Five-dimensional Potential Energy Surface Research Articles

Fission-fragment charge yields: Variation of odd-even staggering with element number, energy, and charge asymmetry

Background: Fission-fragment charge-yield distributions exhibit a pronounced odd-even staggering. For actinide nuclei the staggering decreases with increasing proton number and with increasing excitation energy. In our calculations of fission yields [Phys. Rev. Lett. 106, 132503 (2011)] we obtained charge-yield distributions for a number of actinide nuclides by means of random walks on tabulated five-dimensional potential-energy surfaces. However, because the potential-energy model treats the system as a single, compound system during all stages of the fission process, in which individual fragment properties do not appear, no odd-even staggering appeared in the calculated yield curves.Purpose: We have recently become aware that in the experimental data displayed in Fig. 1 in the above paper, there is a remarkable similarity in the odd-even staggering in fission of $^{240}\mathrm{Pu}$ at thermal neutron energy and fission of $^{234}\mathrm{U}$ in photon-induced fission at around 11 MeV. We discuss how this similarity and how the variation in the magnitude of the odd-even staggering for three Th isotopes with charge asymmetry and isotope can be qualitatively understood based on strongly damped shape evolution on our calculated five-dimensional potential-energy surfaces.Methods: We conduct random walks on our tabulated five-dimensional potential-energy surfaces and study the difference between the total compound-nucleus energy and the potential energy for the different systems from saddle to scission. Under the strong-damping assumption this difference is the internal excitation energy. We also determine this quantity for different charge splits, symmetric and asymmetric.Results: We find that the magnitude of the odd-even staggering in the charge distribution in the several cases studied here correlates well, inversely, with the excitation energy above the potential-energy surface in the postsaddle region.Conclusions: Because the observed magnitude of the odd-even staggering correlates well with excitation energy over the region where the individual character of the fission fragments emerges, the Brownian shape-motion method can be expected to reproduce this feature, provided a potential-energy model is developed that accounts for how the nascent fragment properties are expressed in the calculated potential-energy surfaces.

Analytic Morse/long-range potential energy surfaces and predicted infrared spectra for CO–H2 dimer and frequency shifts of CO in (para-H2)N N = 1–20 clusters

A five-dimensional ab initio potential energy surface (PES) for CO-H2 that explicitly incorporates dependence on the stretch coordinate of the CO monomer has been calculated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for vCO = 0 and 1 to the Morse/long-range potential function form. These fits to 30,206 points have root-mean-square (RMS) deviations of 0.087 and 0.082 cm(-1), and require only 196 parameters. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data: for infrared transitions of para H2-CO and ortho H2-CO, the RMS discrepancies are only 0.007 and 0.023 cm(-1), which are almost in the same accuracy as those values of 0.010 and 0.018 cm(-1) obtained from full six-dimensional ab initio PESs of V12 [P. Jankowski, A. R. W. McKellar, and K. Szalewicz, Science 336, 1147 (2012)]. The calculated infrared band origin shift associated with the fundamental of CO is -0.179 cm(-1) for para H2-CO, which is the same value as that extrapolated experimental value, and slightly better than the value of -0.176 cm(-1) obtained from V12 PESs. With these potentials, the path integral Monte Carlo algorithm and a first order perturbation theory estimate are used to simulate the CO vibrational band origin frequency shifts of CO in (para H2)N-CO clusters for N = 1-20. The predicted vibrational frequency shifts are in excellent agreement with available experimental observations. Comparisons are also made between these model potentials.

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules that has been incarcerated in the molecular cage of C₆₀ to form the endohedral supramolecular complex H₂@C₆₀. In this confinement, hydrogen acquires new properties. Its translation motion, within the C₆₀ cavity, becomes quantized, is correlated with its rotation and breaks inversion symmetry that induces infrared (IR) activity of H₂. We apply IR spectroscopy to study the dynamics of hydrogen isotopologues H₂, D₂ and HD incarcerated in C₆₀. The translation and rotation modes appear as side bands to the hydrogen vibration mode in the mid-IR part of the absorption spectrum. Because of the large mass difference of hydrogen and C₆₀ and the high symmetry of C₆₀ the problem is almost identical to a vibrating rotor moving in a three-dimensional spherical potential. We derive potential, rotation, vibration and dipole moment parameters from the analysis of the IR absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H₂@C₆₀. The same parameters were used to predict H₂ energies inside C₇₀. We compare the predicted energies and the low-temperature IR absorption spectra of H₂@C₇₀.

