Effective Potential Method Research Articles

Band Structure, Phonon Spectrum and Thermoelectric Properties of Ag3CuS2.

Sulfides and selenides of copper and silver have been intensively studied, particularly as potentially efficient thermoelectrics. Ag3CuS2 (jalpaite) is a related material. However very little is known about its physical properties. It has been found that the compound undergoes several structural phase transitions, having the tetrahedral structural modification I41/amd at room temperature. In this work, its band structure, phonon spectrum and thermoelectric properties were studied theoretically and experimentally. Seebeck coefficient, electrical conductivity and thermal conductivity were measured in a broad temperature range from room temperature to 600 K. These are the first experimental data on transport properties of jalpaite. Ab initio calculations of the band structure and Seebeck coefficient were carried out taking into account energy dependence of the relaxation time typical for the scattering of charge carriers by phonons. The results of the calculations qualitatively agree with the experiment and yield large values of the Seebeck coefficient characteristic for lightly doped semiconductor. The influence of intrinsic defects (vacancies) on the transport properties was studied. It was shown that the formation of silver vacancies is the most probable and leads to an increase of hole concentration. Using the temperature dependent effective potential method, the phonon spectrum and thermal conductivity at room temperature were calculated. The measurements yield low lattice thermal conductivity value of 0.5 W/(m K) at 300 K, which is associated with the complex crystal structure of the material. The calculated room temperature values of the lattice thermal conductivity were also small (0.14-0.2 W/(m K)).

Vehicles driving behavior recognition based on transfer learning

Due to the complexity of experiments to test driving behaviors and the high cost of data collection for some types of vehicles, e.g., heavy-duty freight vehicles, it is normally hard to develop a model with a small size of samples for higher performance to correctly recognize driving behavior patterns. This paper proposes an effective recognition method based on the Convolutional Neural Network (CNN) and transfer learning. Firstly, a CNN model was constructed that was coupled with multi-source data fusion, natural driving GPS data, and drivers’ facial expression data of online car-hailing, to recognize the feature maps of five driving behavior patterns, including acceleration, deceleration, turning, lane changing, and lane keeping. Secondly, the transfer learning algorithm was employed to fine-tune the pre-trained CNN model parameters with few natural driving data samples of heavy-duty freight vehicles, where data collection is traditionally very difficult. The experiments showed that this transferred model yields a higher performance with an accuracy score of 0.80 than the non-transferred one with an accuracy of 0.64 only. Additionally, such a transferred model converged very fast with a lower training cost. After only 1,000 training epochs, its performance is much better than that of the non-transferred model after 5,000 epochs. The results demonstrated that transfer learning is an effective potential method for driving behavior recognition and other similar studies where the sample size is relatively small due to various reasons.

Full Temperature-Dependent Potential and Anharmonicity in Metallic Hydrogen: Colossal NQE and the Consequences

The temperature-dependent effective potential (TDEP) method for anharmonic phonon dispersion is generalized to the full potential case by combining with path integral formalism. This extension naturally resolves the intrinsic difficulty in the original TDEP at low temperature. The new method is applied to solid metallic hydrogen at high pressure. A colossal nuclear quantum effect (NQE) and subsequent anharmonicity are discovered, which not only leads to unexpectedly large drift of protons, but also slows down the convergence rate substantially when computing the phonon dispersions. By employing direct ab initio path integral molecular dynamics simulations as the benchmark, a possible breakdown of phonon picture in metallic hydrogen due to colossal NQE is indicated, implying novel lattice dynamical phenomena might exist. Inspired by this observation, a general theoretical formalism for quantum lattice dynamics beyond phonon is sketched, with the main features being discussed.

Modeling Absolute Redox Potentials of Ferrocene in the Condensed Phase.

Absolute thermodynamic quantities for critical chemical reactions are needed to determine the role of solvents and reactive environments in catalysis and electrocatalysis. Theoretical methods can provide such quantification but are often hindered by the innate complexity of electron correlation and dynamic relaxation of solvent environments. We present and validate a protocol for calculating the redox potentials of the ferrocene/ferrocenium redox pair in acetonitrile. Equation-of-motion and effective fragment potential (EFP) methods are used to characterize the adiabatic and vertical ionization potentials as well as the electron affinity processes. We benchmark molecular mechanics against the EFP model to show the differences in the ferrocene electronic polarizability in two redox states. Our best estimate of the redox potential (4.94 eV) agrees well with the experimental value (4.93 eV). This demonstrates the ability of modern computational methods to predict absolute redox potentials quantitatively and to quantify the correlation of dynamic effects, which underlie their origin.

Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations

Inelastic neutron scattering measurements were performed with a time-of-flight chopper spectrometer to observe phonons in all parts of the Brillouin zone of a single crystal of cuprite ${\mathrm{Cu}}_{2}\mathrm{O}$. We reduced the experimental data to phonon dispersions in the high-symmetry directions, and changes between 10 and 300 K are reported. In this paper, we show ab initio quasiharmonic (QH) and anharmonic (AH) calculations of phonon dispersions. We performed all AH calculations with a temperature-dependent effective potential method. Both QH and AH calculations account for the small negative thermal expansion of cuprite at low temperatures. However, the measured temperature-dependent phonon behavior was predicted more accurately with the AH calculations than the QH ones. Nevertheless, at 300 K, the cubic AH used in this paper did not entirely account for the experimental phonon dispersions in cuprite.

Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles.

The ground state intermolecular potential of bimolecular complexes of N‐heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short‐ and long‐distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine–uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.

Semiconducting BaS3 phase featuring v-shape S3 unit at high pressure

Pressure-induced structural transformation of known compounds has become an effective routine to obtain new materials. The sulfur motifs that are present in compounds have a considerable effect on their crystal structures and electronic properties. Here, we focus on exploring the evolution of S motifs in the $\mathrm{Ba}{\mathrm{S}}_{3}$ compound under high pressure. A novel $P{3}_{1}21\text{\ensuremath{-}}\mathrm{Ba}{\mathrm{S}}_{3}$, consisting of an equivalent V-shape ${\mathrm{S}}_{3}$ unit and quasi-hexagon Ba ring, is identified through the combination of first-principles swarm-intelligence search and phonon softening calculations. The bond angle in the ${\mathrm{S}}_{3}$ unit decreases, accompanied by pressure-induced structural phase transition. $P{3}_{1}21\text{\ensuremath{-}}\mathrm{Ba}{\mathrm{S}}_{3}$ shows a semiconducting character, mainly originating from the contribution of S $3p\text{\ensuremath{-}}\mathrm{electron}$ states. Along with the newly proposed $\mathrm{Ba}{\mathrm{S}}_{3}$ structure, the temperature effect on stability is estimated using the temperature-dependent effective potential method. For another S-rich $\mathrm{Ba}{\mathrm{S}}_{2}$, the disappearance of the ${\mathrm{S}}_{2}$ unit induced by pressure ($>150\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$) is mainly responsible for structural instability.

Appraisal of dispersion damping functions for the effective fragment potential method

The effective fragment potential (EFP) is a polarizable force field whose physically-motivated functional form is parameterized in an automated way from ab initio calculations, and whose dispersion potential has been suggested as a correction for Hartree-Fock or density functional theory calculations. However, the parameter-free dispersion damping potentials that are currently used in EFP do not follow from a rigorous derivation and do not satisfy simple limits for the dispersion energy. We introduce several new damping expressions that correct these deficiencies, then evaluate their performance alongside existing damping functions using a new database of ionic liquid constituents. This data set, which we call IL195×8, consists of complete-basis coupled-cluster interaction energies for 195 ion pairs at each of 8 different intermolecular separations. Ultimately, we recommend a new parameter-free dispersion damping function as a replacement for the one that is currently used in EFP.

Rotational and translational diffusion of liquid n-hexane: EFP-based molecular dynamics analysis.

Molecular Dynamics (MD) simulations based on the Effective Fragment Potential (EFP) method are utilized to provide a comprehensive assessment of diffusion in liquid n-hexane. We decompose translational diffusion into components along and orthogonal to the long axis of the molecule. Rotational diffusion is decomposed into tumbling and spinning motions about this axis. Our analysis yields four corresponding diffusion coefficients which are related to diagonal entries in the complete 6 × 6 diffusion tensor accounting for the three rotational and three translational degrees of freedom and for the potential coupling between them. However, coupling between different degrees of freedom is expected to be minimal for a natural choice of the molecular body-fixed axis, so then off-diagonal entries in the tensor are negligible. This expectation is supported by a hydrodynamic analysis of the diffusion tensor which treats the liquid surrounding the molecule being tracked as a viscous continuum. Thus, the EFP MD analysis provides a comprehensive characterization of diffusion and also reveals expected shortcomings of the hydrodynamic treatment, particularly for rotational diffusion, when applied to neat liquids.

