Dynamical quantities density matrix

Like CP, ADMP represents fictitious dynamics where the density matrix is propagated instead of being converged. The accuracy and efficiency is governed by the choice of the fictitious mass tensor, /i hence one must be aware of the limits on this quantity. We have derived two independent criteria [152,154] that place... 

In the present article, we report a study concerning the reaction mechanism of a prototype reaction using both static and dynamic approaches to explore a DFT potential surface. The static approach is the standard IRC model, while the dynamic one is based on a Carr-Parrinello method performed with localized (Gaussian) orbitals, the so-called atom-centered density matrix propagation (ADMP) model.25 Our aim is to elucidate the differences, and the common aspects, between the two approaches in the analysis of bond breaking/formation. To this end, we have chosen topological quantities as probe molecular descriptors. 

Whether the inactive region is a true continuum (e.g., photofragmentation) or a quasi-continuum comprised of an enormous density of rigorously bound eigenstates (polyatomic molecule dynamics, Section 9.4.14) is often of no detectable consequence. The dynamical quantities discussed in Section 9.1.4 (probability density, density matrix, autocorrelation function, survival probability, transfer probability, expectation values of coordinates and conjugate momenta) describe the active space dynamics without any reference to the detailed nature of the inactive space. 

Both TDHF and the TDDFT follow the dynamics of a similar quantity a single Slater determinant that can be uniquely described by an idempotent single-electron density matrix p (with p = p).62,63,77,78 However, they yield different equations of motion for p(t). stemming from the different interpretation of p tj. In the TDHF, p(t) is viewed as an approximation for the actual single-electron density matrix, whereas in TDDFT p(t) is an auxiliary quantity constrained... 

For each of the structures obtained in this way, one has a Langevin equation, see Eq. 2, from whose eigenvalues the usual dynamic quantities follow. These involve for a certain structure S only the eigenvalues density gsM of the corresponding Laplace matrix A. Now, the ensemble-averaged density of eigenvalues is given by... 

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