Brownian shape dynamics in fission

It was recently shown that remarkably accurate fission-fragment mass distributions are obtained by treating the nuclear shape evolution as a Brownian walk on previously calculated five-dimensional potentialenergy surfaces; the current status of this novel method is described here.

Brownian Shape Dynamics in Fission

Abstract Remarkably accurate fission-fragment mass distributions can be obtained by treating the nuclear shape evolution as a Metropolis walk on previously calculated five-dimensional potential-energy surfaces; this novel method is briefly reviewed here.

Brownian shape motion: fission fragment mass distributions

A recently developed novel method for calculating fission-fragment mass distributions is discussed. It treats the nuclear shape evolution as Brownian motion and in its simplest form performs random walks on previously calculated five-dimensional potential-energy surfaces. Remarkably good reproduction of experimentally measured data is obtained without introduction of any new parameters.

CMM-RS Potential for Characterization of the Properties of the Halogen-Bonded OC–Cl2 Complex, and a Comparison with Hydrogen-Bonded OC–HCl

Transitions associated with the vibrations ν₁, ν₁ + ν(b)¹, ν₁ + ν₅¹, and ν₁ + ν₅¹ - ν₅¹ of the complex OC···Cl₂ have been rovibrationally analyzed for several isotopologues involving isotopic substitutions in Cl₂. Spectra were recorded using a recently constructed near-infrared (4.34 to 4.56 μm), quantum-cascade laser spectrometer with cw supersonic slit jet expansion. Spectral analysis allowed precise determination of the ν₅¹ intermolecular vibration of OC-³⁵Cl₂ to be 25.977637(80) cm⁻¹. These results were incorporated with other previously determined data into a spectroscopic database for generation of a five-dimensional morphed potential energy surface. This compound-model morphed potential with radial shifting (CMM-RS) was then used to make more accurate predictions of properties of the OC-³⁵Cl₂ complex including D(e) = 544(5) cm⁻¹, D₀ = 397(5) cm⁻¹, ν₃ = 56.43(4) cm⁻¹, and ν(b)¹ = 85.43(4) cm⁻¹. The CMM-RS potential determined for OC-Cl₂ was also used to compare quantitatively many of the inherent properties of this non-covalent halogen bonded complex with those of the closely related hydrogen-bonded complex OC-HCl, which has a similar dissociation energy D₀. We found that in the ground state, the CO bending amplitude is larger in OC-Cl₂ than in OC-HCl.

Brownian shape motion: Fission fragment mass distributions

It was recently shown that remarkably accurate fission-fragment mass distri- butions can be obtained by treating the nuclear shape evolution as a Brownian walk on previously calculated five-dimensional potential-energy surfaces; the current status of this novel method is described here. As discussed already in the pioneering works by Meitner and Frisch (1) and Bohr and Wheeler (2, 3) in 1939, nuclear fission can be viewed qualitatively as an evolution of the nuclear shape from that of a single compound nucleus to two receding fragments. The character of the shape dynamics is still not well established but, as a step away from a purely statistical approach toward a full dynamical treatment, it is interesting to explore scenarios in which the evolution is strongly dissipative (4, 5). We therefore picture the nuclear fission process as an evolution of the nuclear shape from a rela- tively compact mononucleus to a dinuclear configuration. In the present study, the shape is composed of three smoothly joined quadratic surfaces (6, 7) which are described by a set of parameters,� ={χi}, whose time development is the result of a complicated interplay between a variety of effects.

