![]() LDPE is hence used to make cling wrap, food containers and playground slides. The large distance between adjacent polymers weakens the intermolecular forces between polymers which are easily overcome, thus LDPE has a low melting point and is highly flexible. LDPE is composed of highly-branched polymer chains that do not pack closely together and are randomly oriented relative to one another, i.e. Our “long-wave DFPT” significantly extends the scopes and capabilities of perturbative electronic-structure approaches and opens the door to the systematic exploration of a vast range of gradient-related physical properties.The repeating unit and chains of polyethylene. We obtain excellent agreement with earlier studies, whenever available. We demonstrate our method, which we have implemented in a publicly distributed package ( abinit), by calculating the flexoelectric tensor and the “dynamical quadrupoles” (i.e., the quadrupolar moment of the charge-density response to an atomic displacement) of several materials. This allows one to access a broad range of spatial-dispersion properties at a surprisingly small computational cost and with unprecedented accuracy. Our new approach consists of incorporating the long-wave method, a mainstay of condensed-matter theory since the early days of quantum mechanics, into the modern tools of DFPT. Here, we establish a general and efficient quantum-mechanical formalism to address this broad class of problems.ĭensity-functional perturbation theory (DFPT) is nowadays the state-of-the-art method to accurately calculate from first principles how materials respond to external stimuli. Notable examples are flexoelectricity, the electrical voltage generated by a flexural deformation, and natural optical activity, the rotation of transmitted light polarization by some crystals. While these effects are generally small, they have attracted increasing interest in the past few years. At the macroscopic level, this means that the material response depends on gradients of the applied field, which is known as spatial dispersion. Microscopically, however, the effects of the perturbation always propagate over a neighborhood around the point of application. In materials science and engineering, scientists often assume that crystals respond locally to an externally applied perturbation such as a strain or an electromagnetic field. We demonstrate our method by calculating the flexoelectric and dynamical quadrupole tensors of selected crystalline insulators and model systems. In particular, the physical response to the spatial gradient of any external field can now be calculated at negligible cost by using the response functions to uniform perturbations (electric, magnetic, or strain fields) as the only input. This procedure provides a powerful general framework to access a wide range of spatial dispersion effects that were formerly difficult to calculate by means of first-principles electronic structure methods. Here we show that q can be formally treated as a perturbation parameter and used in conjunction with the established results of perturbation theory (e.g., the “ 2 n + 1” theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wave-vector components. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wave vector q at essentially the same computational cost as the lattice-periodic case. Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and nonlinear-response properties of materials from first principles. ![]()
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