机器学习结合密度泛函理论计算在材料科学中的研究进展

近年来,材料科学研究中密度泛函理论(DFT)计算与机器学习相结合的方法呈现爆炸式增长的趋势。本文综述了DFT及其高通量方法产生的大量计算数据与机器学习相结合的原理和意义,从DFT计算的基本原理出发,重点介绍了机器学习方法的流程、常用的算法及其在催化材料预测热门研究方向中的应用,最后剖析了这个新兴领域目前存在的研究问题、挑战以及未来的发展前景。     

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.     

The SCC-DFTB method and its application to biological systems

The Self-consistent charge density functional tight-binding (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy expression. Here, we review in detail the application of SCC-DFTB to biological systems and several extensions of the original formalism. The biological systems discussed turn out to be a challenge for DFT due to the occurrence of weak binding forces and charge transfer problems, both of which are not properly described by recent DFT-GGA functionals. Possible solutions and alternative strategies are presented and the role of SCC-DFTB in a general quantum chemical approach to biological systems is discussed     

Self-interaction error in density functional theory: a mean-field correction for molecules and large systems

Corrections to the self-interaction error which is rooted in all standard exchange-correlation functionals in the density functional theory (DFT) have become the object of an increasing interest. After an introduction reminding the origin of the self-interaction error in the DFT formalism, and a brief review of the self-interaction free approximations, we present a simple, yet effective, self-consistent method to correct this error. The model is based on an average density self-interaction correction (ADSIC), where both exchange and Coulomb contributions are screened by a fraction of the electron density. The ansatz on which the method is built makes it particularly appealing, due to its simplicity and its favorable scaling with the size of the system. We have tested the ADSIC approach on one of the classical pathological problem for density functional theory: the direct estimation of the ionization potential from orbital eigenvalues. A large set of different chemical systems, ranging from simple atoms to large fullerenes, has been considered as test cases. Our results show that the ADSIC approach provides good numerical values for all the molecular systems, the agreement with the experimental values increasing, due to its average ansatz, with the size (conjugation) of the systems.     

Effects of ligands and spin-polarization on the preferred conformation of distannynes

Recent experimental and theoretical evidence has shown that distannynes, RSnSnR, can adopt either a singly bonded or a multiply bonded structure. Within calculations on small models, such as MeSnSnMe, apparently dramatic differences in conformational preference have been reported. We show that these differences arise due to the treatment of spin-polarization in density functional theory (DFT), and review stability analysis; a diagnostic for the need to include spin-polarization. The low-energy singly bonded structure can only be reached when spin-polarization is allowed. Additional DFT calculations on PhSnSnPh show that the singly bonded structure is the global minimum, leading to a flat torsional potential. The role of electronic effects is further probed by changing the donor-acceptor properties of R. Implications for the structural preference of experimentally synthesized species are discussed.     

Away from generalized gradient approximation: orbital-dependent exchange-correlation functionals

The local-density approximation of density functional theory (DFT) is remarkably accurate, for instance, for geometries and frequencies, and the generalized gradient approximations have also made bond energies quite reliable. Sometimes, however, one meets with failure in individual cases. One of the possible routes towards better functionals would be the incorporation of orbital dependence (which is an implicit density dependency) in the functionals. We discuss this approach both for energies and for response properties. One possibility is the use of the Hartree-Fock-type exchange energy expression as orbital-dependent functional. We will argue that in spite of the increasing popularity of this approach, it does not offer any advantage over Hartree-Fock for energies. We will advocate not to apply the separation of exchange and correlation, which is so ingrained in quantum chemistry, but to model both simultaneously. For response properties the energies and shapes of the virtual orbitals are crucial. We will discuss the benefits that Kohn-Sham potentials can offer which are derived from either an orbital-dependent energy functional, including the exact-exchange functional, or which can be obtained directly as orbital-dependent functional. We highlight the similarity of the Hartree-Fock and Kohn-Sham occupied orbitals and orbital energies, and the essentially different meanings the virtual orbitals and orbital energies have in these two models. We will show that these differences are beneficial for DFT in the case of localized excitations (in a small molecule or in a fragment), but are detrimental for charge-transfer excitations. Again, orbital dependency, in this case in the exchange-correlation kernel, offers a solution.     

Sorption speciation of lanthanides/actinides on minerals by TRLFS, EXAFS and DFT studies: a review

Lanthanides/actinides sorption speciation on minerals and oxides by means of time resolved laser fluorescence spectroscopy (TRLFS), extended X-ray absorption fine structure spectroscopy (EXAFS) and density functional theory (DFT) is reviewed in the field of nuclear disposal safety research. The theoretical aspects of the methods are concisely presented. Examples of recent research results of lanthanide/actinide speciation and local atomic structures using TRLFS, EXAFS and DFT are discussed. The interaction of lanthanides/actinides with oxides and minerals as well as their uptake are also of common interest in radionuclide chemistry. Especially the sorption and inclusion of radionuclides into several minerals lead to an improvement in knowledge of minor components in solids. In the solid-liquid interface, the speciation and local atomic structures of Eu(III), Cm(III), U(VI), and Np(IV/VI) in several natural and synthetic minerals and oxides are also reviewed and discussed. The review is important to understand the physicochemical behavior of lanthanides/actinides at a molecular level in the natural environment.     