Fission-fragment mass distributions from strongly damped shape evolution

Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of motion, which is appropriate for highly dissipative evolutions, we discuss the physical justification for that treatment and investigate the sensitivity of the resulting mass yields to a variety of model ingredients, including in particular the dimensionality and discretization of the shape space and the structure of the dissipation tensor. The mass yields are found to be relatively robust, suggesting that the simple random walk presents a useful calculational tool. Quantitatively refined results can be obtained by including physically plausible forms of the dissipation, which amounts to simulating the Brownian shape motion in an anisotropic medium.

Intermolecular potential energy surface and second virial coefficients for the water–CO2 dimer

A five-dimensional potential energy surface is calculated for the interaction of water and CO(2), using second-order Møller-Plesset perturbation theory and coupled-cluster theory with single, double, and perturbative triple excitations. The correlation energy component of the potential energy surface is corrected for basis set incompleteness. In agreement with previous studies, the most negative interaction energy is calculated for a structure with C(2v) symmetry, where the oxygen atom of water is close to the carbon atom of CO(2). Second virial coefficients for the water-CO(2) pair are calculated for a range of temperatures, and their uncertainties are estimated. The virial coefficients are shown to be in close agreement with the available experimental data.

Analytic Morse/long-range potential energy surfaces and predicted infrared spectra for CO2–H2

Five-dimensional ab initio potential energy surfaces (PESs) for CO(2)-H(2) that explicitly incorporate dependence on the Q(3) asymmetric-stretch normal-mode coordinate of the CO(2) monomer and are parametrically dependent on its Q(1) symmetric-stretch coordinate have been calculated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v(3)(CO(2)) = 0, and 1 to the Morse/long-range potential function form. These fits to 23,113 points have root-mean-square (rms) deviations of 0.143 and 0.136 cm(-1), and require only 167 parameters. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data: for infrared transitions of para- and ortho-H(2)-CO(2), the rms discrepancies are only 0.004 and 0.005 cm(-1), respectively. The calculated infrared band origin shifts associated with the nu(3) fundamental of CO(2) are -0.179 and -0.092 cm(-1) for para-H(2)-CO(2) and ortho-H(2)-CO(2), in good agreement with the (extrapolated) experimental values of -0.198 and -0.096 cm(-1).

A five-dimensional potential-energy surface for the rotational excitation of SO2 by H2 at low temperatures

The SO(2) molecule is detected in a large variety of astronomical objects, notably molecular clouds and star-forming regions. An accurate modeling of the observations needs a very good knowledge of the collisional excitation rates with H(2) because of competition between collisional and radiative processes that excite and quench the different rotational levels of SO(2). We report here a five-dimensional, rigid-body, interaction potential for SO(2)-H(2). As a first application, we present rate constants for excitation/de-excitation of the 31 first levels of SO(2) by para-H(2) at low temperatures. Propensity rules are discussed.

Coupled translation-rotation eigenstates of H2 in C60 and C70 on the spectroscopically optimized interaction potential: Effects of cage anisotropy on the energy level structure and assignments

We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H(2) in C(60) through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H(2) in the vibrationally excited nu=1 state. The PES is based on the three-site H(2)-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H(2) has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H(2)@C(60) to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H(2)-fullerene interaction afforded by the three-site H(2)-C pair potential. The same H(2)-C pair potential spectroscopically optimized for H(2)@C(60) was also used to construct the pairwise additive 5D PES of H(2) (nu=1) in C(70). This PES, because of the lower symmetry of C(70) (D(5h)) relative to that of C(60) (I(h)), exhibits pronounced anisotropy with respect to the direction of the translational motion of H(2) away from the cage center, unlike that of H(2) in C(60). As a result, the T-R energy level structure of H(2) in C(70) from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H(2) are all qualitatively different from those determined previously for H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008).

