Finite Field Approach Research Articles

Automated all-functionals infrared and Raman spectra

AbstractInfrared and Raman spectroscopies are ubiquitous techniques employed in many experimental laboratories, thanks to their fast and non-destructive nature able to capture materials’ features as spectroscopic fingerprints. Nevertheless, these measurements frequently need theoretical and computational support in order to unambiguously decipher and assign complex spectra. Linear-response theory provides an effective way to obtain the higher-order derivatives needed, but its applicability to modern exchange-correlation functionals and pseudopotential formalism remains limited. Here, we devise an automated, open-source, user-friendly approach based on density-functional theory and the electric-enthalpy functional to allow seamless calculation from first principles of infrared absorption and reflectivity, together with zone-center phonons, static dielectric tensor, and Raman spectra. By employing a finite-displacement and finite-field approach, we allow for the use of any functional, as well as an efficient treatment of large low-symmetry structures. Additionally, we propose a simple scheme for efficiently sampling the Brillouin zone at different electric fields. To demonstrate the capabilities of the present approach, we study ferroelectric LiNbO3 crystal as a paradigmatic example, and predict infrared and Raman spectra using various (semi)local, Hubbard corrected, and hybrid functionals. Our results also show how PBE0 and extended Hubbard functionals (PBEsol+U+V) yield for this case the best match in term of peak positions and intensities, respectively.

Optoelectronic investigation and spectroscopic characteristics of polyamide-66 polymer

Abstract A semi-crystalline designated nylon 66 polymer is a crucial, high-performance engineering material that is used in wide variety of industrial applications including sensors, electrical insulators, electronic devices, and automotive sector. Using modules based on density functional theory and finite-field approaches, this work explores the optoelectronic and spectroscopic characteristics of this polymer. Absorption, dielectric function, refractive index, and optical conductivity are the principle topics of this study. The effects indicated that nylon 66 is a first-rate insulator and the degree of crystallinity estimated is 46.44%. The simulated bandgap vs. the Tauc relation value is greater than 7.0 eV and has a proportional inaccuracy of 2.36%. Absorption coefficient value, however, suggests that while the refractive index and dielectric function remain stable, the optical conductivity is elevated. In order to determine the advantages appropriate for many applications, this research develops a strong basis and perception of the linear and nonlinear optical properties of nylon 66.

ELECTRODE: An electrochemistry package for atomistic simulations.

Constant potential methods (CPMs) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics. They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. CPMs model conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here, we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator, which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for nonperiodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using nonideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two coaxial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

External fields in conceptual density functional theory.

The necessity of the recent incorporation of new external variables in the context of conceptual DFT (CDFT) is discussed based on the ever-increasing portfolio of experimental reaction conditions in the endeavor of experimentalists to synthesize new molecules with unprecedented properties. Electric and magnetic fields (ε and B), mechanical forces (F), and confinement are proposed as valuable new variables, extending conventional CDFT and its associated response functions. A finite field approach is used to calculate the evolution of both global and local descriptors in a selected series of atomic and molecular applications, and from it derive new response function involving, with one exception, the first derivative to the field considered. The electricfield results, displaying, for example, a case of a field-induced enantioselectivity in the Fukui function, may be instrumental in the recent upsurge of chemistry in oriented external electric fields. The study of atomic electronegativity and hardness in magnetic fields displays a piecewise behavior, associated to configurational jumps upon increasing field strength and reveals an overall compression of their ranges for stronger fields, which may be guiding upon investigating chemistry in extremely high fields like in white dwarfs. The evolution of the electronegativity and hardness of diatomics under mechanical force can elegantly be traced back to differences in their equilibrium distance in the neutral, cationic, and anionic state. The well-known reduction of the polarizability under confinement can be seen as a fore-runner of the increasing hardness of atoms under pressure, presently under investigation. Periodicity showing up in a spontaneous way in the variety of properties is a leitmotiv in this study, as well as the interconnections/analogies between the different response functions.

A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states

Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. A novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.

