On the accurate estimation of free energies using the jarzynski equality

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, . Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator . Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to . We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional to the Bennett acceptance ratio () estimator. We show that, for Gaussian unidirectional work distributions, is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that and perform better than and , for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.     

Fluxional bonds in quasi-planar and half-sandwich (M = K,Rb, and Cs)

Detailed molecular orbital and bonding analyses reveal the existence of both fluxional σ- and π-bonds in the global minima C_s ( 1 ) and C_s MB₁₈ ( 3 ) and transition states C_s ( 2 ) and C_s ( 4 ) of dianion and monoanions (M = K, Rb, and Cs). It is the fluxional bonds that facilitate the fluxional behaviors of the quasi-planar and half-sandwich which possess energy barriers smaller than the difference of the corresponding zero-point corrections. © 2019 Wiley Periodicals, Inc.     

A Density Functional Theory Study on Nonlinear Optical Properties of Double Cage Excess Electron Compounds: Theoretically Design M[Cu(Ag)@(NH3)n](M = Be,Mg and Ca; n = 1–3)

In this work, we investigated the nonlinear optical (NLO) properties of excess electron electride molecules of M[Cu(Ag)@(NH₃)_n](M = Be, Mg and Ca; n = 1–3) using density functional theory (DFT). This electride molecules consist of an alkaline-earth (Be, Mg and Ca) together with transition metal (Cu and Ag) doped in NH₃ cluster. The natural population analysis of charge and their highest occupied molecular orbital suggests that the M[Cu(Ag)@(NH₃)_n] compound has excess electron like alkaline-earth metal form double cage electrides molecules, which exhibit a large static first hyperpolarizability () (electron contribution part) and one of which owns a peak value of 216,938 (a.u.) for Be[Ag@(NH₃)₂] and vibrational harmonic first hyperpolarizability () (nuclear contribution part) values and the ratio of /, namely, η values from 0.02 for Be[Ag@(NH₃)] to 0.757 for Mg[Ag@(NH₃)₃]. The electron density contribution in different regions on values mainly come from alkaline-earth and transition metal atoms by first hyperpolarizability density analysis, and also explains the reason why values are positive and negative. Moreover, the frequency-dependent values β(−2ω,ω,ω) are also estimated to make a comparison with experimental measures. © 2018 Wiley Periodicals, Inc.     

Substitutional carbon defects in silicon: A quantum mechanical characterization through the infrared and Raman spectra

The infrared (IR) and Raman spectra of eight substitutional carbon defects in silicon are computed at the quantum mechanical level by using a periodic supercell approach based on hybrid functionals, an all electron Gaussian type basis set and the CRYSTAL code. The single substitutional C _s case and its combination with a vacancy (C _sV and C _sSiV) are considered first. The progressive saturation of the four bonds of a Si atom with C is then examined. The last set of defects consists of a chain of adjacent carbon atoms C, with i = 1–3. The simple substitutional case, C _s, is the common first member of the three sets. All these defects show important, very characteristic features in their IR spectrum. One or two C related peaks dominate the spectra: at 596 cm⁻¹ for C _s (and C _sSiV, the second neighbor vacancy is not shifting the C _s peak), at 705 and 716 cm⁻¹ for C _sV, at 537 cm⁻¹ for C and C (with additional peaks at 522, 655 and 689 for the latter only), at 607 and 624 cm⁻¹, 601 and 643 cm⁻¹, and 629 cm⁻¹ for SiC, SiC, and SiC, respectively. Comparison with experiment allows to attribute many observed peaks to one of the C substitutional defects. Observed peaks above 720 cm⁻¹ must be attributed to interstitial C or more complicated defects.     