Pathways and reduced-dimension five-dimensional potential energy surface for the reactions H3++CO→H2+HCO+ and H3++CO→H2+HOC+

To obtain theoretical insight regarding the stability and formation dynamics of the interstellar ions HCO(+) and HOC(+), stationary points and the associated vibrational frequencies on the full nine-dimensional potential energy surface for the electronic ground state have been calculated using coupled-cluster theory with both single and double substitutions (CCSD). The energetics were refined with a higher-level coupled-cluster method CCSD(T), with core-valence electron correlation treated at the complete basis set limit. To elucidate the formation mechanism and internal relaxation processes, the reaction paths for the reactions H(3) (+)+CO-->H(2)+HCO(+) and H(3) (+)+CO-->H(2)+HOC(+) were calculated at the second-order Moller-Plesset (MP2) level, and corresponding single-point energies were obtained at the higher CCSD(T)/aug-cc-pVTZ level. Based on the analysis of the main reaction processes, a reduced-dimension five-dimensional potential energy surface for this system was constructed from 128 440 ab initio points calculated at the CCSD(T)/aug-cc-pVTZ level.

The water-oxygen dimer: First-principles calculation of an extrapolated potential energy surface and second virial coefficients

The systematic intermolecular potential extrapolation routine (SIMPER) is applied to the water-oxygen complex to obtain a five-dimensional potential energy surface. This is the first application of SIMPER to open-shell molecules, and it is the first use, in this context, of asymptotic dispersion energy coefficients calculated using the unrestricted time-dependent coupled-cluster method. The potential energy surface is extrapolated to the complete basis set limit, fitted as a function of intermolecular geometry, and used to calculate (mixed) second virial coefficients, which significantly extend the range of the available experimental data.

Five-dimensional ab initio potential energy surface and predicted infrared spectra of H2–CO2 van der Waals complexes

The authors present a new five-dimensional potential energy surface for H2-CO2 including the Q3 normal mode for the nu3 antisymmetric stretching vibration of the CO2 molecule. The potential energies were calculated using the supermolecular approach with the full counterpoise correction at the CCSD(T) level with an aug-cc-pVTZ basis set supplemented with bond functions. The global minimum is at two equivalent T-shaped coplanar configurations with a well depth of 219.68 cm-1. The rovibrational energy levels for four species of H2-CO2 (paraH2-, orthoH2-, paraD2-, and orthoD2-CO2) were calculated employing the discrete variable representation (DVR) for radial variables and finite basis representation (FBR) for angular variables and the Lanczos algorithm. Our calculations showed that the off-diagonal intra- and intermolecular vibrational coupling could be neglected, and separation of the intramolecular vibration by averaging the total Hamiltonian with the wave function of a specific vibrational state of CO2 should be a good approximation with high accuracy. The calculated band origin shift in the infrared spectra in the nu3 region of CO2 is -0.113 cm-1 for paraH2-CO2 and -0.099 cm-1 for orthoH2-CO2, which agrees well with the observed values of -0.198 and -0.096 cm-1. The calculated rovibrational spectra for H2-CO2 are consistent with the available experimental spectra. For D2-CO2, it is predicted that only a-type transitions occur for paraD2-CO2, while both a-type and b-type transitions are significant for orthoD2-CO2.

Intermolecular potential and second virial coefficient of the water-nitrogen complex

The authors construct a rigid-body (five-dimensional) potential energy surface for the water-nitrogen complex using the systematic intermolecular potential extrapolation routine. The intermolecular potential is then extrapolated to the limit of a complete basis set. An analytic fit of this surface is obtained, and, using this, the global minimum energy is found. The minimum is located in an arrangement in which N2 is near the H atom of H2O, almost collinear with the OH bond. The best estimate of the binding energy is 441 cm-1 (1 cm-1 approximately 1.986 43x10(-23) J). The extrapolated potential is then used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). These calculated second virial coefficients are generally consistent with experimental data, but for the most part the former have smaller uncertainties.

