Analysis of level structure and monopole effects in Ca isotopes

Understanding the properties of nuclei near the double magic nucleus^(40)Ca is crucial for both nuclear theory and experiments.In this study,Ca isotopes were investigated using an extended pairing-plus-quadrupole model with monopole corrections.The negative-parity states of^(44)Ca were coupled with the intruder orbital g_(9/2)at 4 MeV.The values of E_(4+)/E_(2+)agree well with experimental trend from^(42)Ca to^(50)Ca,considering monopole effects between νf_(7/2)and νp_(3/2)(νf_(5/2)).This monopole effect,determined from data of^(48)Ca and^(50)Ca,supports the proposed new nuclear magic number N=34 by predicting a high-energy 2^(+)state in^(54)Ca.

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.

Nuclear volume effects in kinetic isotope fractionation:A case study of mercury oxidation by chlorine species

It is well-known that the equilibrium isotope fractionation of mercury(Hg)includes classical massdependent fractionations(MDFs)and nuclear volume effect(NVE)induced mass-independent fractionations(MIFs).However,the effect of the NVE on these kinetic processes is not known.The total fractionations(MDFs+NVEinduced MIFs)of several representative Hg-incorporated substances were selected and calculated with ab initio calculations in this work for both equilibrium and kinetic processes.NVE-induced MIFs were calculated with scaled contact electron densities at the nucleus through systematic evaluations of their accuracy and errors using the Gaussian09 and DIRAC19 packages(named the electron density scaling method).Additionally,the NVE-induced kinetic isotope effect(KIE)of Hg isotopes are also calculated with this method for several representative Hg oxidation reactions by chlorine species.Total KIEs for 202 Hg/^(198)Hg ranging from−2.27‰to 0.96‰are obtained.Three anomalous^(202)Hg-enriched KIEs(δ^(202)Hg/^(198)Hg=0.83‰,0.94‰,and 0.96‰,)caused by the NVE are observed,which are quite different from the classical view(i.e.,light isotopes react faster than the heavy ones).The electron density scaling method we developed in this study can provide an easier way to calculate the NVE-induced KIEs for heavy isotopes and serve to better understand the fractionation mechanisms of mercury isotope systems.

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.

Nuclear ?eld shift effects on stable isotope fractionation: a review

An anomalous isotope effect exists in many heavy element isotope systems （e.g., Sr, Gd, Zn, U）. This effect used to be called the ＂odd--even isotope effect＂ because the odd mass number isotopes behave differently from the even mass number isotopes. This mass-indepen- dent isotope fractionation driving force, which originates from the difference in the ground-state electronic energies caused by differences in nuclear size and shape, is cur- rently denoted as the nuclear field shift effect （NFSE）. It is found that the NFSE can drive isotope fractionation of some heavy elements （e.g., Hg, T1, U） to an astonishing degree, far more than the magnitude caused by the con- ventional mass-dependent effect （MDE）. For light ele- ments, the MDE is the dominant factor in isotope fractionation, while the NFSE is neglectable. Furthermore, the MDE and the NFSE both decrease as temperatures increase, though at different rates. The MDE decreases rapidly with a factor of 1/T2, while the NFSE decreases slowly with a factor of 1/T. As a result, even at high temperatures, the NFSE is still significant for many heavy element isotope systems. In this review paper, we begin with an introduction of the basic concept of the NSFE, including its history and recent progress, and follow with the potential implications of the inclusion of the NFSE into the kinetic isotope fractionation effect （KIE） and heavy isotope geochronology.

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.

Vital effects of K isotope fractionation in organisms： observations and a hypothesis

Compared with the measureable but limited K isotope variation in geological samples,biological samples have much larger variations in δ^41 values：from-1.3‰ to＋1.1‰ relative to the international K standard NIST SRM 3141a.Notably,higher plants generally have δ^41 values that are lower than igneous rocks,whereas sea plants（algae）have δ^41 values that are higher than seawater;the range in δ^41K values of plants encompasses the δ^41 values of both igneous rocks and seawater.Plant cells utilize different K uptake mechanisms in response to highand low-K conditions.In a low-K environment,plant cells use energy-consuming ion pumps for active uptake of K;plant cells in high-K environments use non-energy-consuming ion channels.Based on these facts and on K isotope data from sea and land plants,it is hypothesized that the different K uptake mechanisms are accompanied by distinct K isotope fractionation behaviors or vital effects.The enrichment of light K isotopes in terrestrial plants could be attributed to preferential transport of isotopically light K in the energy-consuming active uptake process by K ion pumps in the membranes of plant root cells.On the other hand,the enrichment of heavy K isotopes in algae may be caused by a combination of the lack of K isotope fractionation during K uptake from seawater via ion channels and the preferential efflux of light K isotopes across the cell membrane back to the seawater.The large variation of K isotope compositions in biological samples therefore may reflect the diversity of isotopic vital effects for K in organisms,which implies the great potential of K isotopes in biogeochemical studies.