A Computational Analysis of the Intrinsic Plasticity of Five-Coordinate Cu(II) Complexes and the Factors Leading to the Breakdown of the Orbital Directing Effect in Paddlewheel Secondary Building Units

Quantum chemical calculations on model copper paddlewheel (CPW) complexes of general formula [Cu₂(μ₂-O₂CR)₄L₂] establish two local coordination geometries at the metal centers depending on the balance between equatorial and axial ligand fields. When the equatorial field is stronger than the axial field (large ligand field asymmetry), dominates the stereochemical activity of the d⁹ shell resulting in a relatively rigid, “orbitally directed” planar or square pyramidal structure. However, if the axial field is significantly increased, or the equatorial field moderately weakened, a small ligand field asymmetry results and both and are involved in the stereochemical activity. This results in a “plastic,” distorted trigonal bipyramidal geometry where the former axial ligand moves into one of the original four equatorial positions. Linkers already used to synthesize zinc-dabco MOFs (dabco = 1,4-diazabicyclo[2.2.2]octane) are shown to generate plastic CPW secondary building unit analogs with potential implications for conferring breathing behavior for MOFs which would currently be assumed to be rigid. © 2019 Wiley Periodicals, Inc.     

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic and kinetic potentials and electron density allowed partitioning any molecules and crystals into atomic - and potential-based -basins; -basins explicitly account for the electron exchange effect, which is missed for -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of - and -basins. The gap between - and -basins represents the charge transfer, while the gap between - and -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of -, -, and - basin boundaries between interacting atoms was proposed. The position of -boundary between - and -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's -basin penetrates oxygen atom's -basin, while for covalent bonds a -boundary closely approaches a -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the -basin of an electron occupier atom.     

Fluorine Substitution of TCNQ Alters the Redox-Driven Catalytic Pathway for the Ferricyanide-Thiosulfate Reaction

Mechanistic variation in catalysis through substituent-based redox tuning is well established. Fluorination of TCNQ (TCNQ=tetracyanoquinodimethane) provides ~850 mV variation in the redox potentials of the and (n=0, 2, 4) processes. With , catalysis of the kinetically very slow ferrocyanide-thiosulfate redox reaction in aqueous solution occurs via a mechanism in which the catalyst is reduced to when reacting with which is oxidised to . Subsequently, reacts with to form and reform the catalyst, in another thermodynamically favoured process. An analogous mechanism applies with as a catalyst. In contrast, since the reaction of with is thermodynamically unfavourable, an alternative mechanism is required to explain the catalytic activity observed in this non-fluorinated system. Here, upon addition of , reduction of to occurs with concomitant oxidation of to , which then acts as the catalyst for oxidation. Thermodynamic data explain the observed differences in the catalytic mechanisms. (n=0, 4) also act as catalysts for the ferricyanide-thiosulfate reaction in aqueous solution. The present study shows that homogeneous pathways are available following addition of these dissolved materials. Previously, these (n=0, 4) coordination polymers have been regarded as insoluble in water and proposed as heterogeneous catalysts for the ferricyanide-thiosulfate reaction. Details and mechanistic differences were established using UV-visible spectrophotometry and cyclic voltammetry.     

Oxidation of methylamine

A detailed chemical kinetic model for oxidation of methylamine has been developed, based on theoretical work and a critical evaluation of data from the literature. The rate coefficients for the reactions of CHNH + O CHNH / CHNH + HO, CHNH + H CH + NH, CHNH CHNH, and CHNH + O CHNH + HO were calculated from ab initio theory. The mechanism was validated against experimental results from batch reactors, flow reactors, shock tubes, and premixed flames. The model predicts satisfactorily explosion limits for CHNH and its oxidation in a flow reactor. However, oxidation in the presence of nitric oxide, which strongly promotes reaction at lower temperatures, is only described qualitatively. Furthermore, calculated flame speeds are higher than reported experimental values; the model does not capture the inhibiting effect of the NH group in CHNH compared to CH. More work is desirable to confirm the products of the CHNH + NO reaction and to look into possible pathways to NH in methylamine oxidation.     

Mono-silicon isoelectronic replacement in CAl4: van't hoff/le bel carbon or not?

