Effective Potential Method Research Articles

A polar diatomic molecule under a high-frequency laser field: classical analytical solution

AbstractDynamics of a polar diatomic molecule (represented as the oscillating rotator model) under external fields is the most fundamental problem and the testbed in molecular physics—analogously to the dynamics of hydrogenic atom (represented as the model of an electron in the Coulomb field) under external fields being the most fundamental problem and the testbed in atomic physics. We present the classical analytical study of the dynamical Stark effect in the oscillating rotator under a high-frequency laser field. We obtain the analytical results by using the method of effective potentials. We demonstrate that under the laser field, the rotation frequency increases, while the oscillation frequency decreases, and the amplitude of the oscillations increases. More significantly, the laser field causes the generation of the second harmonic in the oscillations of this system. This is an important, counterintuitive result in studying this fundamental physical system. We also drew attention to some flaws in the literature on this subject.

The Degradation of the 2-Hydroxyethylhydrazinium Nitrate Ionic Liquid System.

The mechanism by which the 2-hydroxyethylhydrazinium nitrate (HEHN) ionic liquid (IL) dissociates via the formation and loss of nitric acid is investigated utilizing the effective fragment potential (EFP) method and various ab initio methods. Additionally, the interactions that dictate the stability of the HEHN IL and contribute to the formation of nitric acid are further assessed using the quasi-atomic orbital (QUAO) bonding analysis. From this work, it is suggested that the formation of nitric acid is dictated by the presence of hydrogen-bonding interactions which appear to become increasingly ionic in nature as the system approaches the bulk, limiting the formation of nitric acid.

Inertial amplification as a performance enhancement method for snap-through vibration energy harvester

In recent years, there has been a lot of interest in exploiting the bistable behavior of snap-through systems to harvest energy from vibration sources. The efficient operation of any bistable VEH depends on its ability to exhibit large-amplitude interwell motion. Under weak ambient excitation, bistable VEH performs marginally because of the confinement of motion to a single well. Frequency up-conversion, multi-stability, and adaptive techniques are some of the performance enhancement strategies suggested for bistable-VEH. Considering the VEH's space constraints, the above designs are hard to implement in practical cases. This study introduces an inertial amplification mechanism (IAM) as a simple passive strategy to enhance the performance of a snap-through VEH, a concept not explored in previous studies. The addition of IAM increases the effective mass without increasing the physical mass and thereby enhances energy harvesting, especially from weak ambient excitation sources. The dynamics and performance of the enhanced snap-through VEH are investigated analytically and numerically under harmonic and random excitations. The harmonic balance method (HBM) derives the frequency-amplitude relationship, which shows a hardening behavior and an increase in bandwidth. The effective potential method provides a closed-form expression for the joint probability density function (Joint PDF), which is governed by the Fokker-Planck equation. The joint PDF shows a transition from bimodal to unimodal with an increase in the value of the geometrical parameter. The stochastic averaging method is employed to obtain the stationary probability density function, which defines the long-term dynamics of the VEH. The effects of noise intensity, mass ratio, and inertial amplifier angle on the dynamics are investigated. Finally, the performance of the proposed VEH is compared with a conventional snap-through VEH, an equivalent linear VEH, and a multistable VEH under harmonic and random excitation conditions. The findings suggest that the snap-through VEH with the IAM has advantages over the linear and multistable nonlinear VEH in terms of extracting energy from low-intensity harmonic and random excitation sources. This simple augmentation strategy preserves the original system's bistability, eliminating the need for the complex design of a multistable VEH.

Comparison of lattice thermal conductivity using ab-initio DFT, machine learning interatomic potentials, and temperature dependent effective potential: a case study of hexagonal BN and BP bilayer

Discovering high thermal conductivity materials is essential for various practical applications, particularly in electronic cooling. The significance of two-dimensional (2D) materials lies in their unique properties that emerge due to their reduced dimensionality, making them highly promising for a wide range of applications. Hexagonal boron nitride (BN), both monolayer and bilayer forms, has garnered attention for its fascinating properties. In this work, we focus on bilayer boron phosphide (BP), which is isostructural to its BN analogue. The lattice thermal conductivity of both bilayer BN and BP have been calculated using ab-initio density functional theory, machine learning with the moment tensor potential method, and the temperature-dependent effective-potential method (TDEP). The TDEP approach gives more accurate results for both BN and BP materials. The lattice thermal conductivity of bilayer BP is lower than that of bilayer BN at room temperature, attributed to increased phonon anharmonicity. This study highlights the importance of understanding phonon scattering mechanisms in determining the thermal conductivity of 2D materials, contributing to the broader understanding and potential applications of these materials in future technologies.

