We describe a technique to evaluate projector functions to be used, e.g., in self-interaction corrected versions of the Kohn-Sham equation (or in the LSDA+U method). The projector functions reproduce by construction the expectation values of spin and orbital moments (or any other property one is interested in) for the atomic many-body state. We therefore refer to these projector functions as many-body projector orbitals (MBPO). We describe how, once these projector states have been calculated, one can use them in any electronic structure method for a solid or molecule, to calculate ground-state properties of materials with strongly correlated states. (c) 2005 Wiley Periodicals, Inc.
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.
A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg-Kohn variational procedure yields self-consistent electron densities exhibiting proper atomic shell structure. (C) 2015 Wiley Periodicals, Inc.
Functional properties that are exact for the Hohenberg-Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn-Sham data from an orbital-free density functional framework based on simple one-point functionals by starting from the Levy-Perdew-Sahni formulation. The energy value is obtained from the density-potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.
The difference between density functionals defined by energy criterion and density functionals defined by density criterion is studied for the exchange functional. It is shown that Slater potentials are exact exchange potentials in the sense that they yield the Hartree-Fock electron density if all operators are given by local expressions. (C) 2016 Wiley Periodicals, Inc.
It is shown that the Pauli potential in bound Coulomb systems can in good approximation be composed from the corresponding atomic fragments. This provides a simple and fast procedure how to generate the Pauli potential in bound systems, which is needed to perform an orbital-free density functional calculation. The method is applicable to molecules and solids. (c) 2016 Wiley Periodicals, Inc.
A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree-Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy-Perdew-Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.
Based on the Kohn-Sham Pauli potential and the Kohn-Sham electron density, the upper bound of the Pauli kinetic energy is tested as a suitable replacement for the exact Pauli kinetic energy for application in orbital-free density functional calculations. It is found that bond lengths for strong and moderately bound systems can be qualitatively predicted, but with a systematic shift toward larger bond distances with a relative error of 6% up to 30%. Angular dependence of the energy-surface cannot be modeled with the proposed functional. Therefore, the upper bound model is the first parameter-free functional expression for the kinetic energy that is able to qualitatively reproduce binding curves with respect to bond distortions. (C) 2016 Wiley Periodicals, Inc.
Vibrational spectra for the O-H stretching motion of HDO molecules in different surroundings have been calculated by quantum mechanical ab initio methods and compared with experimental spectra. The free water molecule, water chains, and ion-water clusters are discussed. Solvent effects on OH vibrations in liquid water have been calculated as well as "in-crystal" OH frequencies in some ice and ionic crystalline hydrate structures. The importance of nonadditivity effects, electron correlation (at the MP2 level), and long-range interactions for the total frequency downshift is demonstrated. It is shown that the inclusion of these effects, in conjunction with a variational quantum mechanical treatment of the anharmonic vibrational stretching motion (force constants up to the fourth order), yields vibrational frequencies in quantitative agreement with experiment for a wide range of aqueous systems.
We present a theoretical study of the evolution of the electronic structure of wurtzite GaN nanorods for different lengths (2.415.4 nm) in the [0001] direction and different diameters (0.972.25 nm). This study includes both a hybrid density functional theory study and a comparison with the k.p empirical band structure method. From the quantum chemical calculations, surface effects are found to be important. When these have been compensated for the electronic structure properties as a function of rod length or diameter approximately follow the trend expected from the quantum confinement effect. The k.p method predicts a similar behavior although deviations are apparent for smaller sizes.
Parameters for effective hopping integrals are extracted from ab initio Hartree-Fock calculations on model systems. These effective hoppings can be used to describe the attractive part of the interaction of loosely bonded p-electron systems of various orientations, such as interchain hoppings in conjugated polymers or those between two-dimensional graphitic sheets.
The catalytic decomposition of dinitrotoluene (DNT; 3-4-DNT), a by-product of the explosive trinitrotoluene (trotyl), on a platinum surface is investigated computationally. Reaction paths have been computed for a DNT molecule interacting with a Pt-cluster under varying temperatures using quantum-chemical density functional theory. Two possible initiation steps where DNT split either into nitro-tolyl and NO2, or in nitro-tolyl-oxidanyl and NO, are considered. The energy barrier for the catalytic process is found to decrease significantly for the Pt catalyzed reaction compared with the uncatalyzed reaction.