In cluster studies, the isoelectronic replacement strategy has been successfully used to introduce new elements into a known structure while maintaining the desired topology. The well-known penta-atomic 18 valence electron (ve) species and its Al⁻/Si or Al/Si⁺ isoelectronically replaced clusters CAl₃Si⁻, CAl₂Si₂, , and , all possess the same anti-van't Hoff/Le Bel skeletons, that is, nontraditional planar tetracoordinate carbon (ptC) structure. In this article, however, we found that such isoelectronic replacement between Si and Al does not work for the 16ve-CAl₄ with the traditional van't Hoff/Le Bel tetrahedral carbon (thC) and its isoelectronic derivatives CAl₃X (X = Ga/In/Tl). At the level of CCSD(T)/def2-QZVP//B3LYP/def2-QZVP, none of the global minima of the 16ve mono-Si-containing clusters CAl₂SiX⁺ (X = Al/Ga/In/Tl) maintains thC as the parent CAl₄ does. Instead, X = Al/Ga globally favors an unusual ptC structure that has one long C─X distance yet with significant bond index value, and X = In/Tl prefers the planar tricoordinate carbon. The frustrated formation of thC in these clusters is ascribed to the CSi bonding that prefers a planar fashion. Inclusion of chloride ion would further stabilize the ptC of CAl₂SiAl⁺ and CAl₂SiGa⁺. The unexpectedly disclosed CAl₂SiAl⁺ and CAl₂SiGa⁺ represent the first type of 16ve-cationic ptCs with multiple bonds. © 2019 Wiley Periodicals, Inc.     

Temperature Dependence of 1H Paramagnetic Chemical Shifts in Actinide Complexes,Beyond Bleaney's Theory: The AnVIO22+–Dipicolinic Acid Complexes (An=Np,Pu) as an Example

Actinide +VI complexes ( = , and ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, and complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans’ method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the complex. The temperature dependence of the pNMR chemical shifts has a strong contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the complex and a non-Kramers-doublet model for the complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.     

Size Evolution of Photoabsorption Spectra of Small Clusters: A Computational Study

Photoabsorption spectra of clusters, N=5–9, have been calculated using a diatomics-in-molecules like electronic structure model and a path-integral Monte Carlo sampling method. A qualitative change in the calculated spectra has been observed at N=9, which has been interpreted in terms of a structural transformation in the clusters consisting in a transition from trimer-like ionic cores observed for N≤7 to dimer-like ionic cores prevailing in through an intermediate state (comparable abundances of both types of ionic cores) observed in . The calculated spectra have been thoroughly compared with an earlier calculation on , , and reported from our group and data available for the same cluster sizes from an experiment.     

Photoionization Bands of Cyanogen: Multi-Mode Vibronic Coupling and Renner-Teller Effects

Multi-mode vibronic coupling in the , , and electronic states of Cyanogen radical cation (C N ) is investigated with the aid of ab initio quantum chemistry and first principles quantum dynamics methods. The electronic degenerate states of Π symmetry of C N undergo Renner-Teller (RT) splitting along degenerate vibrational modes of π symmetry. The RT split components form symmetry allowed conical intersections with those from nearby RT split states or with non-degenerate electronic states of Σ symmetry. A parameterized vibronic Hamiltonian is constructed using standard vibronic coupling theory in a diabatic electronic basis and symmetry rules. The parameters of the Hamiltonian are derived from ab initio calculated adiabatic electronic energies. The vibronic spectrum is calculated, assigned and compared with the available experimental data. The impact of various electronic coupling on the vibronic structure of the spectrum is discussed.     

Is it possible to synthesize bulk salt compounds?

The existence and stability of bulk salt compounds are theoretically investigated in this study. This undertaking is carried out to address the following challenge: synthesizing a bulk salt compound containing a noble gas lighter than Kr. The reliability of theoretical calculations on systems is assessed by benchmark calculations of the well-known salt. In the benchmark calculations, a two-pronged evaluation strategy, including direct and indirect evaluation methods, is used to theoretically investigate the spectroscopic constants of cation and the existence and stability of the salt. The validity of the theoretical calculation methods in the benchmark calculations of salt allows us to adopt a similar methodology to effectively predict the existence and stability of salt compounds. Calculations based on the Born-Haber cycle using estimated lattice energies and some necessary ancillary thermochemical data show that salt compounds can be synthesized, and their upper-limit stable temperatures are estimated to be −237.589, −197.76, and −80.539°C. The salt compound is the most promising candidate. Calculations also show that the salt compounds cannot be stabilized.     