Production of D(*)D¯(*) near the thresholds in e+e− annihilation

It is shown that the nontrivial energy dependencies of DD¯, DD¯*, and D*D¯* pair production cross sections in e+e− annihilation are well described within the approach based on an account of the final-state interaction of produced particles. This statement is valid for the production of charged and neutral particles. Interaction of D(*) and D¯(*) is taken into account using the effective potential method. Its applicability is based on the fact that for near-threshold resonance the characteristic width of peak in the wave function is much larger than the interaction radius. The transition amplitudes between all three channels play an important role in the description of cross sections. These transitions are possible since all channels have the same quantum numbers JPC=1−−. Published by the American Physical Society 2024

Zirconium phase diagram from ab initio molecular dynamics

The paper presents analysis of precision of a phonon-based free energy calculation technique (Temperature Dependent Effective Potential method) in comparison with the thermodynamic integration method within classical molecular dynamics. It is shown that the use of the second order force constants is insufficient for accurate calculations of free energies at elevated temperatures due to noticeable anharmonic contributions to lattice vibrations. On the other hand, reliable calculations of the crystal phase equilibrium lines requires free energy accuracy better than 1–3 meV per atom. Based upon the obtained results the Temperature Dependent Effective Potential technique is applied to the detailed study of the solid-state Zr phase diagram from ab initio molecular dynamics that may be achieved if force constants up to the fourth order are used. The calculated zirconium phase diagram is in good agreement with experiment. The α−β−ω triple point was determined at P≈6.74 GPa, T≈837 K.

Microscopic understanding of the in-plane thermal transport properties of 2H transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) are a class of layered materials that hold great promise for a wide range of applications. Their practical use can be limited by their thermal transport properties, which have proven challenging to determine accurately, both from a theoretical and experimental perspective. We have conducted a thorough theoretical investigation of the thermal conductivity of four common TMDs, MoSe2, WSe2, MoS2, and WS2, at room temperature, to determine the key factors that influence their thermal behavior. We analyze these materials using calculations performed with the program, anharmonic lattice dynamics and the Boltzmann transport equation formalism, as implemented in the temperature-dependent effective potentials method. Within this framework, we analyze the microscopic parameters influencing the thermal conductivity, such as the phonon dispersion and the phonon lifetimes. The aim is to precisely identify the origin of differences in thermal conductivity among these canonical TMD materials. We compare their in-plane thermal properties in monolayer and bulk form, and we analyze how the thickness and the chemical composition affect the thermal transport behavior. We showcase how bonding and the crystal structure influence the thermal properties by comparing the TMDs with silicon, reporting the cases of bulk silicon and monolayer silicene. We find that the interlayer bond type (covalent vs. van der Waals) involved in the structure is crucial in the heat transport. In two-dimensional silicene, we observe a reduction by a factor ∼15 compared to the Si bulk thermal conductivity due to the smaller group velocities and shorter phonon lifetimes. In the TMDs, where the group velocities and the phonon bands do not vary significantly passing from the bulk to the monolayer limit, we do not see as strong a decrease in the thermal conductivity: only a factor 2–3. Moreover, our analysis reveals that differences in the thermal conductivity arise from variations in atomic species, bond strengths, and phonon lifetimes. These factors are closely interconnected and collectively impact the overall thermal conductivity. We inspect each of them separately and explain how they influence the heat transport. We also study artificial TMDs with modified masses, in order to assess how the chemistry of the compounds modifies the microscopic quantities and thus the thermal conductivity. Published by the American Physical Society 2024

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems.

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

Detangling Solvatochromic Effects by the Effective Fragment Potential Method.

