Five-dimensional Potential Energy Surface Research Articles

Angular momentum in fission fragments

We suggest that the angular momentum in fission fragments is generated by statistical excitation at scission. The magnitude of the angular momentum is determined by excitation energy and shell structure in the level density. Treating the prescission shape evolution as a diffusive process, implemented as a Metropolis walk on a five-dimensional potential-energy surface, the average magnitudes of the fission fragment angular momenta are calculated for U235(nth,f), assuming that they are perpendicular to the fission axis. The sawtooth behavior of the average angular momentum magnitude as function of mass number is discussed in connection with the similar observed behavior of the average neutron multiplicity, and a good understanding is achieved. The magnitudes of the angular momenta of light and heavy fragments are found to have a weak negative correlation, in accordance with recent experimental results. This correlation arises from the microcanonical sharing of excitation energy by the fragments at scission, where each energy provides a distribution of angular momenta. Published by the American Physical Society 2024

An intramolecular vibrationally excited intermolecular potential energy surface and predicted 2OH overtone spectroscopy of H2O-Kr.

A new five-dimensional potential energy surface (PES) for H2O-Kr which explicitly includes the intramolecular 2OH overtone state of the H2O monomer is presented. The intermolecular potential energies were evaluated using explicitly correlated coupled cluster theory [CCSD(T)-F12] with a large basis set. Four vibrationally averaged analytical intermolecular PESs for H2O-Kr with H2O molecules in its |00+〉, |02+〉, |02-〉, and |11+〉 states are obtained by fitting to the multi-dimensional Morse/Long-Range potential function form. Each vibrationally averaged PES fitted to 578 points has root-mean-square (RMS) deviations smaller than 0.14 cm-1 and requires only 58 parameters. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels for |00+〉, |02+〉, |02-〉, and |11+〉 states of the H2O-Kr complexes. The calculated |02-〉Πf/e(101) ← |00+〉Σe(000) and |02+〉Πf/e(110) ← |00+〉Σe(101) infrared transitions are in excellent agreement with the experimental values with RMS discrepancies being only 0.007 and 0.016 cm-1, respectively. These analytical PESs can be used to provide reliable theoretical guidance for future infrared overtone spectroscopy of H2O-Kr.

Relativistic multimode Jahn-Teller and pseudo-Jahn-Teller effects in tetrahedral systems

The relativistic pseudo-Jahn-Teller effect 2T×(t2+e)=(E1/2+G3/2)×(t2+e) and the Jahn-Teller effect 2E×(t2+e)=G3/2×(t2+e) are considered, employing the microscopic (Breit-Pauli) spin–orbit coupling operator. The orbital and spin-orbital parts of electronic Hamiltonian are expanded up to the second order terms in normal modes. Five-dimensional (t2+e) potential energy surfaces are obtained in analytical form as functions of invariants of the Td group.

A new potential energy surface and rovibrational spectra of the CO-CO2 complex: Dependence on the antisymmetric stretching vibration of CO2.

We present a new ab initio five-dimensional potential energy surface for the CO-CO2 complex containing the Q3 normal mode for the ν3 asymmetric stretching vibration of the CO2 unit. The potential was calculated by the supermolecular approach at the explicitly correlated coupled cluster [CCSD (T)-F12a] level with aug-cc-pVTZ basis set plus midpoint bond functions. Two vibrationally averaged four-dimensional potentials for CO-CO2 with CO2 at the ground and ν3 excited states were generated by the integration of the five-dimensional potential over the Q3 intramolecular coordinate. Each potential displays a T-shaped global minimum with the C end in the CO unit pointing toward the C atom in the CO2 unit and a T-shaped local minimum but with the CO monomer rotated by 180°. The rovibrational bound states and energy levels for the CO-CO2 dimer were obtained employing the radial discrete variable representation/angular finite basis representation method in conjunction with the Lanczos algorithm. The vibrational ground and some lower excited states for CO-CO2 are localized around the global minimum because of the higher potential barriers. The band origin is blueshifted by 0.2089cm-1 for CO-CO2 in the CO2 ν3 range, which is consistent with the experimental result of 0.211cm-1. The geared bending vibrational frequencies for CO-CO2 are 24.7101 and 24.5549cm-1 at the ground and ν3 excited states of CO2, respectively. The predicted rovibrational frequencies, as well as spectral constants, coincide with the available observations, and these parameters show that the CO-CO2 complex is a nearly prolate asymmetric rotor.

