Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in Formic Acid Dimer

We present a quantum dynamics study on the isotope effects of hydro-gen transfer isomerization in the formic acid dimer,and this is achieved by multidimensional dy-namics calculations with an efficient quantum mechanical theoretical scheme developed by our group,on a full-dimensional neural network ab initio potential energy surface.The ground-state and fundamental tun-neling splittings for four deuterium isotopologues of formic acid dimer are considered,and the calculated results are in very good general agreement with the avail-able experimental measurements.Strong isotope effects are revealed,the mode-specific funda-mental excitation effects on the tunneling rate are evidently influenced by the deuterium sub-stitution of H atom with the substitution on the OH bond being more effective than on the CH bond.Our studies are helpful for acquiring a better understanding of isotope effects in the double-hydrogen transfer processes.

Quasi-classical trajectory study of the isotope effect on the stereodynamics in the reaction H(~2S) + CH(X^2Π;u= 0,j= 1) → C(~1D) + H_2(X^1Σ_g^+)

The isotope effect on the stereodynamic properties in the title reaction is investigated by a quasi-classical trajectory （QCT） method on the 11At potential energy surface at a collision energy of 23.06 kcal/mol. The angular distributions P（φr ）, P（θr）, P（θr, φr）, and the polarization-dependent generalized differential cross sections are calculated, which demonstrate the observable influences on the rotational polarization of the product by the isotopic substitution of H with D.

Isotope effect in collision between helium atom and hydrogen bromide molecule

The anisotropic potential developed in our previous research and the close-coupling method are applied to the HBr-3He （4He, 5He, 6He, 7He） system, and the partial cross sections （PCSs） at the incident energy of 60meV are calculated. Based on the calculations, the influences of the isotope helium atom on PCSs are discussed in detail. The results show that the excitation PCSs converge faster than the elastic PCSs for the collision energy and the systems considered here. Also the excitation PCSs converge more rapidly for the high-excited states. The tail effect is present only in elastic scattering and low-exclted states but not in high-excited states. With the increase of reduced mass of the collision system, the converging speed of the elastic and excitation PCSs slows down, and the tail effect goes up.

Theoretical study of stereodynamics for the reaction O(3P) ＋D2 (v=0, j=0) →OD＋D and isotope effect

Quasi-classical trajectory （QCT） calculations have been performed to study the product polarization behaviours in the reaction O（3p） ＋ D2 （v = 0, j = 0） → OD ＋ D. By running trajectories on the 3A′ and 3A″potential energy surfaces （PESs）, vector correlations such as the distributions of the polarization-dependent differential cross sections （PDDCSs）, the angular distributions of P（θr） and P（Фr） are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O（3p） ＋ H2 （v = 0, j = 0） → H ＋ H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces： the isotope mass effect has stronger influence on P（θr） and PDDCSs of the 3A′ PES while the opposite on P（Фr） of the 3A′ potential energy surface.

Isotope effect on the stereodynamics for the collision reaction H+LiF(v=0, j=0)→ HF+Li

Stereodynamics for the reaction H＋LiF（v = 0, j = 0） → HF＋Li and its isotopic variants on the ground-state （12A＇） potential energy surface （PES） are studied by employing the quasi-classical trajectory （QCT） method. At a collision energy of 1.0 eV, product rotational angular momentum distributions P（0r）, P（~r）, and P（Or, Cr）, are calculated in the center-of-mass （CM） frame. The results demonstrate that the product rotational angular momentum j＇ is not only aligned along the direction perpendicular to the reagent relative velocity vector k, but also oriented along the negative y axis. The four generalized polarization-dependent differential cross sections （PDDCSs） are also computed. The PDDCS00 distribution shows a preferential forward scattering for the product angular distribution in each of the three isotopic reactions, which indicates that the title collision reaction is a direct reaction mechanism. The isotope effect on the stereodynamics is revealed and discussed in detail.

Investigation of isotope effects of dynamic properties for H(D) + OF reactions by the quasi-classical trajectory method

Quasi-classical trajectory （QCT） calculations are employed to study the dynamic properties for H（D）＋OF reactions on the adiabatic potential energy surface （PES） of the 1^3A″ triplet state. Obvious differences between the reaction probabilities for J=0, integral cross sections for J≠0, branch ratios of the product and internuclear distances as well as product rotational alignments between the title reactions axe found. These differences are attributed mainly to the different reduced masses of the reactants and the different zero-point energies （ZPEs） of the transition state.

