Density response matrix

From the discussion so far, it is clear that the mapping to a system of noninteracting particles under the action of suitable effective potentials provides an efficient means for the calculation of the density and current density variables of the actual system of interacting electrons. The question that often arises is whether there are effective ways to obtain other properties of the interacting system from the calculation of the noninteracting model system. Examples of such properties are the one-particle reduced density matrix, response functions, etc. An excellent overview of response theory within TDDFT has been provided by Casida [15] and also more recently by van Leeuwen [17]. A recent formulation of density matrix-based TD density functional response theory has been provided by Furche [22]. 

The family of the density-matrix spectral moments is defined as S = L"t] which are the expansion coefficients in the short-time evolution of the density-matrix response function. These moments are used to construct the main DSMA equations - °°... 

One-electron properties calculated as energy derivatives are closely related to the response density. Provided that the basis set chosen is independent of the perturbation the corresponding one-electron property is given as the product of the response density matrix Zy with the corresponding property integrals. 

The usual context for linear response theory is that the system is prepared in the infinite past, —> -x, to be in equilibrium witii Hamiltonian H and then is turned on. This means that pit ) is given by the canonical density matrix... 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

The degradation of the matrix in a moist environment strongly dominates the material response properties under temperature, humidity, and stress fatigue tests. The intrinsic moisture sensitivity of the epoxy matrices arises directly from the resin chemical structure, such as the presence of hydrophilic polar and hydrogen grouping, as well as from microscopic defects of the network structure, such as heterogeneous crosslinking densities. 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

The spin Hamiltonian also forms the theoretical basis for describing the temporal response of the spin system to a pulse sequence and/or mechanical manipulations of the sample via calculations of the evolution of the density matrix. Computer... 

Time-dependent response theory concerns the response of a system initially in a stationary state, generally taken to be the ground state, to a perturbation turned on slowly, beginning some time in the distant past. The assumption that the perturbation is turned on slowly, i.e. the adiabatic approximation, enables us to consider the perturbation to be of first order. In TD-DFT the density response dp, i.e. the density change which results from the perturbation dveff, enables direct determination of the excitation energies as the poles of the response function dP (the linear response of the KS density matrix in the basis of the unperturbed molecular orbitals) without formally having to calculate a(co). 

In order to proceed further a reference system is introduced (bare system) where the interaction between the monomers is removed but the chain connectivity is preserved. The response matrix in the bare system is denoted as X Q,t). Then in the bare system the density response is written as ... 

Polypyrrole has the potential to provide an effective method for reagentless transduction by immobilization of the ssDNA probe within the polymer matrix. Significant differences in the impedance profile of ssDNA and dsDNA have been demonstrated [59]. The differences in the impedance profile are purportedly based on intercalation differences of the polymer with ssDNA compared to dsDNA. The exact mechanism for impedimetric change resulting from conducting polymer films has not been identified, although it is likely linked, much like the impedimetric response of pure DNA, to the change in ion density that accompanies the double strand compared to the... 

Shuai, Z., Bredas, J.L., Saxena, A., Bishop, A.R. Linear and nonlinear optical response of polyenes a density matrix renormalization group study. J. Chem. Phys. 1998, 109(6), 2549. 

Dorando, J.J., Hachmann, J., Chan G.K-L. Analytic response theory for the density matrix renormalization group. J. Chem. Phys. 2009, 130(18), 184111. 

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