Potential of AMnO3 (A=Ca,Sr, Ba,La) as Active Layer in Inorganic Perovskite Solar Cells

Inorganic perovskite CaMnO was proposed as a substitution for the TiO anatase in electron transport layers of solar cells containing the hybrid perovskite CH NH PbI based on increased mobility of electrons and better optical matching. Due to a suitable band gap concerning the absorption of sunlight, we investigate the potential of CaMnO and similar manganite perovskites, where Ca is replaced by either Sr, Ba or La, as an absorber layer in inorganic perovskite solar cells. In this study, we have used optical measurements on the synthesized AMnO (A=Ca, Sr, Ba, La) samples to aid density functional theory calculations (DFT) in order to accurately simulate the electronic and optical properties of AMnO compounds and gauge their potential for the role of absorber layer. Both experimental measurements and theoretical calculations show suitable band gap of 1.1-1.5 eV, depending on the compound, and absorption coefficients of the order of cm in the visible part of the spectrum.     

Ab initio structure and vibration-rotation dynamics of germylene,GeH2

Accurate structure and potential energy surface of germylene, GeH₂, in its ground electronic state ¹A₁ were determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to sextuple-zeta quality. The Born-Oppenheimer equilibrium structural parameters for the ¹A₁ state are estimated to be r_e(GeH) = 1.5793 Å and ∠_e(HGeH) = 91.19^∘. The term value T_e for the lowest excited electronic state ã³B₁ of GeH₂ is predicted to be 9140 cm^–1. The vibration-rotation energy levels for the ¹A₁ state of the ⁷⁴GeH₂, ⁷⁴GeD₂, ⁷²GeH₂, and ⁷⁰GeH₂ isotopologues were determined using a variational approach and compared with the experimental data. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, spin-orbit, and adiabatic effects for prediction of the structure and vibration-rotation dynamics of the GeH₂ molecule is discussed. © 2019 Wiley Periodicals, Inc.     

Development and Verification of a Diagnostic Technology for Waste Battery Deterioration Factors

We defined four major deterioration factors (electrolyte loss (EL), lithium loss (LL), lithium precipitation (LP), and compound deterioration (CD)). Then, we derived eleven key performance indicators (KPIs) for comparative analysis. After that, we fabricated three deteriorated cells for each of three deterioration factors (EL, LL, and LP) and one cell with CD (for verification) with four individual (dis)charging experiment manuals. The two major contributions of this study are the performance of 1) trend analysis to determine a suitable diagnostic metric by inspecting the eleven KPIs and 2) comparison analysis of and to verify the effectiveness of utilizing as a real-time deterioration diagnostic factor using a concept of model-in-the-loop simulation. The results show that 1) has the most conspicuous trendline tendency among the eleven comparison targets for all four major deterioration factors, and 2) the angle difference between the two trends of and lies within a minimum of 9° and a maximum of 43° (with a sscale on the x-axis and a scale on the y-axis for a clear trend line analysis). From this, we can conclude that the trendline-based real-time deterioration analysis employing may be practically applicable to a limited extent.     

Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions

Two pressure-induced phase transitions have been theoretically studied in the layered iron phosphorus triselenide (FePSe₃ ). Topological analysis of chemical bonding in FePSe₃ has been performed based on the results of first-principles calculations within the periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. The first transition at about 6 GPa is accompanied by the symmetry change from to C2/m , whereas the semiconductor-to-metal transition (SMT) occurs at about 13 GPa leading to the symmetry change from C2/m to . We found that the collapse of the band gap at about 13 GPa occurs due to changes in the electronic structure of FePSe₃ induced by relative displacements of phosphorus or selenium atoms along the c-axis direction under pressure. The results of the topological analysis of the electron density and its Laplacian demonstrate that the pressure changes not only the interatomic distances but also the bond nature between the intralayer and interlayer phosphorus atoms. The interlayer P–P interactions are absent in two non-metallic FePSe₃ phases while after SMT the intralayer P–P interactions weaken and the interlayer P–P interactions appear.