Influence of Isotope Effects on Product Polarizations of N(~2D)+D_2, N(~2D)+H_2 and N(~2D)+HD Reactive Systems

To figure out the influence of isotope effect on product polarizations of the N（2D）＋D2 reactive system and its isotope variants, quasi-classical trajectory（QCT） calculation was performed on Ho＇s potential energy surface（PES） of 2A″ state. Product polarizations such as product distributions of P（θr）, P（φr） and P（θr,φr）, as well as the generalized polarization-dependent differential cross sections（PDDCSs） were discussed and compared in detail among the four product channels of the title reactions. Both the intermolecular and intramolecular isotope effects were proved to be influential on product polarizations.

Oxygen Isotope Effects on T_(c) Related to Polaronic Superconductivity in Underdoped Cuprates

The planar oxygen isotope effect on Tc observed in copper oxide superconductors is remarkable in that it increases from near nil at optimal doping to a value twice that derived from BCS theory in the underdoped region. This behavior is quantitatively followed by a formula proposed by Kresin and Wolf in 1994 for polarons along the c-axis. Herein it is revisited in a more transparent way, and it is pointed out that the heterogeneity of pairing is relevant and has to be taken into account to explain the unusual planar isotope effects on Tc in underdoped cuprates.

Study of the Isotope Effects of Novel Superconducting LaH₁₀-LaD₁₀and H₃S-D₃S Systems

This paper is directed to study the isotope effects of some superconducting materials that have a strong coupling coefficient λ > 1.5, and focuses on new superconducting materials whose critical temperature is close to room temperature, specifically LaH10-LaD10 and H3S-D3S systems. The Eliashberg-McMillan (EM) model and the recent Gor’kov-Kresin (GK) model for evaluating the isotope effects coefficient α were examined for these systems. The predicted values of α as a function of pressure, as compared to experimental values led to inference that these two models, despite their importance and simplicity, cannot be considered complete. These models can be used to calculate isotope effect of most superconducting materials with strong coupling coefficients but with critical reliability. The significance of studying the isotope effect lies in the possibility of identifying the interatomic forces that control the properties of superconducting materials such as electrons-mediated phonons and Coulomb interactions.

Hydrogen isotope effects: A new path to high-energy aqueous rechargeable Li/Na-ion batteries

Aqueous rechargeable Li/Na-ion batteries have shown promise for sustainable large-scale energy storage due to their safety,low cost,and environmental benignity.However,practical applications of aqueous batteries are plagued by water's intrinsically narrow electrochemical stability window,which results in low energy density.In this perspective article,we review several strategies to broaden the electrochemical window of aqueous electrolytes and realize high-energy aqueous batteries.Specifically,we highlight our recent findings on stabilizing aqueous Li storage electrochemistry using a deuterium dioxide-based aqueous electrolyte,which shows significant hydrogen isotope effects that trigger a wider electrochemical window and inhibit detrimental parasitic processes.

Isotope effect on the Casimir force

Isotopic dependence of the Casimir force is key to probing new physics and pushing novel technologies at the micro and nanoscale, but is largely unexplored. In 2002, an isotope effect of 10^(-4) was estimated for metals—orders of magnitude beyond the experimental resolution. Here, by employing the Lifshitz theory, we reveal a significant isotope effect of over 10^(-1) for polar dielectrics. This effect arises from the isotope-mass-induced line shift of the zone-center optical phonons and is insensitive to the linewidth. We perform numerical analyses on both the imaginary and real-frequency axes, and derive analytical formulas for predicting the isotope effect. The three-orders-of-magnitude difference between polar dielectrics and metals arises from the distinct isotopic dependence of the phonon and plasma frequencies. Our work opens up a new avenue for engineering forces at small scales and may also facilitate the quest for the fifth force of nature.

Vibronic effect study of ^(1)A_(2) state of H_(2)O and D_(2)O

The generalized oscillator strengths of the dipole-forbidden excitations of the ^(1)A_(2) of H_(2)O and D_(2)O were calculated with the time dependent density functional theory,by taking into account the vibronic effect.It is found that the vibronic effect converts the dipole-forbidden excitation of the ^(1)A_(2) into a dipole-allowed one,which enhances the intensities of the corresponding generalized oscillator strength in the small squared momentum transfer region.The present investigation shows that the vibronic effect of H_(2)O is slightly stronger than that of D_(2)O,which exhibits a clear isotopic effect.

