…
Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
2010
Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help ration…
Natural occupation numbers: When do they vanish?
2013
The non-vanishing of the natural orbital occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' Theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wave function leads, in general, to a power law decay of the natural occupations, whe…
A practicableγ 5-scheme in dimensional regularization
1992
We present a new simpleγ5 regularization scheme. We discuss its use in the standard radiative correction calculations including the anomaly contributions. The new scheme features an anticommutingγ5 which leads to great simplifications in practical calculations. We carefully discuss the underlying mathematics of ourγ5-scheme which is formulated in terms of simple projection operations.
Sum Frequency Generation Spectra from Velocity-Velocity Correlation Functions: New Developments and Applications
2018
At the interface, the properties of water can be rather different from those observed in the bulk. In this chapter we present an overview of our computational approach to understand water structure and dynamics at the interface including atomistic and electronic structure details. In particular we show how Density Functional Theory-based molecular dynamics simulations (DFT-MD) of water interfaces can provide a microscopic interpretation of recent experimental results from surface sensitive vibrational Sum Frequency Generation spectroscopy (SFG). In our recent work we developed an expression for the calculation of the SFG spectra of water interfaces which is based on the projection of the at…
Revised values for the nuclear quadrupole moments ofS33andS35
2014
High-level quantum-chemical calculations are reported for the sulfur electric-field gradients of the CS and SiS molecules. Highly accurate values are obtained in these calculations by using coupled-cluster methods for the treatment of electron correlation together with large atomic-orbital basis sets and by taking into account relativistic effects. The computational results for the sulfur electric-field gradient are used to determine revised values for the $^{33}\mathrm{S}$ and $^{35}\mathrm{S}$ quadrupole moments, thereby taking advantage of available accurate values for the sulfur quadrupole couplings of CS and SiS from the analysis of rotational spectra. The derived values of $\ensuremat…
Modeling vibrating panels excited by a non-homogeneous turbulent boundary layer
2021
Abstract Predicting the vibration response of an elastic structure excited by a turbulent flow is of interest for the civil and military transportation sector. The models proposed in the literature are generally based on the assumption that the turbulent boundary layer (noted TBL in the following) exciting the structure is spatially homogeneous. However, this assumption is not always fulfilled in practice, in particular when the excited area is close to the starting point of the TBL or with curved structures. To overcome this issue, this work proposes to extend two approaches generally used for dealing with homogeneous TBL, namely the spatial and the wavenumber approaches. The extension of …
Atoms and molecules in cavities: A method for study of spatial confinement effects
1995
A general method for solving the problems of spatially confined quantum mechanical systems is proposed. The method works within the framework of the model space approximation. In the case of atoms and molecules trapped into any-shape microscopic cavity (like molecular sieves or fullerenes), the method reduces to a simple modification of the commonly used basis-set quantum chemical calculations. The modification consists of a particular rotation and projection in the model space, leading to solutions better adapted to the boundary conditions of the spatial confinement than the functions that describe the free systems. To illustrate how this method works, it has been applied to the hydrogen a…
Modeling harmonic generation by a degenerate two-level atom
1996
An analytical theory of the generation of high-order harmonics of laser radiation has been developed on the basis of a two-level model atom with degenerate levels. Among other parameters, onset, width, and cutoff of the plateau in the harmonic spectrum are obtained in simple analytical forms that connect the basic problem parameters and permit a transparent interpretation of the mechanism underlying the spectrum formation for this specific case. Selected numerical calculations are reported to corroborate the analytical findings and to investigate other harmonic-spectrum features.
Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons
2001
Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.