A five-dimensional potential energy surface and predicted infrared spectra for the N2O-hydrogen complexes

We present a five-dimensional potential energy surface for the N(2)O-hydrogen complex using supermolecular approach with the full counterpoise correction at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level. The normal mode Q(3) for the nu(3) antisymmetric stretching vibration of the N(2)O molecule was included in the calculations of the potential energies. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm were employed to calculate the rovibrational energy levels for four species of N(2)O-hydrogen complexes (N(2)O-para-H(2), -ortho-H(2), -ortho-D(2), and -para-D(2)) without separating the inter- and intramolecular vibrations. The calculated band origins are all blueshifted relative to the isolated N(2)O molecule and in good agreement with the experimental values. The calculated rotational spectroscopic constants and molecular structures agree well with the available experimental results. The frequencies and line intensities of the rovibrational transitions in the nu(3) region of N(2)O for the van der Waals ground vibrational state were calculated and compared with the observed spectra. The predicted infrared spectra are consistent with the observed spectra and show that the N(2)O-H(2) complexes are mostly a-type transitions while both a-type and b-type transitions are significant for the N(2)O-D(2) complexes.

Barrier for cold-fusion production of superheavy elements

We estimate the fusion-barrier height ${B}_{\mathrm{fu}}^{\text{(two-body)}}$ for approaching ions in cold-fusion reactions in a model where the projectile deformation and quadrupole zero-point vibrational energy are taken into account. This barrier height is defined as the barrier energy at the target and projectile separation distance where an original oblate deformation of projectile and/or target caused by a repulsive Coulomb force turns into a large prolate deformation caused by the attractive nuclear force as the target and projectile come closer. The instability develops before touching because the attractive short-range nuclear force overcomes the repulsive Coulomb force and the shape-stabilizing effect of shell structure. The shell structure of the doubly magic $^{208}\mathrm{Pb}$ target is sufficiently strong that its shape remains very close to spherical in all cases studied here. The fusion potential for approaching ions in the two-body channel is calculated in the macroscopic-microscopic model with the quadrupole vibrational zero-point energy obtained in the WKB approximation. We compare our results with data from 10 experimental cold-fusion reactions and with the Bass barriers. Differences and similarities between the Yukawa-plus-exponential model and the Bass model are discussed. We also calculate five-dimensional potential-energy surfaces for the single compound system and show that well-established fission and fusion valleys are both present. For heavy systems, ${B}_{\mathrm{fu}}^{\text{(two-body)}}$ becomes lower than the fission barrier just beyond the ground state of the compound system. In the vicinity of this transition, the optimum collision energy for formation of evaporation residues can be expected to depend in a delicate fashion on the interplay among ${B}_{\mathrm{fu}}^{\text{(two-body)}}$, the fusion valley, the fission barrier of the compound system, and the one- and two-neutron separation energies ${S}_{1n}$ and ${S}_{2n}$. We discuss these issues in detail and calculate fission-barrier heights. Except for reactions in which the projectile is doubly magic or near doubly magic, the calculated quantities are consistent with the observed optimal energies for evaporation-residue formation.

Exit interaction effect on nascent product state distribution of O(1D)+N2O-->NO+NO.

We have determined the rotational state distributions of NO(v'=0,1,2) products produced from the reaction O(1D)+N2O. This is the first full characterization of the product rotational distribution of this reaction. The main part of each rotational distribution (up to j' approximately 80) has rotational temperature approximately 20,000 K and all these distributions are quite near to those predicted by the phase space theory (PST). This observation and previously reported vibrational distribution indicate that the most part of the energy partitioning of the reaction products is at least apparently statistical although the intermediate of this reaction is not so stable as to ensure the long lifetime. On the other hand, the distributions in the high rotational levels (j'=80-100) are found to decrease more sharply as j' increases than the PST predictions. The origin of the observed decrease of the distribution is discussed with quasiclassical trajectory (QCT) calculations on a five-dimensional ab initio potential energy surface (PES). The observed near-statistical distribution and the sharp decrease in the high-j' levels are well reproduced by a "half-collision" QCT calculation, where statistical distribution at the reaction intermediate is assumed. This agreement shows the rotation-translation interaction in the exit region has an effect of yielding small high-j' populations. However, a little bias of the calculated distribution toward lower rotational excitation than the observed one indicates that the combination of the statistical intermediate and the exit interaction on the current PES does not completely describe the real system. It is suggested that the reaction intermediate is generated with the distribution which is close to statistical but a little biased toward yielding high-j' products, and that the interaction in the exit region of the PES results in the sharp decrease in the high-j' levels.