How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

The Rayleigh distillation isotope fractionation(RDIF) model is one of the most popular methods used in isotope geochemistry. Numerous isotope signals observed in geologic processes have been interpreted with this model. The RDIF model provides a simple mathematic solution for the reservoir-limited equilibrium isotope fractionation effect. Due to the reservoir effect, tremendously large isotope fractionations will always be produced if the reservoir is close to being depleted. However, in real situations, many prerequisites assumed in the RDIF model are often difficult to meet. For instance, it requires the relocated materials, which are removed step by step from one reservoir to another with different isotope compositions(i.e., with isotope fractionation), to be isotopically equilibrated with materials in the first reservoir simultaneously. This ‘‘quick equilibrium requirement’’ is indeed hard to meet if the first reservoir is sufficiently large or the removal step is fast. The whole first reservoir will often fail to re-attain equilibrium in time before the next removal starts.This problem led the RDIF model to fail to interpret isotope signals of many real situations. Here a diffusion-coupled and Rayleigh-like(i.e., reservoir-effect included) separation process is chosen to investigate this problem. We find that the final isotope fractionations are controlled by both the diffusion process and the reservoir effects via the disequilibrium separation process. Due to its complexity, we choose to use a numerical simulation method to solve this problem by developing specific computing codes for the working model.According to our simulation results, the classical RDIF model only governs isotope fractionations correctly at the final stages of separation when the reservoir scale(or thickness of the system) is reduced to the order of magnitude of the quotient of the diffusivity and the separation rate. The RDIF model fails in other situations and the isotope fractionations will be diffusion-limited when the reservoir is relatively large, or the separation rate is fast. We find that the effect of internal isotope distribution inhomogeneity caused by diffusion on the Rayleigh-like separation process is significant and cannot be ignored. This method can be applied to study numerous geologic and planetary processes involving diffusion-limited disequilibrium separation processes including partial melting,evaporation, mineral precipitation, core segregation, etc.Importantly, we find that far more information can be extracted through analyzing isotopic signals of such ‘‘disequilibrium’’processes than those of fully equilibrated ones, e.g., reservoir size and the separation rate. Such information may provide a key to correctly interpreting many isotope signals observed from geochemical and cosmochemical processes.

Germanium isotope effect induced guest rattling and cage distortion in clathrates

Intermetallic clathrates are materials characterized by a large cage structure where guest atoms can move anharmonically,providing these materials exotic thermoelectric properties.Unfortunately,the dynamical and atomic nature of the rattling phonons,and their interactions with the electronic structure,are not fully understood.Here,we report that a germanium isotope effect can trigger an inherent guest rattling and cage distortion in clathrate Ba8Ga16Ge30(BGG).Raman-scattering spectroscopy and advanced electron microscopy demonstrate that the atomic germanium isotope effect induces an offcentre rattling at the 6d sites as well as a tetrakaidecahedron deformation which is anisotropic for ntype BGG but isotropic for p-type BGG.The present findings indicate that the large n-type germanium isotope effect arises from the strong electron-phonon coupling,which opens up a novel avenue for manipulating dynamical motions of phonons via atomic isotope engineering.

Manipulation of Molecular Qubits by Isotope Effect on Spin Dynamics

Controlling spin behavior via external stimuli is a key route to develop molecular spintronics devices.Photons,temperature,pressure,chemicals,and electric field are the possible stimuli.Herein,we report a new method,the isotope effect,to control spin behavior in molecule magnet systems.It can not only control the relaxation of magnetization,but also regulate the spin lifetime of quantum coherence.

Laser phase effect on asymmetric harmonic distribution in H_2^+

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation（MHHG） spectrum from H_2~＋ is theoretically investigated through solving the Non-Bohn-Oppenheimer（NBO） time-dependent Schrodinger equation（TDSE）.The results are shown as follows,（i） The generated harmonics from the two nuclei each present an asymmetric distribution.Particularly,when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π,the contribution from the negative-H plays a main role in harmonic generation.When the laser phases are chosen from 0.7πto 1.6k,the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H.The electron localization,the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H_2~＋,which provides us with a method to control the electron motion in molecules,（ⅱ） As the pulse duration increases,the asymmetric distributions of the MHHG in two H nuclei decrease,（ⅲ） Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus（i.e.,D_2~＋）.