Spectroscopic investigation and density functional theory prediction of first and second order hyperpolarizabilities of 1-(4-bromophenyl)-3-(2,4-dichlorophenyl)‑prop-2-en-1-one

This work presents the spectroscopic analysis and nonlinear optical (NLO) behaviour of 1-(4-Bromophenyl)-3-(2,4-dichlorophenyl)‑prop-2-en-1-one (DCBC). The motivation behind choosing chalcone derivative DCBC for NLO studies is its crystallization in non-centrosymmetric structure, excellent second harmonic generation efficiency (SHG) and flexibility in structure of chalcones due to donor-acceptor groups. The compound was characterized by FT-IR, FT-Raman, UV–vis and NMR techniques. The structural and spectroscopic features of the molecule were calculated using density functional theory (DFT) employing B3LYP/6–311++G(d,p) basis set and compared with the experimental values. The complete vibrational assignments were made on the basis of potential energy distribution (PED). The Natural Bond Orbital (NBO) analysis of DCBC has been done in order to provide the detailed insight into the nature of electronic conjugation between the bonds in this molecule. The second-order perturbation theory analysis of Fock matrix in the NBO basis of the molecule shows the strong intramolecular hyperconjugative interactions between σ (Cl3-C28) to σ*(C26-C28), n(1)(Cl3) to σ*(C26-C28) and π(C6-C8) to π*(C5-C13) resulting in large stabilization energies leading to large delocalization. A time-dependant variant of DFT (TD-DFT) is applied to calculate the electronic properties such as oscillator strengths, absorption maxima and HOMO and LUMO energies. The HOMO-LUMO energy gap is found to be 3.882 eV and is used to calculate global reactivity parameters. Isotropic chemical shifts were calculated using gauge invariant atomic orbital (GIAO) method and these matched well with the experimental results, indicating the accuracy of calculation method. Molecular Electrostatic Potential (MEP) surface has been depicted to know the chemically active regions of the molecule. The nonlinear optical properties of title molecule were addressed theoretically by the determination of two contributions, vibrational and electronic, to polarizability (α) and the first and the second order hyperpolarizabilities (β and γ). The electronic first and second order hyperpolarizabilities of DCBC determined by Finite Field approach method are found to be 17.805 × 10−30 and 6.0 × 10−41 e.s.u. respectively. These values are comparable to other chalcones and organic NLO materials which indicate that the studied molecule is responsive to nonlinear optical (NLO) effect and has enhanced applicability in the development of nonlinear optical devices.

Relativistic normal coupled-cluster theory analysis of second- and third-order electric polarizabilities of Zn I

We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results including those are obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. We also give a term-by-term comparison of contributions from our CC and NCC calculations in order to show differences in the results from these two methods. Moreover, we present results from other lower-order methods to understand the role of electron correlation effects in the determination of the above quantities. A machine learning based scheme to generate optimized basis functions for atomic calculations is developed and applied here. From the analysis of the dipole polarizability result, accuracy of the calculated quadrupole and third-order polarizability values are ascertained, for which no experimental values are currently available.

A finite field approach to the Carlitz–Riordan q-Catalan numbers

A finite field approach to the Carlitz–Riordan q-Catalan numbers

Fully periodic, computationally efficient constant potential molecular dynamics simulations of ionic liquid supercapacitors.

Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at a specified potential difference, but the inclusion of CPM can be computationally expensive. We demonstrate the computational savings available in CPM MD simulations of ionic liquid supercapacitors when the usual non-periodic slab geometry is replaced with fully periodic boundary conditions. We show how a doubled cell approach, previously used in non-CPM MD simulations of charged interfaces, can be used to enable fully periodic CPM MD simulations. Using either a doubled cell approach or a finite field approach previously reported by others, fully periodic CPM MD simulations produce comparable results to the traditional slab geometry simulations with a nearly double speedup in computational time. Indeed, these savings can offset the additional cost of the CPM algorithm, resulting in periodic CPM MD simulations that are computationally competitive with the non-periodic, fixed charge equivalent simulations for the ionic liquid supercapacitors studied here.

