Theoretical study of kinetic isotope effects for vacancy diffusion of impurity in solids

Theoretical studies of the diffusionalisotope effect in solids are still stuck in the 1960s and 1970s.With the development of high spatial resolution mass spectrometers,isotopic data of mineral grains are rapidly accumulated.To dig up information from these data,molecularlevel theoretical models are urgently needed.Based on the microscopic definition of the diffusion coe fficient(D),a new theoretical framework for calculating the diffusional isotope effect(DIE(v))(intermsofD*/D)forvacancy-mediated impurity diffusion in solids is provided based on statistical mechanics formalism.The newly derived equation shows that theDIE(v)can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained.The calculatedDIE(v)values of^(199)Au/^(195)Au and^(60)Co/^(57)Co during diffusion in Cu and Au metals are all within 1%of errors compared to the experimental data,which shows that this theoretical model is reasonable and precise.

Isotope Effects on Two-Photon Population Transfer Processes of HF and DF

The isotope effects of XF （X=H, D） on the population transfer process via two-photon resonance excitation are investigated by solving the time-dependent SchrSdinger equation. The vibrational levels v=0 and 2 of the ground electronic state are taken to be the initial and target states, respectively, for the two molecular systems. The influences of the field peak amplitude and pulse duration on the population transfer process are discussed in detail. The pulse duration is required to be longer than 860 fs for the DF molecule to achieve a relatively high transfer probability （more than 80%）, while the one for the HF molecule is just required to be longer than 460 fs. Moreover, the intermediate level v=1 and the higher level v=3 may play more important roles in the two-photon resonance process for the DF molecule, compared to the roles in the process for the HF molecule.

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.

Quasi-classical Trajectory Study of the Intramolecular Isotope Effect in the Reaction O（3p）＋H2/HD

Theoretical studies of the dynamics of the reactions O（3p）＋H2/HD（ν=0, j=0）→OH＋H have been performed with quasi-classical trajectory method （QCT） on an ab initio potential surface for the lowest triplet electronic state of H2O（aA＂）. The QCT-calculated integral cross sections are in good agreement with the earlier time-dependent quantum mechanics results. The state-resolved rotational distributions reveal that the product OH rotational distributions for O＋HD have a preference for populating highly internally excited states compared with the O＋H2 reaction. Distributions of differential cross sections show that directions of scattering are strongly dependent on the choice of quantum state. The polarization dependent generalized differential cross-sections and the distributions were calculated and a pronounced isotopic effect is revealed. The calculated results indicate that the product polarization is very sensitive to the mass factor.

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.

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 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.

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.

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.

Deuterium Isotope Effects in Oxidative Deamination of L-Alanine Catalyzed by L-Alanine Dehydrogenase

Solvent and kinetic isotope effects in the reaction of oxidative deamination of L-alanine, catalyzed by L-alanine dehydrogenase, AIaDH, （EC 1.4.1.1） were determined using a non-competitive spectroscopic method. The progress of the reaction was monitored spectrophotometrically by measuring the increasing absorbance of the reduced form of NADH at 340 nm. L-alanine, stereospecifically labeled with deuterium was synthesized by enzymatic reductive amination of pyruvate in presence of [（4R）-2H]-NADH, which was obtained by deuterium transfer from deuteriated formic acid to NAD~ catalyzed by FDH （formate dehydrogenase） （EC 1.2.1.2）. [2-2H]-L-alanine, the product of enzymatic synthesis catalyzed by AIaDH, was obtained with 75% deuterium enrichment and values of isotopic effects were approximated to the values corresponding to 100% of deuterium incorporation. The enzyme AIaDH isolated from Bacillus subtilis shows pro-R stereospecificity, what indicates that hydrogen is exclusively transferred from pro-R position at C-4 of the nicotinamide ring of NADH to C-2 of pyruvate to form L-alanine. Some intrinsic mechanistic details of enzymatic oxidative deamination of L-alanine were discussed using determined numerical values of kinetic and solvent isotope effects on Vmax and Vmax,│KM

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.

Isotope effect of the phonons mean free path in graphene by micro-Raman measurement

The isotope labeled graphene was synthesized in the concentration of 13 C carbon atom in 1%, 25%, 50%, 75% and 99%. The isotope effect on the phonon behavior in graphene was investigated based on the micro-Raman analysis of 13 C isotope labeled graphene samples. We found that the phonon scattering is affected by the isotopic carbon atom as a point defect. Based on the experiment results, the Klemens-Callaway model and uncertainty principle were used to obtain the mean free path of the G and D phonons. The results agree with the thermal conductivity measurement by non-contact optical method and with other theoretical calculations.

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.

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.

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.

Computation of kinetic isotope effects for enzymatic reactions

We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical(QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory,and(2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects(KIEs).In this approach,which is called the PI-FEP/UM method,a light(heavy) isotope is mutated into a heavy(light) counterpart in centroid path integral simulations.The method is illustrated in the study of primary and secondary KIEs in two enzyme systems.In the case of nitroalkane oxidase,the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water.In the dopa delarboxylase reaction,there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions.These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions.

^(59)Co-NMR MEDIUM EFFECT, ISOTOPE EFFECT AND CHELATE COMPLEX STEREOISOMERS

The ^(59)Co-NMR spectra of several cobalt (Ⅲ) complexes have been directly recorded bypulsed Fourier transform nuclear magnetic resonance (FT-NMR) technique. The influences ofsolvents, concentration and temperature on ^(59)Co spectra have been investigated. Optical andgeometric isomers of the chelate complexes have been distinguished by ^(59)Co-NMR spectra. ForCo(±pn)_3Cl_3, the resonances of Δ(λλλ) and Δ(δδδ) appeared at the lower field, the δ_(mer) beinggreater than δ_(fac), followed by the peaks of Δ(λλδ) and Δ(δδλ). For Co(en)_3Cl_3-D_n, all the13 isotopic isomers, from D_0 to D_(12), have been resolved in their ^(59)Co spectra. Each H/Dexchange causes ^(59)Co peaks to move upfield 5.4 ppm. The factors affecting the direction andmagnitude of isotopic shift and its additivity have been discussed. Chemical equilibrium isotopiceffect has also been studied.

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.