Adiabatic density-functional perturbation theory

Lithium-Boron (Li-B) Monolayers: First-Principles Cluster Expansion and Possible Two-Dimensional Superconductivity

Recent works demonstrated that the superconductivity at two-dimensional (2-D) can be achieved in Li-decorated graphene (Nature Phys. 2012, 8, 131 and Proc. Natl. Acad. Sci. 2015, 112, 11795). Inspired by the progress made in graphene, we predict by using the first-principles calculations that Li-incorporated B monolayers (Li-B monolayers) can be alternative 2-D superconductors. First-principles cluster expansion approach was used to evaluate the structural diversity and energetic stability of the 2-D Li-B monolayers by treating them as ternary Lix⬡yB1-x-y pseudoalloys (⬡ refers to B hexagonal hole). After thoroughly exploring the Li-B configuration space, several well-ordered and stable Li-B monolayers were identified. Detailed analyses regarding the electronic structures and lattice dynamics properties of the predicted Li-B monolayers were performed. Compared with the non-superconducting pure B-sheet, some predicted Li-B monolayers can exhibit the phonon-mediated superconducting properties above the liquid helium temperature.

Raman scattering investigation of the quasi-one-dimensional superconductor Ta₄Pd₃Te₁₆

We have performed polarized Raman scattering measurements on the newly discovered superconductor Ta4Pd3Te16 (T(c) = 4.6 K). We observe 28 out of 33 Raman active modes, with frequencies in good accordance with first-principles calculations. Although most of the phonons observed vary only slightly with temperature and do not exhibit any asymmetric profile that would suggest strong electron-phonon coupling, the linewidth of the A(g) phonon mode at 89.9 cm(-1) shows an unconventional increase with temperature decreasing, which is possibly due to a charge-density-wave transition or the emergence of charge-density-wave fluctuations below a temperature estimated to fall in the 140-200 K range.

Vibrational Spectroscopy and Phonon-Related Properties of the L-Aspartic Acid Anhydrous Monoclinic Crystal

The infrared absorption and Raman scattering spectra of the monoclinic P21 l-aspartic acid anhydrous crystal were recorded and interpreted with the help of density functional theory (DFT) calculations. The effect of dispersive forces was taken into account, and the optimized unit cells allowed us to obtain the vibrational normal modes. The computed data exhibits good agreement with the measurements for low wavenumbers, allowing for a very good assignment of the infrared and Raman spectral features. The vibrational spectra of the two lowest energy conformers of the l-aspartic molecule were also evaluated using the hybrid B3LYP functional for the sake of comparison, showing that the molecular calculations give a limited description of the measured IR and Raman spectra of the l-aspartic acid crystal for wavenumbers below 1000 cm(-1). The results obtained reinforce the need to use solid-state calculations to describe the vibrational properties of molecular crystals instead of calculations for a single isolated molecule picture even for wavenumbers beyond the range usually associated with lattice modes (200 cm(-1) < ω < 1000 cm(-1)).

A database to enable discovery and design of piezoelectric materials

Piezoelectric materials are used in numerous applications requiring a coupling between electrical fields and mechanical strain. Despite the technological importance of this class of materials, for only a small fraction of all inorganic compounds which display compatible crystallographic symmetry, has piezoelectricity been characterized experimentally or computationally. In this work we employ first-principles calculations based on density functional perturbation theory to compute the piezoelectric tensors for nearly a thousand compounds, thereby increasing the available data for this property by more than an order of magnitude. The results are compared to select experimental data to establish the accuracy of the calculated properties. The details of the calculations are also presented, along with a description of the format of the database developed to make these computational results publicly available. In addition, the ways in which the database can be accessed and applied in materials development efforts are described.