Boosting the OEP2-sc method with spin-component scaling

The semi-canonical second-order optimised effective potential (OEP2-sc) method [R.J. Bartlett, I. Grabowski, S. Hirata and S. Ivanov, J. Chem. Phys. 122, 034104 (2005). doi:10.1063/1.1809605] is one of the most stable and efficient correlated OEP approaches. In this work, we introduce its scaled-opposite-spin (SOS) variant, named OEP2-SOS-sc. This new method further improves over the OEP2-sc for various properties, including correlation potentials, relaxed densities, and energies, fully retaining the good stability of the original approach. Thus, the OEP2-SOS-sc is an efficient and promising tool for high-level density functional theory simulations.

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles.

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N - 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.

Fermionic neural network with effective core potential

Deep learning techniques have opened a new venue for electronic structure theory in recent years. In contrast to traditional methods, deep neural networks provide much more expressive and flexible wave function Ans\"atze, resulting in better accuracy and timescale behavior. In order to study larger systems while retaining sufficient accuracy, we integrate a powerful neural-network-based model (FermiNet) with the effective core potential method, which helps to reduce the complexity of the problem by replacing inner core electrons with additional semilocal potential terms in the Hamiltonian. In this work, we calculate the ground-state energy of $3d$ transition metal atoms and their monoxides, which is quite challenging for the original FermiNet work, and the results are consistent with both experimental data and other state-of-the-art computational methods. Our work is an important step for a broader application of deep learning in the electronic structure calculation of molecules and materials.

Attaining Low Lattice Thermal Conductivity in Half-Heusler Sublattice Solid Solutions: Which Substitution Site Is Most Effective?

Low thermal conductivity is an important materials property for thermoelectricity. The lattice thermal conductivity (LTC) can be reduced by introducing sublattice disorder through partial isovalent substitution. Yet, large-scale screening of materials has seldom taken this opportunity into account. The present study aims to investigate the effect of partial sublattice substitution on the LTC. The study relies on the temperature-dependent effective potential method based on forces obtained from density functional theory. Solid solutions are simulated within a virtual crystal approximation, and the effect of grain-boundary scattering is also included. This is done to systematically probe the effect of sublattice substitution on the LTC of 122 half-Heusler compounds. It is found that substitution on the three different crystallographic sites leads to a reduction of the LTC that varies significantly both between the sites and between the different compounds. Nevertheless, some common criteria are identified as most efficient for reduction of the LTC: The mass contrast should be large within the parent compound, and substitution should be performed on the heaviest atoms. It is also found that the combined effect of sublattice substitution and grain-boundary scattering can lead to a drastic reduction of the LTC. The lowest LTC of the current set of half-Heusler compounds is around 2 W/Km at 300 K for two of the parent compounds. Four additional compounds can reach similarly low LTC with the combined effect of sublattice disorder and grain boundaries. Two of these four compounds have an intrinsic LTC above ∼15 W/Km, underlining that materials with high intrinsic LTC could still be viable for thermoelectric applications.

Molecular interactions in diffusion-controlled aldol condensation with mesoporous silica nanoparticles.

The aldol reaction of p-nitrobenzaldehyde in amino-catalyzed mesoporous silica nanoparticles (MSN) has revealed varying catalytic activity with the size of the pores of MSN. The pore size dependence related to the reactivity indicates that the diffusion process is important. A detailed molecular-level analysis for understanding diffusion requires assessment of the noncovalent interactions of the molecular species involved in the aldol reaction with each other, with the solvent, and with key functional groups on the pore surface. Such an analysis is presented here based upon the effective fragment potential (EFP). The EFP method can calculate the intermolecular interactions, decomposed into Coulomb, polarization, dispersion, exchange-repulsion, and charge-transfer interactions. In this study, the potential energy surfaces corresponding to each intermolecular interaction are analyzed for homo- and hetero-dimers with various configurations. The monomers that compose dimers are five molecules such as p-nitrobenzaldehyde, acetone, n-hexane, propylamine, and silanol. The results illustrate that the dispersion interaction is crucial in most dimers.