Understanding molecular interactions in complex systems opens avenues for the efficient design of new materials with target properties. Energy decomposition methods provide a means to obtain a detailed picture of intermolecular interactions. This work introduces a molecular modeling approach for decomposing the solvatochromic shifts of the electronic excited states into the contributions of the individual molecular fragments of the environment surrounding the chromophore. The developed approach is implemented for the QM/EFP (quantum mechanics/effective fragment potential) model that provides a rigorous first-principles-based description of the electronic states of the chromophores in complex polarizable environments. On the example of two model systems, water pentamer and hydrated uracil, we show how the decomposition of the solvatochromic shifts into the contributions of individual solvent water molecules provides a detailed picture of the intermolecular interactions in the ground and excited states of these systems. The analysis also demonstrates the nonadditivity of solute-solvent interactions and the significant contribution of solute polarization to the total values of solvatochromic shifts.

Exchange energies with forces in density-functional theory.

We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.

R-8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method.

The anisotropic and isotropic R-8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang-Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole-octopole polarizability tensor and the quadrupole-quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. While the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang-Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

Revisiting four-phonon scattering in WS2 monolayer with machine learning potential

Recently, the importance of the higher-order anharmonic effect on the thermal transport has been demonstrated in a few two-dimensional (2D) materials. As a member of 2D materials, the WS2 monolayer possesses excellent properties, but its higher-order phonon anharmonic effect is still unclear. As an emerging tool for atomistic simulations, the machine learning Gaussian approximation potential (GAP) has good computational speed and accuracy. In this work, the effect of the four-phonon scattering on the thermal transport properties of the WS2 monolayer is systematically investigated by combining a well-trained GAP with the Boltzmann transport equation. We find that the in-plane thermal conductivity of the WS2 monolayer decreases by 34.68% at 300 K compared to the results without considering the four-phonon scattering, which mainly originates from the strong low-frequency redistribution scattering process. The temperature-induced phonon renormalization in WS2 monolayer is investigated using the temperature-dependent effective potential method. The results show that phonon modes slightly soften with increasing temperature, and the temperature effect weakens the four-phonon scattering while hardly affect the three-phonon scattering. Our work reveals that previous studies considering only the three-phonon scattering and the temperature effect are insufficient, and the four-phonon interaction must be introduced to accurately describe the thermal transport properties of the WS2 monolayer.

Two-channel thermal transport and scattering channel of high-temperature phase SnSe using temperature-dependent effective potential

To resolve the imaginary phonon frequency of high-temperature phase SnSe (853 K) caused by ground-state theory, the temperature-dependent effective potential (TDEP) method is used to evaluate the temperature-dependent interatomic force constants (IFCs). Based on the Boltzmann transport equation, both two-channel transport and scattering channel are studied using the temperature-dependent IFCs. Considering three-phonon and four-phonon scattering, the particle-like thermal conductivity along the xx axis, yy axis, and zz axis is 0.66, 0.34, and 0.61 W/mK, respectively. For glass-like thermal conductivity, the value along the xx axis, yy axis, zz axis are 0.0777, 0.0316, and 0.0791 W/mK, respectively. For the three-phonon scattering channel, the scattering channels of X + O/A→O and X→O+O/A play a major role. For four-phonon scattering channel, the major scattering channels are X + O+A→O, X + A+A→O, X + O-O/A→A, X + A-O→A, X-O/A-O/A→O, X-O-A→A. By utilizing the crystal orbital Hamilton population (COHP) analysis, the low lattice thermal conductivity is attributed to the weak chemical bonds from anti-bonding orbitals between Se4p and Sn5s states. This work provides new insight into the physical mechanisms for thermal transport of high-temperature phase SnSe with strong anharmonic effects.

Reciprocal space temperature-dependent phonons method from ab-initio dynamics

We present a robust reciprocal-space implementation of the temperature-dependent effective potential method, our implementation can scale easily to large cell and long sampling time. It is interoperable with standard ab-initio molecular dynamics and with Langevin dynamics. We prove that both sampling methods can be efficient and accurate if a thermostat is used to control temperature and dynamics parameters are used to optimize the sampling efficiency. By way of example, we apply it to study anharmonic phonon renormalization in weakly and strongly anharmonic materials, reproducing the temperature effect on phonon frequencies, crossing of phase transition, and stabilization of high-temperature phases.

Benchmarking Aspects of Ab Initio Fragment Models for Accurate Excimer Potential Energy Surfaces.