Experimental (X-ray, (13)C CP/MAS NMR, IR, RS, INS, THz) and Solid-State DFT Study on (1:1) Co-Crystal of Bromanilic Acid and 2,6-Dimethylpyrazine

A combined structural, vibrational spectroscopy, and solid-state DFT study of the hydrogen-bonded complex of bromanilic acid with 2,6-dimethylpyrazine is reported. The crystallographic structure was determined by means of low-temperature single-crystal X-ray diffraction, which reveals the molecular units in their native protonation states, forming one-dimensional infinite nets of moderate-strength O···H-N hydrogen bonds. The nature of the crystallographic forces, stabilizing the studied structure, has been drawn by employing the noncovalent interactions analysis. It was found that, in addition to the hydrogen bonding, the intermolecular forces are dominated by stacking interactions and C-H···O contacts. The thermal and calorimetric analysis was employed to probe stability of the crystal phase. The structural analysis was further supported by a computationally assisted (13)C CP/MAS NMR study, providing a complete assignment of the recorded resonances. The vibrational dynamics was explored by combining the optical (IR, Raman, TDs-THz) and inelastic neutron scattering (INS) spectroscopy techniques with the state-of-the-art solid-state density functional theory (DFT) computations. Despite the quasi-harmonic approximation assumed throughout the study, an excellent agreement between the theoretical and experimental data was achieved over the entire spectral range, allowing for a deep and possibly thorough understanding of the vibrational characteristics of the system. Particularly, the significant influence of the long-range dipole coupling on the IR spectrum has been revealed. On the basis of a wealth of information gathered, the recent implementation of a dispersion-corrected linear-response scheme has been extensively examined.

Atomic-scale origin of piezoelectricity in wurtzite ZnO

ZnO has been extensively studied by virtue of its remarkably high piezoelectric responses, especially in nanowire forms. Currently, the high piezoelectricity of wurtzite ZnO is understood in terms of the covalent-bonding interaction between Zn 3d and O 2p orbitals. However, the Zn 3d orbitals are not capable of forming hybridized orbitals with the O 2pz orbitals since the Zn ion is characterized by fully filled non-interacting 3d orbitals. To resolve this puzzling problem, we have investigated the atomic-scale origin of piezoelectricity by exploiting density-functional theory calculations. On the basis of the computed orbital-resolved density of states and the band structure over the Γ-M first Brillouin zone, we propose an intriguing bonding mechanism that accounts for the observed high piezoelectricity - intra-atomic 3dz(2)-4pz orbital self-mixing of Zn, followed by asymmetric hybridization between the Zn 3dz(2)-4pz self-mixed orbital and the O 2pz orbital along the polar c-axis of the wurtzite ZnO.

Polymorphism of resorcinol explored by complementary vibrational spectroscopy (FT-RS, THz-TDS, INS) and first-principles solid-state computations (plane-wave DFT)

The polymorphism of resorcinol has been complementary studied by combining Raman, time-domain terahertz, and inelastic neutron scattering spectroscopy with modern solid-state density functional theory (DFT) calculations. The spectral differences, emerging from the temperature-induced structural phase transition, have been successfully interpreted with an emphasis on the low-wavenumber range. The given interpretation is based on the plane-wave DFT computations, providing an excellent overall reproduction of both wavenumbers and intensities and revealing the source of the observed spectral differences. The performance of the generalized gradient approximation (GGA) functionals in prediction of the structural parameters and the vibrational spectra of the normal-pressure polymorphs of resorcinol has been extensively examined. The results show that the standard Perdew, Burke, and Ernzerhof (PBE) approach along with its "hard" revised form tends to be superior if compared to the "soft" GGA approximation.

Nuclear dynamics in the metastable phase of the solid acid caesium hydrogen sulfate

Neutron spectroscopy and first-principles calculations unveil the quantum character of atomic motions in the solid acid CsHSO₄.

Computational modeling of the size effects on the optical vibrational modes of H-terminated Ge nanostructures

The vibrational dispersion relations of porous germanium (pGe) and germanium nanowires (GeNWs) were calculated using the ab initio density functional perturbation theory with a generalized gradient approximation with norm-conserving pseudopotentials. Both pores and nanowires were modeled using the supercell technique. All of the surface dangling bonds were saturated with hydrogen atoms. To address the difference in the confinement between the pores and the nanowires, we calculated the vibrational density of states of the two materials. The results indicate that there is a slight shift in the highest optical mode of the Ge-Ge vibration interval in all of the nanostructures due to the phonon confinement effects. The GeNWs exhibit a reduced phonon confinement compared with the porous Ge due to the mixed Ge-dihydride vibrational modes around the maximum bulk Ge optical mode of approximately 300 cm⁻¹; however, the general effects of such confinements could still be noticed, such as the shift to lower frequencies of the highest optical mode belonging to the Ge vibrations.

