Theoretical Investigation on Nearsightedness of Finite Model and Molecular Systems Based on Linear Response Function Analysis

Abstract

Abstract:We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, |r−r′|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems' counterparts, H2, He2 2+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.

Nearsightedness-related indices of finite systems based on linear response function: one-dimensional cases

“…In fact, we previously confirmed their statement with inspecting linear response function (LRF) of density, (δρ(r)/δv(r )) N , which is the density responses at positions (δρ(r)) due to virtual perturbations at other points (δv(r )), for several model and molecular systems with the various numbers of electrons [7,8]. For instance, we showed that, for a one-dimensional (1D) square-well potential system and the hydrogen molecular system, the calculated LRFs were remarkably delocalised for two-electrons [8].…”

“…In fact, we previously confirmed their statement with inspecting linear response function (LRF) of density, (δρ(r)/δv(r )) N , which is the density responses at positions (δρ(r)) due to virtual perturbations at other points (δv(r )), for several model and molecular systems with the various numbers of electrons [7,8]. For instance, we showed that, for a one-dimensional (1D) square-well potential system and the hydrogen molecular system, the calculated LRFs were remarkably delocalised for two-electrons [8]. A remaining problem is, as the number of electrons increases from two, say, in molecules of hydrogen molecule, to hundreds or thousands, which are the typical number of electrons in large molecular systems that has been treated with QM/MM calculations in the field of quantum chemistry, which size does NEM start to hold for?…”

“…A remaining problem is, as the number of electrons increases from two, say, in molecules of hydrogen molecule, to hundreds or thousands, which are the typical number of electrons in large molecular systems that has been treated with QM/MM calculations in the field of quantum chemistry, which size does NEM start to hold for? In the previous report [8], we also showed that LRF becomes gradually localised as the number of electrons (N) increases, but of which the explicit dependency on N has not been analysed yet. As a continuation of the previous report, we introduce several indices to analyse the dependency of localisability of the LRFs on the number of electrons explicitly in this study.…”

“…The original NEM scenario focuses on density changes at partial regions in infinite systems [2], i.e., (δρ(r)/δv(r )) μ . By contrast, a main interest of both our study and conceptual DFT lies in LRF at constant N, (δρ(r)/δv(r )) N , of finite systems [7,8,[16][17][18][19][20][21][22][23][24][25]. This is reasonable in the context of quantum chemistry calculations: the number of electrons is usually conserved.…”

“…On the basis of Equation (2), we have employed (δρ(r)/δν(r )) N to assess the locality and nonlocality of finite systems in our previous studies [7,8]. In the following, we omit the notation for being constant N, and simply write LRF as δρ(r)/δν(r ).…”