While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits the degree for which these methods can be applied. In this work different aspects of fragment-based approaches are studied on noncovalently bound molecular complexes with interacting chromophores of the fragments, such as π-stacked nucleobases. The interaction of the fragments is considered at two distinct steps. First, the states localized on the fragments are described in the presence of the other fragment(s); for this we test two approaches. One method is founded on QM/MM principles, only including the electrostatic interaction between the fragments in the electronic structure calculation with Pauli repulsion and dispersion effects added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation, includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al. was found to provide an adequate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling provides accurate splitting of the energies of interacting chromophores that are separated by more than 4 Å.

Effective local potentials for density and density-matrix functional approximations with non-negative screening density.

A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. 136, 224109 (2012)]. As illustrated, a convenient variational quantity in that approach is the "screening" or "electron repulsion" density, ρrep, corresponding to the local, KS Hartree, exchange and correlation potential through Poisson's equation. Two constraints, applied to this minimization, largely remove self-interaction errors from the effective potential: (i) ρrep integrates to N - 1, where N is the number of electrons, and (ii) ρrep ≥ 0 everywhere. In this work, we introduce an effective "screening" amplitude, f, as the variational quantity, with the screening density being ρrep = f2. In this way, the positivity condition for ρrep is automatically satisfied, and the minimization problem becomes more efficient and robust. We apply this technique to molecular calculations, employing several approximations in DFT and in reduced density matrix functional theory. We find that the proposed development is an accurate, yet robust, variant of the constrained effective potential method.

Accurate Vertical Electron Detachment Energies and Multiphoton Resonant Photoelectron Spectra of Biochromophore Anions in Aqueous Solution.

We introduce a new methodology for calculating vertical electron detachment energies (VDEs) of biologically relevant chromophores in their deprotonated anionic forms in aqueous solution. It combines a large-scale mixed DFT/EFP/MD approach with the high-level multireference perturbation theory XMCQDPT2 and the Effective Fragment Potential (EFP) method. The methodology includes a multiscale flexible treatment of inner (∼1000 water molecules) and outer (∼18000 water molecules) water shells around a charged solute, capturing both the effects of specific solvation and the properties of bulk water. VDEs are calculated as a function of system size for getting a converged value at the DFT/EFP level of theory. The XMCQDPT2/EFP approach, adapted for calculating VDEs, supports the DFT/EFP results. When corrected for a solvent polarization contribution, the XMCQDPT2/EFP method yields the most accurate estimate to date of the first VDE for aqueous phenolate (7.3 ± 0.1 eV), which agrees well with liquid-jet X-ray photoelectron spectroscopy data (7.1 ± 0.1 eV). We show that the geometry of the water shell and its size are essential for accurate VDE calculations of aqueous phenolate and its biologically relevant derivatives. By simulating photoelectron spectra of aqueous phenolate upon two-photon excitation at wavelengths resonant with the S0 → S1 transition, we also provide interpretation of recent multiphoton UV liquid-microjet photoelectron spectroscopy experiments. We show that its first VDE is consistent with our estimate of 7.3 eV, when experimental two-photon binding energies are corrected for the resonant contribution.

Performance enhancement of snap-through vibration energy harvester with displacement amplifier

Vibration energy harvesters (VEH) based on bistable and snap-through mechanisms are being widely employed to harvest energy from different vibration sources. However, under weak ambient excitation, the performance of these systems is marginal. Multi-stability and enhancement techniques, such as displacement amplifier, are being used with bistable VEH to improve its performance. Similar to this, multi-stable snap-through VEH has also been developed; however, the usage of a displacement amplifier in the context of snap-through VEH has not yet been investigated. In this novel study, a displacement amplifier/ displacement amplification mechanism (DAM) is integrated into a snap-through VEH, and the enhanced performance under weak excitation is investigated. A generalized transformation is applied to develop a reduced-order model of the proposed system, and its dynamics and performance under harmonic and random excitation are investigated analytically and numerically. The frequency–amplitude relationship is derived under harmonic excitation, and a detailed investigation of the influence of system parameters on the frequency and force responses is performed. It is observed that by adjusting the mass and stiffness ratio between the VEH and DAM, it is possible to harvest more energy under harmonic excitation of low intensity. In the case of Gaussian white noise excitation, effective potential, and stochastic averaging methods are used to obtain marginal, joint, and stationary probability density functions and mean square power. The influence of noise intensity and other system parameters on the aforementioned measures is thoroughly investigated. It is observed that for specific parameter values, the proposed VEH can harvest 3.3 times more power under harmonic excitation and four times more power under random excitation compared to the snap-through VEH without DAM.

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.