Partitioning Of Total Energy Research Articles

Seamless Multilayer─A Novel Total Energy Partition Scheme for Embedded and Hybrid Calculations.

In this paper, we provide general formulation of a multilayer approach, covering both additive and subtractive quantum mechanics/molecular mechanics (QM/MM) as special cases. After that, we suggest a novel definition of QM/MM total energy based on the consideration of a system divided into three layers. In a simplified form, it is , where layers 1, 2, and 3 represent inner QM, outer QM, and classical MM regions, respectively. The novel formulation is also not limited by only QM/MM combination of methods─in fact, any computational methods can be combined in a hybrid calculation. In this paper, we call the new approach seamless multilayer. Test calculations performed for silica and boric oxide show that the new approach requires no QM/MM interface parameterization as well as no or very simple correction terms for boundary atoms. This can greatly facilitate QM/MM studies of covalent inorganic solids. However, test calculations of α-Al2O3 show that for ionic compounds, the new method requires some additional development.

UnderstandingRamachandranplot for dipeptide: A density functional theory and information‐theoreticapproach study

AbstractThe Ramachandran plot in biochemistry visualizes the propensity of amino acid residues to assume different secondary structures. It can be obtained by different approaches such as bioinformatics and molecular dynamics. In this work, we systematically scan the two single bonds around the α‐carbon of a peptide to generate the three‐dimensional potential energy surface and then project it onto the coordinate plane to generate the Ramachandran plot. Using the two schemes of the total energy partition and information‐theoretic approach in density functional theory, we analyze the plot and find out that the dominant contributor to determine the local minima of secondary structures, especially β‐sheets, in the Ramachandran plot is the electrostatic interaction, whereas steric and exchange‐correlation contributions play minor yet indispensable roles, especially for determining α‐helixes. As the generalization of our prior studies for systems with one rotatable bond, our current results confirm what we yielded before from the viewpoint of energetic contributions, and at meanwhile provide an in‐depth understanding about the nature and origin of secondary structure propensities from the Ramachandran plot.

Cooperativity and reactivity properties of medium-sized boron clusters: a combined density functional theory and information-theoretic approach study

In continuation of our previous work of small boron clusters [Phys. Chem. Chem. Phys. 23, 24118 (2021)], we systematically examined the neutral and negatively charged boron clusters B n /B − (nε{8–38}) with planar or quasi-planar conformations, whose exotic properties have aroused considerable interest in the literature. We make use of two total energy partition schemes, conceptual density functional theory, and the information-theoretic approach to appreciate the cooperativity and reactivity properties. We found that neutral boron clusters are positively cooperative, but negatively charged boron clusters are negatively cooperative. Our results show that the origin of the cooperativity effect for the negatively cooperative boron clusters is much more complicated than the neutral boron clusters. For chemical reactivity, we unveil that the reactive sites are around the cluster periphery and boron atoms can be both electrophilic and nucleophilic. Global and local aromaticity for the boron clusters can be totally different. For the first time, we have observed helical spin density distributions for negatively charged boron clusters (B16 – and B20 – ), which is reminiscent of helical molecular orbitals [Chem. Sci. 4, 4278 (2013)] in allenes, cumulenes, and oligoynes (polyalkynes). Collectively, our results should provide more insights to understand the exotic properties of boron clusters and henceforth yield novel potential applications.

The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry

This study investigates the vertical structure of the dynamical properties of a warm-core ring in the Gulf of Mexico (Loop Current ring) using glider observations. We introduce a new method to correct the glider’s along-track coordinate, which is, in general, biased by the unsteady relative movements of the glider and the eddy, yielding large errors on horizontal derivatives. Here, we take advantage of the synopticity of satellite along-track altimetry to apply corrections on the glider’s position by matching in situ steric height with satellite-measured sea surface height. This relocation method allows recovering the eddy’s azimuthal symmetry, precisely estimating the rotation axis position, and computing reliable horizontal derivatives. It is shown to be particularly appropriate to compute the eddy’s cyclo-geostrophic velocity, relative vorticity, and shear strain, which are otherwise out of reach when using the glider’s raw traveled distance as a horizontal coordinate. The Ertel potential vorticity (PV) structure of the warm core ring is studied in details, and we show that the PV anomaly is entirely controlled by vortex stretching. Sign reversal of the PV gradient across the water column suggests that the ring might be baroclinically unstable. The PV gradient is also largely controlled by gradients of the vortex stretching term. We also show that the ring’s total energy partition is strongly skewed, with available potential energy being 3 times larger than kinetic energy. The possible impact of this energy partition on the Loop Current rings longevity is also discussed.