Efficiently accounting for ion correlations in electrokinetic nanofluidic devices using density functional theory

The electrokinetic behavior of nanofluidic devices is dominated by the electrical double layers at the device walls. Therefore, accurate, predictive models of double layers are essential for device design and optimization. In this paper, we demonstrate that density functional theory (DFT) of electrolytes is an accurate and computationally efficient method for computing finite ion size effects and the resulting ion-ion correlations that are neglected in classical double layer theories such as Poisson-Boltzmann. Because DFT is derived from liquid-theory thermodynamic principles, it is ideal for nanofluidic systems with small spatial dimensions, high surface charge densities, high ion concentrations, and/or large ions. Ion-ion correlations are expected to be important in these regimes, leading to nonlinear phenomena such as charge inversion, wherein more counterions adsorb at the wall than is necessary to neutralize its surface charge, leading to a second layer of co-ions. We show that DFT, unlike other theories that do not include ion-ion correlations, can predict charge inversion and other nonlinear phenomena that lead to qualitatively different current densities and ion velocities for both pressure-driven and electro-osmotic flows. We therefore propose that DFT can be a valuable modeling and design tool for nanofluidic devices as they become smaller and more highly charged.     

Density Functional Theory as a Data Science

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange‐correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange‐correlation function‐ als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.     

Comparative performance of exchange and correlation density functionals in determining intermolecular interaction potentials of the methane dimer

We have calculated the interaction potentials of the methane dimer for the minimum-energy D(3d) conformation using the density functional theory (DFT) with 90 density functionals chosen from the combinations of nine exchange and 10 correlation functionals. Several hybrid functionals are also considered. While the performance of an exchange functional is related to the large reduced density gradient of the exchange enhancement factor, the correlation energy is determined by the low-density behavior of a correlation enhancement factor. Our calculations demonstrate that the correlation counterpart plays an equally important role as the exchange functional in determining the van der Waals interactions of the methane dimer. These observations can be utilized to better understand the seemingly unsystematic DFT interaction potentials for weakly bound systems.     

Inverse‐Electron‐Demand Diels–Alder Reactions: Principles and Applications

Inverse‐electron‐demand Diels–Alder (iEDDA) reactions are an intriguing class of cycloaddition reactions that have attracted increasing attention for their application in bioorthogonal chemistry, the total synthesis of natural products, and materials science. In many cases, the application of the iEDDA reaction has been demonstrated as an innovative approach to achieve target structures. The theoretical aspects of this class of reactions are of particular interest for scientists as a means to understand the various factors, such as steric strain and electron density of the attached groups, that govern the reaction and thus to elucidate the reaction mechanism. This review aims to summarize both theoretical investigations and application‐driven research work on the iEDDA reaction. First, the historical aspects and the theoretical basis of the reaction, especially recent advances in time‐dependent density functional theory (TD‐DFT) calculations, as well as catalysis strategies will be highlighted and discussed. Second, the applications of this novel reaction in the context of materials science, bioorthogonal chemistry, and total synthesis of natural products will be elaborated with selected recent examples. The challenges and opportunities of the iEDDA reaction will be highlighted to give more insight into its potential applications in many other research areas.     

Density functional theory for encapsidated polyelectrolytes: A comparison with Monte Carlo simulation

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.     

The role of fluctuations in both density functional and field theory of nanosystems

The role of fluctuations in both the density functional theory (DFT) and the field theory (FT) of nanosystems is studied. It turns out that although fluctuations are rigorously incorporated into the general formalism of DFT, they are often omitted in the choice of an approximate free energy functional that must be constructed in order to solve the basic integral equation appearing in DFT. Aside from the analytical discussion, it is demonstrated, in connection with a particular system (fluid in a nanopore) that the effects of fluctuation are missing when one of the most common functionals for this system is used. The demonstration involves a comparison of the results of Monte Carlo simulation with the predictions of DFT when this free energy functional is used. The applicability of FT and DFT in the context of the theory of nucleation is also discussed.     

Analysis of the performance of DFT functionals in the study of light emission by oxyluciferin analogs

Firefly bioluminescence has attracted much attention from the research community due to its most intriguing multicolor bioluminescence. Computational studies have been fundamental to the clarification of this phenomenon. However, no clear demonstration of the accuracy of the theoretical methods used in this field of research has been provided. In this work, we have used luciferin and dehydroluciferin in water as a model for the calculation of the emission wavelength of oxyluciferin and analogs. This model was used in a density functional theory (DFT) benchmarking in which 24 functionals were tested. A non‐negligible “case to case” dependence was observed. However in general, the better classes of the DFT functionals are generalized gradient approximation (GGA) and meta GGA. The generalized gradient exchange functional TPSSVWN5, the hybrid‐meta GGA functional mPWKCIS, and the hybrid GGA functional MPWLYP1M also present good results. For the contrary, the popular hybrid GGA functionals present a worse performance. © 2012 Wiley Periodicals, Inc.