Effect of new DFT methods on spectroscopy and NLO analysis of 2-Bromo-5-nitrothiozole and nitrosodimethylamine.

The present study reports the effect of new DFT methods introduced in Gaussian 16 viz B2PLYP, B2PLYPD, DSDPBEP86, and MPW2LPLYP on spectroscopy and nonlinear optical (NLO) properties. The 2-Bromo-5-nitrothiozole and nitrosodimethylamine are considered for the study. In addition to new methods, old DFT, MP2, and HF methods are also considered. The spectroscopic study of geometrical parameters, vibrational, electronic absorption spectra, and HOMO-LUMO gap with their molecular orbitals have been reported. The geometrical parameters such as optimized energy, dipole moment, bond length, and angles have been reported. The diffuse and polarized basis set 6-311 + + G(d,p) has been used for the study. The first- and second-order hyperpolarizabilities have also been reported for both molecules at all methods. This study shows that these two molecules are responsive to nonlinear optical (NLO), which reflects its enhanced applicability in the development of photonic devices. The finite field approach has been applied for calculating first (β) and second hyperpolarizabilities (ϒ) respectively. The HOMO-LUMO energy gap of nitrosodimethylamine is found to be greater than that of 2-Bromo-5-nitrothiozole. Gaussian16 program package has been used for all these calculations.

Promising computational, structural, vibrational and optical properties of piperazinium bis(2-carboxypyridine)monohydrate (PBCPM) crystal for NLO device applications

The Slow Evaporation Solution Technique (SEST) was used to produce a single crystal of piperazinium bis(2-carboxypyridine)monohydrate (PBCPM). The lattice parameters and molecular structure of the grown crystal were determined using Single Crystal X-Ray Diffraction. The intramolecular and intermolecular interactions were visualised using Hirshfeld surface analysis. The B3LYP level of theory with a 6–31++G (d,p) basis set was used to compute the Molecular optimised geometry. The FT-IR and FT-R spectral studies that have been reported look at the modes of vibration of various functional groups in the PBCPM crystal. The grown crystal has a high transmittance in the entire visible field, according to UV–vis transmittance reports. Based on the finite-field approach, the polarizability and hyperpolarizability of PBCPM is determined using the DFT-B3LYP method and the 6–311G(d,p) basis set. The Z-scan technique is used to perform third order NLO studies on the PBCPM crystal. The result discussed confirms that PBCPM crystal is a potential candidate for future NLO device applications.

Benchmarking many-body approaches for the determination of isotope-shift constants: Application to the Li, Be+ , and Ar15+ isoelectronic systems

We have applied relativistic coupled-cluster (RCC) theory to determine the isotope shift (IS) constants of the first eight low-lying states of the Li, Be$^+$ and Ar$^{15+}$ isoelectronic systems. Though the RCC theory with singles, doubles and triples approximation (RCCSDT method) is an exact method for these systems for a given set of basis functions, we notice large differences in the results from this method when various procedures in the RCC theory framework are adopted to estimate the IS constants. This has been demonstrated by presenting the IS constants of the aforementioned states from the finite-field, expectation value and analytical response (AR) approaches of the RCCSDT method. Contributions from valence triple excitations, Breit interaction and lower-order QED effects to the evaluation of these IS constants are also highlighted. Our results are compared with high-precision calculations reported using few-body methods wherever possible. We find that results from the AR procedure are more reliable than the other two approaches. This analysis is crucial for understanding the roles of electron correlation effects in the accurate determination of IS constants in the heavier atomic systems, where few-body methods cannot be applied.