Nature and origin of γ-gauche effect in sulfoxides: A density functional theory and information-theoretic approach study

Bulky vicinal groups around a single bond usually prefer to be in the opposite (anti) conformation but when extra interactions come into play, more stable could be the gauche conformer, where the neighboring groups embrace a dihedral angle around 60°. This is called the gauche effect. The γ-gauche effect historically features the upfield shift of 13C NMR spectra when a carbon atom and its nonprotonic γ-substituent are in a gauche arrangement. In this work, using sulfoxides as illustrative examples, we show that the nature of the γ-gauche effect is the same as that of the gauche effect, i.e., the gauche conformation is more stable than the anti conformation. To unveil the origin of this effect, we employ two total energy partition schemes in density functional theory and four quantities from the information-theoretic approach. Our results unambiguously show that the γ-gauche effect is of the stereoelectronic origin with a multifaceted nature. Its origin can be understood from a few different perspectives including energetic contributions, dipole moment, charge distribution, hyperconjugation, and information theory. Substantially different from other stereoelectronic effects such as anomeric and generalized anomeric effects, this effect has its unique features as demonstrated from our results in the present work. Having successfully established the link of the γ-gauche with other gauche effects and unveiled its multi-faceted origin, this study should shed new light towards the comprehensive understanding about this important effect of conformational stability in sulfoxides and other systems alike.

Locality of the Thomas\u2013Fermi\u2013von Weizs\xe4cker Equations

We establish a pointwise stability estimate for the Thomas–Fermi–von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas–Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

Revisiting the beryllium bonding interactions from energetic and wavefunction perspectives

Not too much is known about the beryllium bonding interactions. Here, the total energy partition schemes as well as DFT-SAPT are used to explore the origin and nature of the beryllium bonds from an energetic point of view. In addition, Shannon entropy and Fisher information, which are based upon the electron probability density, rather than the shape function, are adopted to dissect the impact resulted from a wavefunction perspective. Results reveal that the electrostatic potential largely causes the formation of beryllium bonds. Moreover, there are strong linear relationships between atomic Shannon entropy and Fisher information of Be atoms, which can aid to distinguish the different sources of noncovalent weak interactions.

Adjustment to Injections of Mass, Momentum, and Heat in a Compressible Atmosphere

Abstract This study compares the response to injections of mass, heat, and momentum during hydrostatic and geostrophic adjustment in a compressible atmosphere. The sensitivity of the adjustment to these different injection types is examined at varying spatial and temporal scales through analysis of the transient evolution of the fields as well as the partitioning of total energy between acoustic waves, buoyancy waves, Lamb waves, and the steady state. The effect of a cumulus cloud on its larger-scale environment may be represented as a vertical mass source/sink and a localized warming. To examine how the response to such injections may differ, injections of mass and heat that generate identical potential vorticity (PV) distributions and, hence, identical steady states, are compared. When the duration of the injection is very short (e.g., a minute or less), the injection of mass generates a very large acoustic wave response relative to the PV-equivalent injection of heat. However, the buoyancy wave response to these two injection types is quite similar. The responses to injections of divergent momentum in the vertical and horizontal directions are also compared. It is shown that neither divergent momentum injection generates any PV and, thus, there is no steady-state response to these injections. The waves excited by these injections generally propagate their energy in the direction of the injection. Consequently, an injection of vertical momentum is an efficient generator of vertically propagating, horizontally trapped, high-frequency buoyancy waves. Such waves have a short time scale and are therefore very sensitive to the injection duration. Analogously, an injection of divergent horizontal momentum is an efficient generator of horizontally propagating, vertically trapped low-frequency buoyancy waves that are relatively insensitive to the injection duration. Because of this difference in the response to horizontal and vertical injections of momentum, the response to the injection of an isolated updraft differs depending on whether a compensating horizontal inflow/outflow is also specified. This additional specification of inflow/outflow helps filter acoustic waves and encourages a stronger updraft that is not removed as rapidly by the buoyancy waves. This finding is relevant to the initialization of updrafts in compressible numerical weather prediction models. Injection of nondivergent momentum generates waves in the regions of convergence/divergence produced by the deflection of the current by Coriolis forces. The energy partitioning for such an injection is sensitive to the width and depth of the current relative to the Rossby radius of deformation, but the response is insensitive to the duration of injection for time scales shorter than several hours.