Theoretical investigations of spectroscopic parameters and molecular constants for electronic ground state of Cl_2 and its isotopes

The potential energy curve of the C12 （X1∑g＋） is investigated by the highly accurate valence internally contracted multireference configuration interaction （MRCI） approach in combination with the largest correlation-consistent basis set, aug-cc-pV6Z, in the valence range. The theoretical spectroscopic parameters and the molecular constants of three isotopes, 35Cl2, 35Cl37Cl and 37Cl2, are studied. For the 35Cl2（X1∑g＋）, the values of Do, De, Re, We, we）we, ae and Be are obtained to be 2.3921 eV, 2.4264 eV, 0.19939 nm, 555.13 cm-1, 2.6772 cm-1, 0.001481 cm-1 and 0.24225 cm-1, respectively. For the 356137Cl（X1∑g＋）, the values of Do, De, Re, We, WeXe, ae and Be are calculated to be 2.3918 eV, 2.4257 eV, 0.19939 nm, 547.68 cm-1, 2.6234 cm-1, 0.00140 cm^1 and 0.23572 cm-1, respectively. And for the 37Cl2（X1∑g＋）, the values of Do, De, Re, We, WeXe, ae and Be are obtained to be 2.3923 eV, 2.4257 eV, 0.19939 nm, 540.06 cm-1, 2.5556 cm-1, 0.00139 cm-1 and 0.22919 cm-1, respectively. These spectroscopic results are in good agreement with the available experimental data. With the potential of Cl2 molecule determined at the MRCI/aug-cc-pV6Z level of theory, the total of 59 vibrational states is predicted for each isotope when the rotational quantum number J equals zero （J = 0）. The theoretical vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0, which are in excellent accordance with the available experimental findings.

Spectroscopic parameters and molecular constants of HI(X^1Σ^+),DI(X^1Σ^+) and TI(X^1Σ^+) isotope molecules

The potential energy curve （PEC） of HI（X^1∑^＋） molecule is studied using the complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction approach at the correlation-consistent basis sets, aug-cc-pV6Z for H and aug-cc-pV5Z-pp for I atom. Using the PEG of HI（X^1∑^＋）, the spectroscopic parameters of three isotopes, HI（X1E＋）, DI（X^1∑^＋） and TI（X^1∑^＋）, are determined in the present work. For the HI（X^1∑^＋）, the values of Do, De, Re, ωe, ωeχe, αe and Be are 3.1551 eV, 3.2958 eV, 0.16183 nm, 2290.60 cm^-1, 40.0703 cm^-1, 0.1699 cm^-1 and 6.4373 cm^-1, respectively; for the DI （X^1∑^＋）, the values of D0, De, Re, ωe, ωeχe, αe and Be are 3.1965 eV, 3.2967 eV, 0.16183 nm, 1626.8 cm^-1, 20.8581 cm^-1, 0.0611 cm^-1 and 3.2468 cm^-1, respectively; for the TI （X^1∑^＋）, the values of Do, De, Re, ωe, ωeχe, αe and Be are of 3.2144 eV, 3.2967 eV, 0.16183 nm, 1334.43 cm^-1, 14.0765 cm^-1, 0.0338 cm^-1 and 2.1850 cm^-1, respectively. These results accord well with the available experimental results. With the PEC of HI（X^1∑^＋） molecule obtained at present, a total of 19 vibrational states are predicted for the HI, 26 for the DI, and 32 for the TI, when the rotational quantum number J is equal to zero （J = 0）. For each vibrational state, vibrational level G（v）, inertial rotation constant By and centrifugal distortion constant Dv are determined when J = 0 for the first time, which are in excellent agreement with the experimental results.

Rate Coecients and Kinetic Isotope E ects of Cl+XCl→XCl+Cl(X=H,D,Mu)Reactions from Ring Polymer Molecular Dynamics

The ring-polymer molecular dynamics(RPMD)was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl+XCl→XCl+Cl(X=H,D,Mu).For the Cl+HCl reaction,the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory.And the RPMD results are also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics.The most novel finding is that there is a double peak in Cl+MuCl reaction near the transition state,leaving a free energy well.It comes from the mode softening of the reaction system at the peak of the potential energy surface.Such an explicit free energy well suggests strongly there is an observable resonance.And for the Cl+DCl reaction,the RPMD rate coefficient again gives very accurate results compared with experimental values.The only exception is at the temperature of 312.5 K,results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value,which indicates experimental or potential energy surface deficiency.

Impact of the mass isotope on plasma confinement and transport properties in the HL-2A tokamak

The impact of the mass isotope on plasma conflnement and transport properties has been investigated in Ohmically-heated hydrogen and deuterium plasmas in the HL-2 A tokamak.Experimental results show that under similar discharge parameters the deuterium plasma has better conflnement and lower turbulent transport than the hydrogen one,and concomitantly,it is found that the magnitude of geodesic acoustic mode zonal flows,the tilting angle of the Reynolds stress tensor and the turbulence correlation lengths are all larger in the edge region of the deuterium plasma.The results provide direct experimental evidence on the importance of the nonlinear energy coupling between ambient turbulence and zonal flows for governing the isotope effects in fusion plasmas.