Phonon lifetimes from first-principles self-consistent lattice dynamics

Phonon lifetime calculations from first principles usually rely on time-consuming molecular dynamics calculations, or density functional perturbation theory where the zero-temperature crystal structure is assumed to be dynamically stable. Here is presented a new and effective method for calculating phonon lifetimes from first principles. This method is not limited to crystallographic phases stable at 0 K and provides a scheme more effective than most corresponding molecular dynamics calculations. The method is based on the recently developed self-consistent ab initio lattice dynamical method and is here tested by calculating the bcc phase phonon lifetimes of Li, Na, Ti and Zr as representative examples.

Temperature accelerated Monte Carlo (TAMC): a method for sampling the free energy surface of non-analytical collective variables

We introduce a new method to simulate the physics of rare events. The method, an extension of the Temperature Accelerated Molecular Dynamics, comes in use when the collective variables introduced to characterize the rare events are either non-analytical or so complex that computing their derivative is not practical. We illustrate the functioning of the method by studying the homogeneous crystallization in a sample of Lennard-Jones particles. The process is studied by introducing a new collective variable that we call Effective Nucleus Size N. We have computed the free energy barriers and the size of critical nucleus, which result in agreement with data available in the literature. We have also performed simulations in the liquid domain of the phase diagram. We found a free energy curve monotonically growing with the nucleus size, consistent with the liquid domain.

First-principles study of the ferroelectric and nonlinear optical properties of the LiNbO3-type ZnSnO3

Electronic structures, spontaneous polarization, dynamical and nonlinear optical (NLO) properties of polar oxide ZnSnO(3) with LiNbO(3) (LN)-type structure have been investigated in the framework of density functional theory. By analyzing the Born effectives of LN-type ZnSnO(3), we find that Z* of Zn atoms show relatively large anomalous behavior. The spontaneous polarization is attributed to the large displacement of Zn atoms because of the mixed ionic-covalent character between the Zn-O bonds. The optical dielectric tensor is nearly the same; however the static dielectric tensor shows strongly anisotropy. Furthermore, the nonlinear optical properties are calculated by using 2n + 1 theorem applied to an electric-field dependent energy functional. The large dielectric constants and NLO susceptibilities indicate that the LN-type ZnSnO(3) would be a candidate as a high-performance dielectric and nonlinear optical material.

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

First-principle studies of the lattice dynamics of crystals, and related properties

The crystal lattice is never rigid. Due to temperature, external fields or pressure, the nuclei vibrate, the lattice distorts, and instabilities can induce phase transitions. We review the basic concepts of density-functional perturbation theory, a computational method especially suited to determine from first-principles the microscopic parameters governing such behaviour. Then, we present the additional formalism leading to the following properties of minerals: the infra-red and Raman spectra; the prediction of (meta)stability or instability of a crystalline phase, based on the phonon spectrum; the computation of thermodynamics quantities like the free energy, entropy, specific heat; the atomic temperature factors. For each property, examples are given. When appropriate, we mention the computation of related properties, like dielectric tensor and Born effective charges that are needed to get infra-red spectra. Finally, we discuss briefly, on one hand, other applications of the density-functional perturbation theory, and, on the other hand, an alternative technique, the finite-difference computation of dynamical matrices.

Electronic structure and magnetic properties of solids

We review basic computational techniques for simulations of various magnetic properties of solids. Several applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and temperature dependent magnetisations for a number of real systems are presented for illustrative purposes.

Calculation of the vibrational properties of LiMgAs

We have studied the vibrational properties of the filled tetrahedral semiconductor LiMgAs and its binary analog AlAs by using the plane-wave pseudopotential method within density functional theory. The calculated lattice constants for the studied compounds are in good agreement with previous theoretical and experimental results. The phonon dispersion curves and phonon density of states are calculated by using density functional perturbation theory. The sound speeds in different directions are quantitatively similar in LiMgAs and AlAs. The assignment of the zone center modes to the relative motion of the atoms shows that the lower optic modes are due to the Mg-As pair vibrations, while for the upper ones the Li-Mg pair dominates, which is attributed to the smaller Mg atom mass. The longitudinal interatomic force constant of Mg-As is about 66% higher than that of Li-As, showing the relatively high covalency of the former bond.

General Performance of Density Functionals

The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.