Wave Response during Hydrostatic and Geostrophic Adjustment. Part I: Transient Dynamics

Abstract The adjustment of a compressible, stably stratified atmosphere to sources of hydrostatic and geostrophic imbalance is investigated using a linear model. Imbalance is produced by prescribed, time-dependent injections of mass, heat, or momentum that model those processes considered “external” to the scales of motion on which the linearization and other model assumptions are justifiable. Solutions are demonstrated in response to a localized warming characteristic of small isolated clouds, larger thunderstorms, and convective systems. For a semi-infinite atmosphere, solutions consist of a set of vertical modes of continuously varying wavenumber, each of which contains time dependencies classified as steady, acoustic wave, and buoyancy wave contributions. Additionally, a rigid lower-boundary condition implies the existence of a discrete mode—the Lamb mode— containing only a steady and acoustic wave contribution. The forced solutions are generalized in terms of a temporal Green's function, which represents the response to an instantaneous injection. The response to an instantaneous warming with geometry representative of a small, isolated cloud takes place in two stages. Within the first few minutes, acoustic and Lamb waves accomplish an expansion of the heated region. Within the first quarter-hour, nonhydrostatic buoyancy waves accomplish an upward displacement inside of the heated region with inflow below, outflow above, and weak subsidence on the periphery—all mainly accomplished by the lowest vertical wavenumber modes, which have the largest horizontal group speed. More complicated transient patterns of inflow aloft and outflow along the lower boundary are accomplished by higher vertical wavenumber modes. Among these is an outwardly propagating rotor along the lower boundary that effectively displaces the low-level inflow upward and outward. A warming of 20 min duration with geometry representative of a large thunderstorm generates only a weak acoustic response in the horizontal by the Lamb waves. The amplitude of this signal increases during the onset of the heating and decreases as the heating is turned off. The lowest vertical wavenumber buoyancy waves still dominate the horizontal adjustment, and the horizontal scale of displacements is increased by an order of magnitude. Within a few hours the transient motions remove the perturbations and an approximately trivial balanced state is established. A warming of 2 h duration with geometry representative of a large convective system generates a weak but discernible Lamb wave signal. The response to the conglomerate system is mainly hydrostatic. After several hours, the only signal in the vicinity of the heated region is that of inertia–gravity waves oscillating about a nontrivial hydrostatic and geostrophic state. This paper is the first of two parts treating the transient dynamics of hydrostatic and geostrophic adjustment. Part II examines the potential vorticity conservation and the partitioning of total energy.

Total energy partitioning within a one-electron formalism: A Hamilton population study of surface–CO interaction in the c(2×2)-CO/ Ni(100) chemisorption system

A scheme for total electronic energy partitioning within the framework of a one-electron theory of the extended Hückel-type is presented, with a view to extending and augmenting the capabilities of existing theoretical electronic structure analysis tools, specifically overlap population analysis. A total electronic energy partitioning is developed first for molecular and subsequently extended materials. In constructing the partitioning, we define molecular orbital Hamilton populations (MOHP’s) for discrete systems, and Crystal Orbital Hamilton Populations (COHP’s) for extended systems. The various energy partitionings and overlap population analyses are exemplified and contrasted for HX (X=F,Cl,Br), ethane, and a [PtH4]2− polymer. The utility of energy partitioning is demonstrated by effecting a COHP partitioning of the surface–CO interaction for the c(2×2)-CO/Ni(100) chemisorption system. Aspects of the surface–CO interaction less amenable to overlap population analysis are addressed, specifically the role of energetically low-lying filled CO orbitals and the relative contributions of surface s, p, and d bands to surface–CO interaction. Hamilton population analysis leads to a CO (4σ, 5σ)–metal forward donation, metal–CO(2π*) backdonation model for the surface–CO interaction. The metal σ contribution to surface–CO bonding is described as sp dominated metal spd hybrid–CO bonding, modifying slightly the metal d–CO σ bonding model proposed by Blyholder. The metal d-2π* backdonation of the Blyholder model remains. The role of the CO(1π) orbitals is also discussed in the context of CO orbital mixing on binding CO to the Ni(100) surface.

Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies

The purpose of this work is to study the asymptotic partition of total energy for the solutions of the mixed initial boundary value problem within the context of the thermoelasticity of initially stressed bodies.

Interpretation of photoelectron spectra in terms of the semi-empirical AM1 method

Equilibrium torsional angles of 2-phenylpyrroles and their radical cations in the ground and ionized states have been estimated using UV photoelectron and electron spectroscopies, respectively, in combination with AM1 quantum-chemical calculations. A theoretical study of the internal rotation potential by means of the total energy partitioning approach has led to the following conclusions. a) In the case of molecules and radical cations of biphenyl and its heteroanalogs, the tendency to adopt a planar conformation (V2 barrier) is determined, in the first place, by the contribution of the two-center resonance component of the interannular bond energy. b) Non-valence interactions are vital for the stabilization of the gauche conformation. Their effect on theV4 barrier of biphenyls is stronger than that observed for 2-phenylpyrroles.

Basicity of azoles. 1. Investigation of total energy of pyrazole and imidazole derivatives by the partitioning method

1. Calculations by the total energy partitioning method, applied to a broad group of substituted azoles, have shown that the degree of destabilization of the -π-electron system in heterocyclic compounds upon protonation can provide an explanation for only the difference in principle between the basicities of pyrazoles and imidazoles. Within each series of compounds, the proton affinity is not determined by the magnitude of destabilization of the π-electron system. 2. Among the calculated molecular orbital characteristics of pyrazoles and imidazoles — total and π-electron charges on the basic center, their changes upon protonation, the energy of the N-H bond in the cations, the magnitude of change in one-center components of the total energy upon adding a proton, and the charge characteristics of the pyrrole N atom in the ground and ionic states — there is no characteristic that can provide an adequate description of the changes in proton affinity of these compounds. 3. For practical purposes in determining the relative basicities of azoles, it is possible to use a correlation of the proton affinity with a readily calculated parameter, the charge on the proton in the cation.

ChemInform Abstract: THEORETICAL STUDY ON THE MOLECULAR STRUCTURE OF FLUOROETHANES

Abstract Semiempirical NDDO calculations using experimental molecular geometries have been performed for all staggered and eclipsed forms of ethane and all the fluoroethanes. The NDDO method produces correct results for the stabilities of molecules with only one staggered and one eclipsed form. For fluoroethanes with two staggered and two eclipsed forms the gauche form is favoured by the calculation, producing incorrect results in two cases. Total-energy partitioning was used to interpret conformer stabilities. The experimentally established trends concerning the dependence of given bond lengths on changes in groups within the fluoroethanes are correlated with partitioned energy terms.

Theoretical study on the molecular structure of fluoroethanes

Semiempirical NDDO calculations using experimental molecular geometries have been performed for all staggered and eclipsed forms of ethane and all the fluoroethanes. The NDDO method produces correct results for the stabilities of molecules with only one staggered and one eclipsed form. For fluoroethanes with two staggered and two eclipsed forms the gauche form is favoured by the calculation, producing incorrect results in two cases. Total-energy partitioning was used to interpret conformer stabilities. The experimentally established trends concerning the dependence of given bond lengths on changes in groups within the fluoroethanes are correlated with partitioned energy terms.

Interactions intramoléculaires en serie cyclohexanique, partie 1: fluoro-2 etchloro-2 cyclohexanones

CNDO/2 calculations have been performed on cyclohexanone, chloro-2 and fluoro-2 cyclohexanone. The intramolecular interactions are discussed in terms of orbital interactions, and quantitatively analysed by means of the total energy partition introduced by Pople[11].

On the electronic origins of barriers to methyl rotation: CNDO/2 calculations on (CH 3) 2XH n (X = C, Si, N, P, O, S) molecules

CNDO calculations are performed for the homogeneous series of (CH 3) 2XH n compounds (X = C, Si, N, P, O, S) in order to determine the molecular equilibrium configuration. In agreement with available experimental data, for all investigated molecules, the theoretical energy minimum is found for the (θ = 60°, ψ = 60°) conformation in which one hydrogen of each methyl group is in the X heavy atoms plane but pointing outside the CXC angle. A partitioning of total energy shows that the variations of this quantity are completely reflected by the variations of the interaction energy between non-bonded terms. A more detailed analysis reveals, only for the third-row compounds, the essential role of the interactions between central atom and methyl hydrogens.