The subsystem functional scheme (Kohn and Mattsson, Phys Rev Lett 1998, 81, 3487; Armiento and Mattsson Phys Rev B 2002, 66, 165117) is a recently proposed framework for constructing exchange-correlation density-functionals for use in density functional theory based calculations. The fundamental principle is to describe the physics in a real material by mapping onto model systems that exhibit the characteristic physics in each separate part of the real system. The local density approximately (LDA) functional can be seen as a subsystem functional: in all parts of the real material the assumption is that the needed physics is well described by the uniform electron gas model system. It is well known that this assumption is very accurate for surprisingly large classes of materials. The Armiento Mattsson 2005 (AM05) (Armiento and Mattsson, Phys Rev B 2005, 72, 085108; Mattsson and Armiento, Phys Rev B 2009, 79, 155101) functional takes this a step further by distinguishing between two separate types of regions in a real material, one type that is assumed to be well described by the uniform electron gas, and the other type of region assumed to be well described by a surface model system. AM05 gives a consistent improvement over LDA. One important consequence of the subsystem functional scheme is that it is known what physics is included in a functional. Based on the performance of AM05 for a number of different systems, we discuss where the model systems included are enough and when additional physics need to be included in a new functional. Improvement of AM05 is possible by fine-tuning the details in the construction. But a new major step in accuracy improvement is only expected if new physics is integrated in a functional via an additional model system. We discuss what type of physics would be needed and what model systems could be used for this next step beyond AM05. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2274-2282, 2010
This article presents calculations of the structure, binding energetics, potential energy surfaces, and vibrational spectra of the H_{5}O ion. The 15-dimensional potential energy surface for the seven nuclei in the ionic complex was computed by pointwise ab initio Møller-Plesset second-order perturbation (MP2) calculations, using the correlation-consistent pVTZ basis set augmented with diffuse basis functions on oxygen. The potential energy surface for the proton-transfer mechanism was investigated, and the effects of surrounding water molecules on the proton-transfer potential energy curve was studied. Density functional calculations for the proton-transfer potential surface are compared to the MP2 results. Geometry-optimized structures, binding energies, and harmonic vibrational spectra of H_{5}O and H_{9}O are presented. The energy-minimum structure of H_{5}O using the augmented pVTZ basis set is of C_{2} symmetry, whereas for H_{9}O, using the TZ2P basis set, it is of C_{3} symmetry. The H-bonded OH stretching harmonic frequency of H_{5}O is very low, 913 cm^{−1}, whereas for H_{9}O it is 2927 cm^{−1}. The subspace spanned by the hydrogen-bonded OH distance and the OO distance were used in one- and two-dimensional calculations of the anharmonic vibrational spectrum using collocation methods. The coupling of the OH stretch with the OO vibration causes a redshift and the anharmonicity a blueshift of the OH frequency: the resulting fundamental frequency of the H-bonded OH vibration is 1275 cm^{−1}. Zero-point energies of the proton vibration and pathways for exchange of protons within H_{5}O are discussed. © 1995 John Wiley & Sons, Inc.
This tutorial review describes how recent quantum chemical calculations and non‐adiabatic molecular dynamics simulations have provided valuable guidelines and insights for the design of more powerful synthetic rotary molecular motors. Following a brief overview of the various types of rotary motors synthesized to date, we present computationally identified steric and electronic approaches to significantly reduce the free‐energy barriers of the critical thermal isomerization steps of chiral overcrowded alkenes, a main class of motors whose potential for many different kinds of applications is well documented. Furthermore, we describe how computational research in this field has provided new motor designs that differ from overcrowded alkenes by either (1) completing a full 360° rotation through fewer steps, (2) exhibiting more efficient photochemical steps, or (3) requiring fewer chiral features for their function, including a design that even in the absence of a stereocenter achieves unidirectional rotary motion from two Z/E photoisomerizations alone.
Results from ab initio Hariree-Fock and gradient-corrected density functional theory calculations of formic acid interactions with ZnO (1010) surfaces are reported. Surface relaxation is found to affect equilibrium geometries and adsorption energies significantly. Large variations in adsorption energy with coverage and ordering of the adsorbates are revealed and explained in terms of strong and highly anisotropic electrostatic adsorbate-adsorbate interactions. The results are compared to published experimental and theoretical results, and differences in suggested binding geometries from the different studies are discussed. Dynamic properties of the adsorption, surface mobility, and surface reactivity are inferred from key elements of the potential energy surface obtained from the quantum chemical computations and supported by ab initio molecular dynamics simulations. (C) 2002 Wiley Periodicals, Inc.