Wave packet spreading and localization in electron-nuclear scattering

Abstract

Despite its promise as a method for the simulation of time-dependent many-body quantum mechanics problems, wave packet molecular dynamics (WPMD) is limited in its use by wave packet spreading when applied to dense plasma systems. We employ more accurate methods to determine if spreading really occurs and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for the comparison. We compare the numerically exact split operator Fourier transform (SOFT) method, the Wigner trajectory method (WTM), and the time dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP). We then generalize this form to include multiple Gaussian for the single electron as in the split WP propagation method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical behavior of WPMD at high temperatures.Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

Orbital-dependent second-order scaled-opposite-spin correlation functionals in the optimized effective potential method

“…Several studies have suggested that these two contributions are not completely independent, but rather approximately proportional to each other, and that the overall description of the correlation might be improved by a proper scaling of the two terms [58,60,105]. In fact, as shown in Figure 1, the SS and OS potential and DRD, show a very high degree of proportionality, and a proper scaling of the SS potential can reproduce the OS potential [58]. However, so far, this proportionality has been been investigated only in a qualitative manner, we now perform a more quantitative analysis.…”

“…One of these is based on a modified MBPT(2) functional with a semi-canonical transformation of the Hamiltonian (OEP2-sc) [14,15,57]. As an alternative, recently a new method (OEP2-SOS) [58] has been proposed in this context, based on the spin-resolved second-order correlation energy expression [59], and especially on the scaled-oppositespin (SOS) variant thereof. This method takes advantage of the improved accuracy demonstrated for spincomponent-scaled (SCS) and SOS second-order Møller-Plesset (MP2) calculations [59,60] and provides an accurate OEP correlation functional that largely outperforms the OEP-GL2 approach [58].…”

“…Moreover, the OEP2-SOS method demonstrated a clear advantage over the OEP-GL2 method, converging also in difficult cases (e.g., the Beryllium atom). In fact the OEP2-SOS method employs a scaled (smaller) correlation potential as compared to OEP-GL2, and thus the former yields larger energygaps and it is less prone to variational collapse than the latter [58]. Finally, because only the opposite-spin correlation is involved in its formulation, the OEP2-SOS functional has a favourable computational cost with respect to other second-order approaches (O(N 4 ) vs. O(N 5 )).…”

Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

“…Taking the decoherence problem into account, the temperature effect on the spreading of wave packet is an essential feature [16]. The theoretical description of relaxation and decoherence processes in open quantum systems often leads to a non-Markovian dynamics which is determined by pronounced memory effects.…”

Assessment of the TCA functional in computational chemistry and solid-state physics

“…There is a great variety of XC approximations. They are usually classified on the so called Jacob's ladder of DFT [3], which includes several families of functionals: local [4][5][6], semilocal [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], hybrid [27][28][29][30][31][32][33] and fully nonlocal [34][35][36][37] functionals. Each one these families has its own advantages and limitations in terms of accuracy and computational cost.…”