Relativistic Coupled-Cluster Calculations of Isotope Shifts for the Low-Lying States of Ca II in the Finite-Field Approach

We have evaluated the isotope shift (IS) constants of the first five low-lying fine-structure states of the singly charged calcium ion (Ca II) by adopting a finite-field (FF) approach in the relativistic coupled-cluster (RCC), a method developed by us and by using a code also developed by us. A similar previous calculation using singles and doubles approximation RCC theory (RCCSD method), gives results for the individual states in the FF approach that deviate substantially, while the differential values (the shifts of the spectral lines) agree reasonably well with other theoretical results and with experiments. However, we find a contrasting trend from the FF approach using our RCCSD method although calculations with the Dirac–Hartree–Fock (DHF) method shows good agreement. Our results also show that inclusion of partial triple excitations in the perturbative approach (RCCSD(T) method) through energy derivation lessens accuracy, but these results can be improved when triple excitations are included in the wave function that determines the RCC equations. The differences between the RCCSD and RCCSD(T) results demonstrate the importance of triple excitations in evaluating energies and IS constants for Ca II. Finally, we also present ab initio values of IS’s between the S–P, S–D, and D–P transitions in the DHF, and RCCSD and RCCSD(T) approximations and this is compared to the previously reported values (theoretical as well as experimental).

An efficient synthesis, characterization, DFT study and molecular docking of novel sulfonylcycloureas

Sulfonylcycloureas derivatives (3a-3e) are novel heterocyclic compounds synthesized by condensation reaction of several sulfonamides derived from aminoesters (1a-1e) with ethyl bis(2-chloroethyl)carbamate 2b. Series of these desired products are obtained from good to excellent yields within 3–4 h in all cases. All the synthesized compounds are characterized by 1H, 13C, NMR, and mass spectroscopy. Molecular docking are used to study the anticancer activity of the most active compounds. Molecular docking of the molecule 3 into the AKR1C1 crystal structure reveals the key interactions with the active site. The theoretical calculations for the compounds 3a-3e were performed using DFT/B3LYP/6-31 G (d,p) method. The optimized structural parameters, Frontier molecular orbitals (FMO's) and global reactivity descriptors were determined. The dipole moment (μ), polarizability (α) and first order hyperpolarizability (β) values of the title compound have been computed at the same level of theory on the finite field approach.

Ab initio relativistic treatment of the [formula omitted][formula omitted] and [formula omitted] systems of the CO molecule

The spin-forbidden a3Π−X1Σ+,a′3Σ+−X1Σ+ and spin-allowed A1Π−X1Σ+ electronic transitions dipole moments of carbon monoxide have been ab initio studied in the framework of multi-reference Fock space coupled cluster method combined with the finite-field approach and the generalized relativistic pseudo-potential model for the effective introducing the relativity in all-electron correlation treatment. Radiative lifetimes, τi(v′,J′), of the upper i∈[a3Π,A1Π] states were evaluated as a function of vibrational, v′, and rotational, J′, quantum numbers. The τa-values derived for the triplet a3Π1(0,1) and a3Π2(0,2) states at the highest level of computation were found to be 2.59 and 142 ms, which are near perfect agreement with their best experimental counterparts (J. J. Gilijamse, et al., J. Chem. Phys., 127, 221102 (2007)). The intercombination a−X,a′−X transition probabilities were numerically proved to be proportional to α2, where α=e2/ℏc is the fine structure constant.

Electric dipole and quadrupole properties of the Cd atom for atomic-clock applications

We present accurate values of the atomic properties that are sensitive to an external electric field in an experiment, such as static electric dipole and quadrupole polarizabilities, hyperpolarizabilities, and quadrupole moments of the low-lying $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$, $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$, and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ states of the Cd atom. The four-component relativistic coupled-cluster theory is employed to determine the atomic wave functions and energies. The finite-field approach is adopted to estimate the above quantities from the evaluated energies. The roles of electron correlation effects in the calculations are demonstrated by giving results that are obtained with different approximations. Precise knowledge of the above spectroscopic properties is useful for estimating typical systematics of the optical clocks built using the Cd atoms.

Modeling interactions of natural and two-phase fluid-filled fracture propagation in porous media

In this paper, a novel computational framework is introduced for simulation of multiphase flow, geomechanics, and fracture propagation in porous media based on Biot’s model for poroelasticity by focusing on interactions between hydraulic and natural fractures. Since realistic porous media contain many natural fractures, it is important not only to stimulate hydraulic fractures but also to study the interaction between natural and hydraulic fractures. Here, state-of-the-art numerical modeling of natural and hydraulic fractures using a diffusive adaptive finite element phase field approach is employed. The locally mass conservative enriched Galerkin finite element methods (EG) are utilized to model two-phase flow in propagating fractures with relative permeability and capillary pressure. Geomechanics approximated by a continuous Galerkin finite element method is coupled to multiphase flow by applying an iteratively coupled scheme. Numerical examples are presented that demonstrate the effectiveness of this framework for different propagation scenarios by varying the degrees of physics. In addition, the capabilities to perform high-fidelity simulations on complex fracture networks, with randomly joined diffusive natural fractures, are illustrated.

Growth and dielectric studies of toluidine tartrate single crystals:A novel organic NLO material

The crystal of nonlinear optical (NLO) interest, organic compound Toluidine Tartrate (TT) with molecular formula C11 H15 N O6 has been crystallized from solvent ethanol at room temperature using slow evaporation solution growth technique. Single crystal XRD analysis was performed and reveals that the crystal is grown with triclinic system with non centrosymmetric space group P1. Various functional groups of the compound were analysed using FTIR and FTRaman spectral analysis. The molecular structure was confirmed by 1H NMR study. The cut-off wavelength of the grown material is 239 nm and shows a low absorption in the near IR region. The first order hyperpolarizibility (βijk) of TT is calculated using the B3LYP/6-31G (d,P) basis set based on finite field approach. Dielectric and hardness studies were also performed. The second harmonic generation (SHG) relative efficiency was found to be 1.2 times of KDP. Thus, the characterization of the grown crystal reveals the suitability of the material for NLO applications.

Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit.

The asymptotic, R → ∞, behavior of the potential-energy and dipole-moment functions (PEFs and DMFs) for all six (1,2)Σ+, (1,2)Π, Σ-, and Δ electronic states converging to the ground C(3P) + O(3P) dissociation limit of the CO molecule are studied in the framework of long-range (LR) perturbation theory. The analytical expressions for the leading coefficients of the LR expansion, C5/R5 for PEF and d4/R4 for DMF, in terms of the atomic quadrupole constants and static dipole polarizabilities are derived. The exact relationships between the LR coefficients for the states of different spatial symmetry are established as well. The analytical results are complemented with the first-principles calculation of the PEFs and DMFs for all the above states at large distances (R = 5-20 Å). The electronic structure calculation is conducted by means of the multi-reference configuration interaction and the averaged-coupled-pair functional methods, which both implemented the aug-cc-pwCVXZ (X = T, Q, and 5) basis sets and finite-field approach. The dispersion coefficients, C5 and C6, extracted from the ab initio PEFs, are found to be very close to their present and previous theoretical counterparts. The analytically estimated d4 = -5 DÅ4 obtained for the ground X1Σ+ state perfectly agrees with the present ab initio DMF but diverges significantly from the literature data.

Electromagnetic modelling with topography on regular grids with equivalent materials

SUMMARY Maxwell’s equations are valid regardless of the choice of the coordinate system. By this property a change of coordinates can be equivalently expressed as a change of the material parameters. This idea opens a new approach to the problem of accurate electromagnetic modelling in the vicinity of steep topography or bathymetry. Via a change of coordinates, any earth model with complicated layer interfaces can be represented by an equivalent model where those interfaces are flat, but with its materials correspondingly altered. This new model could then be discretized on a regular mesh and fields could be computed by an appropriate finite difference or integral equation code. Unfortunately, this is not straightforward because both the new electric and magnetic materials are fully anisotropic. By instead applying a finite element secondary field approach to the equivalent model, we can completely account for the topography interface in the planar layered background model. The only modification required to existing finite element formulations is a slightly more complicated right-hand side of the linear system of equations, whereas the system matrix is unchanged in any coordinate system. In a numerical modelling experiment we confirm that our technique gives increased accuracy when compared with a recently published technique for dealing with topography in a secondary field formulation for the case of a magnetotelluric source field. In turn, in the vicinity of conductivity anomalies, accuracy can also be negatively affected.