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.

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.

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.

Equilibrium mercury and lead isotope fractionation caused by nuclear volume effects in crystals

To investigate equilibrium mercury(Hg)and lead(Pb)isotope fractionation caused by the nuclear volume effect(NVE)in crystals,the electron densities at nuclei(i.e.,|Ψ(0)|2)for Hg-or Pb-bearing crystalline compounds were investigated by using the relativistic spin orbit zeroth-order regular approximation(ZORA)method with a three-dimensional periodic boundary condition based on the density functional theory(DFT).Many isotope fractionation factors of crystalline compounds are provided for the first time.Our results show,even at1000℃,NVE-driven Hg and Pb isotope fractionation are meaningfully large,i.e.,range from 0.12‰to 0.49‰(202Hg/^(198)Hg),from-0.20‰to 0.17‰(208Pb/^(206)Pb)and from-0.08‰to 0.06‰(207Pb/^(206) Pb)relative to Hg0 vapor and Pb0 vapor,respectively.Specifically,the fractionations range from-0.06‰to-0.20‰(208Pb/^(206)Pb)and from-0.02‰to-0.08‰(207Pb/^(206)Pb)for Pb2+-bearing species,from 0.10‰to 0.17‰(208Pb/^(206)Pb)and from 0.04‰to 0.06‰(207Pb/^(206)Pb)for Pb4+-bearing species in crystals.All calculated Hg-bearing species in crystals will enrich heavier isotope(202Hg)relative to Hg0 vapor.Meanwhile,Pb4+-bearing species enrich heavier Pb isotopes(208Pb and 207Pb)than Pb^(2+)-bearing species in crystals,which the enrichment can be up to 0.37‰(208-Pb/^(206)Pb)and 0.14‰(207Pb/^(206)Pb)at 1000℃,due to their NVEs are in opposite directions.The NVE-driven MIFs of Hg isotopes,which are compared to the Hg202-Hg198baseline,are up to-0.158‰(ΔNV199Hg),-0.024‰(ΔNV200Hg)and-0.094‰(ΔNV201Hg)relative to Hg0 vapor at5000 C.For all studied Hg-bearing species in crystals,the MIFs of two odd-mass isotopes(i.e.,ΔNV199Hg andΔNV201Hg)will be changed proportionally and their ratio(i.e.,ΔNV199Hg/ΔNV201Hg)will be a constant 1.67.The NVE can also cause mass-independent fractionations for 207Pb and 204 Pb compared to the baseline of 208Pb and 206Pb.The largest NVEdriven MIFs are 0.043‰(ΔNV207Pb)and-0.040‰(ΔNV204Pb)among all the studied species relative to Pb0 vapor at 5000 C.The magnitudes of odd-mass isotope MIF(ΔNV207Pb)and even-mass isotope MIF(ΔNV204Pb)are almost the same but with opposite signs,leading to the MIF ratio of them(i.e.,ΔNV207Pb/ΔNV204Pb)is-1.08.

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.

Isotope effect and Coriolis coupling effect forthe Li + H(D)Cl → LiCl + H(D) reaction

A time-dependent quantum wave packet method is used to investigate the dynamics of the Li + H(D)Cl reaction based on a new potential energy surface(J. Chem. Phys. 146 164305(2017)). The reaction probabilities of the Coriolis coupled(CC) and centrifugal sudden(CS) calculations, the integral cross sections, the reaction rate constants are obtained. The rate constants of the Li + HCl reaction are within the error bounds at low temperature. A comparison of the CC and CS results reveals that the Coriolis coupling plays an important role in the Li + H(D)Cl reaction. The CC cross sections are larger than the CS results within the entire energy range, demonstrating that the Coriolis coupling effect can more effectively promote the Li + DCl reaction than the Li + HCl reaction. It is found that the isotope effect has a great influence on the title reaction.

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.

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.

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.

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.