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, He22+, 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.
Highlights
Karplus, Warshel and Levitt won the 2013 Novel Prize in Chemistry for developing the multiscale models, i.e., quantum mechanics/molecular mechanics (QM/MM) models, for complex chemical systems [1,2]
We focus our attention on whether and how the nearsightedness holds for the finite model systems as well as molecular systems
The linear response function (LRF) for numbers of occupied orbitals (Nocc) = 50 shown in Figure 5i is similar to that of the single-well potential shown in Figure 1i, implying that nearsightedness of electronic matter (NEM) is a result of destructive interference among density amplitudes in this case
Summary
Warshel and Levitt won the 2013 Novel Prize in Chemistry for developing the multiscale models, i.e., quantum mechanics/molecular mechanics (QM/MM) models, for complex chemical systems [1,2]. We assume that the artificial Coulomb potentials due to the point charges do not deteriorate description of electronic structures of the QM sites In other words, this type of approaches relies on nearsightedness of electronic matter (NEM) as proposed by Kohn and Prodan [3,4], the fact that the changes of electric potentials at any points that are far enough from a specific point do not affect significantly electronic properties at the point. In order to provide answers to these questions, we examined two types of systems: the first one is simple model systems such as electrons in square-well potential and electrons in harmonic oscillator potential These systems are simple models for molecular systems, but without the intrinsic structure due to the existence of atoms such as atomic orbitals and chemical bonds. Due to virtual perturbations (δv(r′)) are the results of different type of effects
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