Circular Rydberg States of Lithium Atoms or Lithium-like Ions in a High-Frequency Laser Field: The Break of the Algebraic Symmetry

There have been publications presenting studies of relatively simpleatomic systems in a high-frequency laser field. The systems studied under sucha field were highly excited (Rydberg) hydrogen atoms and hydrogen-like ions, aswell as highly-excited helium atoms and helium-like ions. These studies wereperformed classically, as appropriate for Rydberg states and revealed celestialanalogies, various kinds of the precession of the electron orbit and a shift ofthe energy. In the current paper we analyze a lithium atom or a lithium-likeion, one of the three electrons being in a Rydberg state, subjected to a laserfield of high frequency. We used the generalized method of effectivepotentials. We showed that for a relatively small distance of the outerelectron from the nucleus, the system has higher than geometrical symmetry. Foran arbitrary separation of the outer electron from the nucleus, we dealt withthe broken algebraic symmetry reduced to the geometrical (axial) symmetry. Wedescribe analytically the following two outcomes for circular Rydberg states.One of the outcomes is the precession of the plane of the orbit of the highlyexcited electron – the precession whose frequency we calculate analytically. Itleads to the following modification of the radiation spectrum: The appearanceof satellites at the distances from the unperturbed frequency of the spectralline equal to multiples of the precession frequency. The other outcome is anenergy shift of the Rydberg electron. Its dependence on the nuclear charge wasfound to be a non-monotonic function. This is a counterintuitive result.

Study of structural phase transition and elastic properties of ZnTe semiconducting compound under high pressure

The high-pressure structural phase transition and pressure induced elastic properties of cubic zinc-blende phase (B3) to rock-salt phase (B1) structure of Zinc Telluride (ZnTe) semiconducting compound were studied by using the effective inter-ionic potential method, which contains the long-range Coulomb and van der Waals (vdW) interactions and the short-range repulsive interaction of up to second-neighbor ions within the Hafemeister and Flygare approach. The structural phase transition from B3 to B1 structure is reflected using estimated values of phase transition pressure and volumetric abrupt changes in the pressure–volume phase diagram. The calculated results first predict the phase transformation of ZnTe from B3 to B1, which occurs at 19GPa and is consistent with the reported data. Later on, using the effective inter-ionic potential technique, we were able to predict the second order elastic characteristics of the ZnTe system.

Chasing the Critical Wetting Transition. An Effective Interface Potential Method.

Wettablity is one of the important characteristics defining a given surface. Here we show that the effective interface potential method of determining the wetting temperature, originally proposed by MacDowell and Müller for the surfaces exhibiting the first order wetting transition, can also be used to estimate the wetting temperature of the second order (continuous) wetting transition. Some selected other methods of determination of the wetting temperature are also discussed.

Lattice thermal conductivity of half-Heuslers with density functional theory and machine learning: Enhancing predictivity by active sampling with principal component analysis

Low lattice thermal conductivity is essential for high thermoelectric performance of a material. Lattice thermal conductivity is often computed using density functional theory (DFT), typically at a high computational cost. Training machine learning models to predict lattice thermal conductivity could offer an effective procedure to identify low lattice thermal conductivity compounds. However, in doing so, we must face the fact that such compounds can be quite rare and distinct from those in a typical training set. This distinctness can be problematic as standard machine learning methods are inaccurate when predicting properties of compounds with features differing significantly from those in the training set. By computing the lattice thermal conductivity of 122 half-Heusler compounds, using the temperature-dependent effective potential method, we generate a data set to explore this issue. We first show how random forest regression can fail to identify low lattice thermal conductivity compounds with random selection of training data. Next, we show how active selection of training data using feature and principal component analysis can be used to improve model performance and the ability to identify low lattice thermal conductivity compounds. Lastly, we find that active learning without the use of DFT-based features can be viable as a quicker way of selecting samples.

Martensitic transformation mechanism of Mg-Sc lightweight shape memory alloys

Mg-Sc alloys are known as novel and promising lightweight shape memory alloys (LWSMAs), which have outstanding performance. Yet, a precise understanding of the microscopic picture and interactions governing the martensitic transformation (MT) remains elusive. We systematically investigate the MT of Mg-Sc alloys using first-principles methods. The result of generalized solid-state nudged elastic band methods confirms that no energy barrier inhibits the MT. We show that the bcc structure of Mg26Sc6 is dynamical instability at 0 K caused by electron-phonon coupling and Fermi surface nesting. Particularly, the high-temperature stability of Mg26Sc6 is revealed for the first time using the temperature-dependent effective potential method. The softening of the acoustic mode at Γ-R corresponds to two neighboring (1 0 1) planes moving towards each other, and forms martensite phase. Our calculations provide the complete and atomic-level mechanism for the MT of Mg-Sc alloys and shed some light on the design of new LWSMAs.

The evolutions of the innermost stable circular orbits in dynamical spacetimes

In this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr–Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes.