Expansion Of Potential Energy Research Articles

Accounting impacts of renewable energy expansions on ecosystem services to balance the trade-offs

Renewable energy systems and ecosystem services, both vital for human society, are often at odds. The land cover change brought about by renewable energy expansions tends to degrade ecosystem services. An effective approach for appraising the effects of renewable energy expansions on ecosystem services is therefore urgently needed. Faced with recent acute power shortages, Pakistan has embarked on renewable energy expansions to meet its future energy demands. These expansions, in turn, will degrade ecosystems in the country, leading to a further decline in the value of its already dwindling ecosystem services. To quantify this decline, I combine spatially explicit modeling and ecosystem services valuation techniques to monetize the impacts of the potential expansions of three energy systems: solar, wind, and hydro. The results show that 18.35 % of Pakistan's total area is suitable for potential renewable energy expansion, with 14.83 % of that total appropriate for solar, 3.48 % for wind, and 0.04 % for hydropower. The average value of ecosystem services from the areas of impact by potential expansions of solar, wind, and hydropower energy systems are respectively $2026, $2160, and $2824 per hectare per year (in 2020 U.S. dollars). Furthermore, the permanent loss of ecosystem services from the expansions decreases in the order of hydropower > solar > wind. The renewable energy expansions based on the potential energy mix for the year 2030 will cause a total impact of up to $9617 million per year thereafter, with a complete loss of $1259.4 million per year in ecosystem services values. These results can help achieve a finely balanced trade-off between renewable energy expansions and ecosystem services in the country. This novel approach for assessing the environmental footprints of energy expansions can be a trailblazer for countries and regions aiming at transitioning to renewable energy systems.

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions.

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the sole exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

Numerical and Analytical Investigation of Stability of the Reinforced Plate

The work is aimed at the construction of an algorithm for studying the equilibrium states of a reinforced plate near critical points, using the first (cubic terms) nonlinear terms of the potential energy expansion. Using geometrically nonlinear analysis of displacement, deformation and stress fields, the Eigenforms of buckling were calculated and bifurcation solutions and solutions for equilibrium curves with limit points were constructed depending on the initial imperfections.

High-temperature expansion of the grand thermodynamic potential for scalar particles in crossed electromagnetic fields

The problem of a scalar particle in a constant crossed electromagnetic field ($\mathbf{E}\perp\mathbf{H}$ and $|\mathbf{E}|=|\mathbf{H}|$) is examined. The high-temperature expansion of the grand thermodynamic potential and vacuum energy with account for non-perturbative corrections are derived. The contribution from particles and antiparticles is considered separately. It is shown that the non-perturbative corrections depend on boundary conditions but do not depend on fields.

Atomic-scale design of friction and energy dissipation

Study of friction and energy dissipation always relied on direct observations. Actual theories provide limited prediction on the frictional and dissipative properties if only the material chemistry and geometry are known. We here develop a framework to study intrinsic friction and energy dissipation based on the only knowledge of the normal modes of the system at equilibrium. We derive an approximated expression for the first anharmonic term in the potential energy expansion which does not require the computation of the third-order force constants. Moreover, we show how to characterize the frequency content of observed physical quantities and individuate the dissipative processes active during experimental measurements. As a case study, we consider the relative sliding motion of atomic layers in molybdenum disulfide dry lubricant, and we discuss how to extract information on the energetics of sliding from atomic force microscopy signals. The presented framework switches the investigation paradigm on friction and energy dissipation from dynamic to static studies, paving avenues to explore for the design of alternative anisotropic tribological and thermal materials.

Spectroscopy, decay properties and Regge trajectories of the B and Bs mesons**A. K. Rai acknowledges the financial support extended by the Department of Science of Technology, India under SERB fast track scheme SR/FTP /PS-152/2012

A Gaussian wave function is used for detailed study of the mass spectra of the B and BS mesons using a Cornell potential incorporated with a \U0001d4aa(1/m) correction in the potential energy term and expansion of the kinetic energy term up to \U0001d4aa(p10) for relativistic correction of the Hamiltonian. The predicted excited states for the B and Bs mesons are in very good agreement with results obtained by experiment. We assign B2(5747) and Bs2(5840) as the 13P2 state, B1(5721) and Bs1(5830) as the 1P1 state, B0(5732) as the 13P0 state, Bs1(5850) as the state and B(5970) as the 23S1 state. We investigate the Regge trajectories in the (J,M2) and (nr,M2) planes with their corresponding parameters. The branching ratios for leptonic and radiative-leptonic decays are estimated for the B and BS mesons. Our results are in good agreement with experimental observations as well as outcomes of other theoretical models.

Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules

In the theory of anharmonic vibrations of a polyatomic molecule, mixing the zero-order vibrational states due to cubic, quartic and higher-order terms in the potential energy expansion leads to the appearance of more-or-less isolated blocks of states (also called polyads), connected through multiple resonances. Such polyads of states can be characterized by a common secondary integer quantum number. This polyad quantum number is defined as a linear combination of the zero-order vibrational quantum numbers, attributed to normal modes, multiplied by non-negative integer polyad coefficients, which are subject to definition for any particular molecule. According to Kellman's method [J. Chem. Phys. 93, 6630 (1990)], the corresponding formalism can be conveniently described using vector algebra. In the present work, a systematic consideration of polyad quantum numbers is given in the framework of the canonical Van Vleck perturbation theory (CVPT) and its numerical-analytic operator implementation for reducing the Hamiltonian to the quasi-diagonal form, earlier developed by the authors. It is shown that CVPT provides a convenient method for the systematic identification of essential resonances and the definition of a polyad quantum number. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms. The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.

Origin of the diffuse vibrational signature of a cyclic intramolecular proton bond: Anharmonic analysis of protonated 1,8-disubstituted naphthalene ions

We analyze the structures and spectral signatures of the cyclic intramolecular proton bond, N-H(+)-A, A = O and F, formed when an excess proton is added to derivatives of the 1,8-disubstituted naphthalene scaffold. These compounds provide a quasi-rigid framework with which to study the spectral complexity often associated with the N-H(+)-A entity. Vibrational spectra were obtained by monitoring photodissociation of weakly bound H2 adducts of the mass-selected ions cooled close to 10 K. Several bands across the 900-3500 cm(-1) spectral range were traced to involvement of the bridging proton by their telltale shifts upon selective H∕D isotopic substitution at that position. We account for the complex patterns that occur near the expected locations of the NH stretching fundamentals in the context of background levels mixing with a "bright" zero-order state through cubic terms in the potential energy expansion. Thus, this system provides a detailed picture of one of the mechanisms behind the line broadening often displayed by embedded excess protons. It does so in a sufficiently sparse density of states regime that many discrete transitions are observed in the vicinity of the harmonic stretching transition involving displacement of the trapped proton.

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions

This article concerns an extension of the topological derivative concept for 2-D potential problems involving penetrable inclusions, whereby a cost function J is expanded in powers of the characteristic size ε of a small inclusion. The O( ε 4) approximation of J is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivity, and then generalized to several such inclusions. Simpler and more explicit versions of this result are obtained for a centrally-symmetric inclusion and a circular inclusion. Numerical tests are performed on a sample configuration, for (i) the O( ε 4) expansion of potential energy, and (ii) the identification of a hidden inclusion. For the latter problem, a simple approximate global search procedure based on minimizing the O( ε 4) approximation of J over a dense search grid is proposed and demonstrated.

EXPONENTIAL-TYPE BASIS FUNCTIONS: SINGLE- AND DOUBLE-ZETA [formula omitted] FUNCTION BASIS SETS FOR THE GROUND STATES OF NEUTRAL ATOMS FROM Z = 2 TO Z = 36

Roothaan–Hartree–Fock (RHF) calculations have been carried out for the ground states of the atoms from helium to krypton using certain exponential-type functions, the B functions. We report a compilation of single- and double-zeta (SZ and DZ) wave functions. A comparison with the conventional SZ and DZ RHF wave functions is also presented. For each atom, the total energy, kinetic energy, potential energy, virial ratio, orbital energies, and orbital expansion coefficients and exponents are tabulated.

Higher-order perturbation theory for the thermodynamic properties of a solid with a truncated potential energy expansion

A perturbation theory (PT) is developed in the classical limit which is based on an infinite series of diagrams composed of the loops and bubbles arising from the first- and second-order matrix elements of the PT, respectively. This theory leads to a closed form expression for the free energy, which on expansion gives an infinite power series in the temperature. Results from this theory are obtained for a Hamiltonian in which the Taylor expansion of the potential energy is truncated at the quartic term. These results are compared with results of finite summation versions of the theory up to O(λ8), with results of standard PT of O(λ2) and O(λ4), and with results of molecular dynamics (MD) simulations carried out for the same potential energy surface (i.e., the potential energy expansion truncated at the quartic term). The results show that the theory which includes all powers of temperature gives better agreement with the MD results throughout a wide temperature range than does the standard PT of O(λ2) and O(λ4).

Theory of thermal expansivity and bulk modulus for MgO and other minerals at high temperatures

The Grüneisen theory of thermal expansion as formulated by Born and Huang has been modified by including higher-order terms for the change in volume in the expansion of potential energy. New expressions are obtained for the thermal expansivity and bulk modulus, and used to estimate these quantities for MgO and other minerals in the temperature range 300–1800 K. The results are found to present close agreement with the experimental data.

Molecular dynamics simulations of the effects of truncation of the Taylor expansion of the potential energy on the thermodynamic properties of a crystal

Molecular dynamics simulations are carried out on a Lennard-Jones crystal, for the potential energy surfaces generated from the full Hamiltonian and the Taylor expansion of the potential energy truncated at the quartic term, to determine the accuracy of the quartic truncation with regard to the thermodynamic properties of a crystal. The results show that the errors arising from the quartic truncation become significant only for temperatures T≳0.2Tm, and are only on the order of 5% at T=0.8Tm, where Tm is the melting temperature. The quartic truncation represents a significant improvement over the quadratic (harmonic) truncation, and the errors associated with the quadratic truncation are decreased by 75%. The sources of error in the λ2 perturbation theory are investigated; the errors are found to arise from the truncation of the potential energy expansion at low temperatures, and primarily from the truncation of the perturbation expansion at high temperatures.

Variational solution of the two-center Dirac-Coulomb problem in the free-particle representation

The problem of the hydrogen molecular ion H 2 + is considered in the free-particle momentum-space representation of the Dirac equation. This representation permits a straightforward interpretation of the relativistic energy corrections arising from the kinetic and the potential energy expansion as well as the contribution from virtual electron-positron pairs.

Anisotropic anharmonicity of lattice and molecular vibrations of 1,2,4,5-tetrabromobenzene determined by piezomodulated Raman spectroscopy

Strain-induced coupling constants for the anharmonicity of Raman-active lattice and certain molecular modes of vibration in 1,2,4,5-tetrabromobenzene (TBB) crystals have been determined using piezomodulated Raman spectroscopy. These constants, which are directly related to the first anharmonic term in the potential energy expansion for lattice dynamical calculations, are a quantitative measurement of the modal anharmonicities in the TBB molecular crystal. Application of uniaxial stress in the experiments permits the anisotropy of the anharmonicity to be determined as well as its magnitude. The TBB lattice modes are significantly coupled by the induced strains and the effects of coupling were observed to be dependent on the direction and symmetry of the strains. The molecular modes investigated were, by comparison, less coupled by the acoustic phonons and generally exhibited less anharmonic response with increasing frequency.

レーザ照射によるｆｃｃ金属の溶融・蒸発過程の研究 分子動力学シミュレーション

Considering the principle of minimum potential energy and thermal expansion, atomic array model of fcc metal is constructed at room temperature through the molecular dynamics, where 12000 atoms are arranged in 60 atoms per layer in the direction of width and 200 layers in the direction of depth. It is confirmed that velocity of atoms at room temperature has a Maxwell distribution. A simple model of laser absorption of crystal and a method to estimate stress state of atoms are proposed. Applying molecular dynamics, atomic behavior of copper, aluminum and lead with laser irradiation is simulated. Variation of atomic array and stress state of atoms during and after laser irradiation are shown visually. Main conclusions obtained are summarized as follows : (1) Thermal shock wave travels to interior of material with laser irradiation. Especially, when surface vapors explosively, large compressed-field occurs due to its reaction. (2) Propagation velocity of thermal shock wave is equal to elastic wave velocity. (3) Particles scatter in pieces as relatively fine cluster when power density is higher. On the other hand, the vicinity of surface bounds out forming relatively large lumps when power density is lower. (4) Degree of these phenomena varies with material and depends on the well depth of pair potential.

Rydberg states near the ionization continuum: Autoionization in ammonia

Previously undetected autoionizing Rydberg levels of ammonia which exist in the energy region between the first ionization continuum and the first excited vibrational level of the NH+3 ion have been measured. Jet cooled ammonia molecules in high lying Rydberg levels were detected by a two-color, three-photon excitation resonantly enhanced multiphoton ionization process, 2+1′. The Rydberg series can be assigned to a continuation of the (a2″)(nsa1′) series to which the Ã, D̃′, and Ẽ″ states belong. A vibronic autoionization mechanism based on the electrostatic and linear terms [V0 and (∂V/∂Q)Q, respectively] in the potential energy expansion has been suggested.

Vibrational Spectra of hexaaqua complexes. II. external motions of water molecules in the spectra of AlCl 3 · 6H 2O

The infrared spectra of powdered samples of various AlCl 3 · 6(H,D) 2O isotopomers were recorded at room temperature (RT) and at the boiling temperature of liquid nitrogen (LNT). The RT Raman spectrum of the protiated compound was also studied. It appears that despite the low site symmetry ( C 1), the force field around H 2O has approximately C 2 v symmetry. The librational bands were assigned according to the criteria of Eriksson and Lindgren [1]. The rocking ( r) mode was found at highest frequency (≈ 840 cm −1, the twisting ( t) and wagging ( w) bands being close to each other (≈ 600 and ≈ 540 cm −1, respectively). A strong band at around 1150 cm −1 was found in both infrared (IR) and Raman spectra. It was assigned to second-order transitions of wagging and twisting motions of the water molecules. Strong mechanical anharmonicity in the w(H 2O) and t(H 2O) motions is apparently present, arising probably from large quartic terms in the potential energy expansion.