London dispersion forces by range-separated hybrid density functional with second order perturbational corrections: The case of rare gas complexes

A satisfactory account of the van der Waals (vdW) (London dispersion) forces is, in general not possible by the Kohn-Sham method using standard local, semilocal generalized gradient approximation (GGA), or meta-GGA density functionals. The recently proposed range-separated hybrid (RSH) approach, supplemented by second order perturbational corrections (MP2) to include long-range dynamic correlation effects, offers a physically consistent, seamless description of dispersion forces. It is based on a rigorous generalization of the Kohn-Sham method, where long-range exchange and correlation effects are treated by wave function methods, while short-range electron exchange and correlation are handled by local or semilocal functionals. The method is tested on a series of rare gas dimers in comparison with standard wave function theory and density functional theory approaches. In contrast to the most successful exchange correlation functionals, which describe at best the vdW minimum, the RSH+MP2 approach is valid also in the asymptotic region and the potential curve displays the correct 1/R(6) behavior at large internuclear separations. In contrast to usual MP2 calculations, the basis set superposition error is considerably reduced, making RSH+MP2 an ideal tool for exploring the potential energy surface of weakly bound molecular complexes.

Linear-scaling density matrix perturbation treatment of electric fields in solids

We develop a novel linear-scaling [O(N)] algorithm for calculating the optical dielectric constant and Born effective charge. Our method relies on the fact that only the sum of the nondiagonal parts of the electric field perturbation in solids contributes to the first-order derivative density matrix, which can then be obtained through the density-matrix perturbation method. The optical dielectric constant of amorphous SiO(2) is computed using a realistic model for the first time.

Calculation of nonadiabatic couplings with restricted open-shell Kohn-Sham density-functional theory

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT.

First-Principles Calculations within Periodic Boundary Conditions of the NMR Shielding Tensor for a Transition Metal Nucleus in a Solid State System: The Example of 51V in AlVO4

We present the first density functional theory based calculations of NMR shielding parameters for a transition metal nucleus using periodic boundary conditions. These calculations employ the gauge-including projected augmented-wave pseudopotential approach. The quality of this method is discussed by comparing experimental and calculated chemical shift tensor eigenvalues for the quadrupolar 51V nucleus in the diamagnetic solid-state compound AlVO4. Furthermore, the combination of shielding tensor with fast and accurate projector augmented-wave electric field gradient tensor calculations allows us to determine the relative orientation of these two tensors.

First-principles calculations of vibrational lifetimes and decay channels: hydrogen-related modes in Si

The vibrational lifetimes and decay channels of local vibrational modes are calculated from first principles at various temperatures. Our method can be used to predict the temperature dependence of the lifetime of any normal mode in any crystal. We focus here on the stretch modes of H2*, H+(BC), and VH x HV in Si. The frequencies are almost identical, but the lifetimes vary from 4 to 295 ps. The calculations correctly predict the lifetimes for T > 50 K and illustrate the critical importance of pseudolocal modes in the decay processes of high-frequency local vibrational modes.

Current Densities and Nucleus-Independent Chemical Shift Maps from Reciprocal-Space Density Functional Perturbation Theory Calculations

A method to calculate condensed-matter nucleus independent chemical shift maps (NICS maps) from first principles in the framework of density functional theory is presented. I use a pseudopotential plane-wave approach in which the electronic current density and the NICS map are obtained from an inverse Fourier transformation of the induced magnetic field represented in reciprocal space (G space). Due to its intrinsically periodic description, the method is suitable for isolated molecules (by using a supercell technique) and for condensed-phase systems like solids. The periodic NICS method was applied to hydrogen-bonded calixhydroquinone nanotubes, crystalline graphite, and two carbon nanotube systems.

Calculation of optical rotation with time-periodic magnetic-field-dependent basis functions in approximate time-dependent density-functional theory

We report the implementation of a method for the calculation of optical rotation. This method is based on the time-dependent density-functional theory and utilizes time-periodic magnetic-field-dependent basis functions. The calculations are based on a density fit. It is demonstrated that additional terms in the analytical expression appearing from derivatives of the approximated Coulomb potential are necessary to provide the gauge-origin independence of the results within a given numerical accuracy. Contributions from these terms also restore the symmetry between the electric and magnetic perturbations in the optical rotation tensor.