Ab initio study of the O3-N2 complex: Potential energy surface and rovibrational states.

The formation and destruction of O3 within the Chapman cycle occurs as a result of inelastic collisions with a third body. Since N2 is the most abundant atmospheric molecule, it can be considered as the most typical candidate when modeling energy-transfer dynamics. We report a new ab initio potential energy surface (PES) of the O3-N2 van der Waals complex. The interaction energies were calculated using the explicitly correlated single- and double-excitation coupled cluster method with a perturbative treatment of triple excitations [CCSD(T)-F12a] with the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set. The five-dimensional PES was analytically represented by an expansion in spherical harmonics up to eighth order inclusive. Along with the global minimum of the complex (De = 348.88cm-1), with N2 being perpendicular to the O3 plane, six stable configurations were found with a smaller binding energy. This PES was employed to calculate the bound states of the O3-N2 complex with both ortho- and para-N2 for total angular momentum J = 0 and 1, as well as dipole transition probabilities. The nature of the bound states of the O3-oN2 and O3-pN2 species is discussed based on their rovibrational wave functions.

Potential Energy Surfaces for Water Interacting with Heteronuclear Diatomic Molecules: H2O–HF as a Case Study

We present an analytical model, suitable for molecular dynamics applications, of a five-dimensional potential energy surface, based on the expansion in spherical harmonics, for non-linear-triatomic molecule (C2v) – heteronuclear-diatomic molecule systems, with both molecules having a rigid structure. The method consists in the exact transformation of quantum chemical input data related to a minimal number of significant configurations. This approach is applied to the case study of H2O–HF at various levels of theory. The interaction potential has been analyzed and compared with state-of-art theoretical models. Pros and cons of the method are presented and discussed.

Potential energy surface and bound states of the H2O-HF complex.

We present the first global five-dimensional potential energy surface for the H2O-HF dimer, a prototypical hydrogen bonded complex. Large scale ab initio calculations were carried out using the explicitly correlated coupled cluster approach with single- and double-excitations together with non-iterative perturbative treatment of triple excitations with the augmented correlation-consistent triple zeta basis sets, in which the water and hydrogen fluoride monomers were frozen at their vibrationally averaged geometries. The ab initio data points were fitted to obtain a global potential energy surface for the complex. The equilibrium geometry of the complex corresponds to the formation of a hydrogen bond with water acting as a proton acceptor and a binding energy of De = 3059 cm-1 (8.75 kcal/mol). The energies and wavefunctions of the lowest bound states of the complex were computed using a variational approach, and the dissociation energies of both ortho-H2O-HF (D0 = 2089.4 cm-1 or 5.97 kcal/mol) and para-H2O-HF (D0 = 2079.6 cm-1 or 5.95 kcal/mol) were obtained. The rotational constant of the complex was found to be in good agreement with the available experimental data.

Macroscopic–microscopic calculations of fission potential surface of uranium isotopes in the three quadratic surfaces parametrization

Five-dimensional (5D) fission potential energy surfaces (PES) for uranium nuclei are investigated based on the macroscopic–microscopic Lublin–Strasbourg drop model in the three-quadratic-surface parametrization, and the heights of static fission barriers are obtained. Asymmetric and symmetric fission paths are presented on the 5D PES of 236U for different nuclear shapes. The calculated barrier heights, EA and EB, are quite consistent with the experimental data for all even–even nuclei of uranium isotopes, from 230U to 244U.

Ab initio potential energy surface and microwave spectrum of the NH3-N2 van der Waals complex.

We present a five-dimensional intermolecular potential energy surface (PES) of the NH3-N2 complex, bound state calculations, and new microwave (MW) measurements that provide information on the structure of this complex and a critical test of the potential. Ab initio calculations were carried out using the explicitly correlated coupled cluster [CCSD(T)-F12a] approach with the augmented correlation-consistent aug-cc-pVTZ basis set. The global minimum of the PES corresponds to a configuration in which the angle between the NH3 symmetry axis and the intermolecular axis is 58.7° with the N atom of the NH3 unit closest to the N2 unit, which is nearly parallel to the NH3 symmetry axis. The intermolecular distance is 7.01 a0, and the binding energy De is 250.6 cm-1. The bound rovibrational levels of the four nuclear spin isomers of the complex, which are formed when ortho/para (o/p)-NH3 combines with (o/p)-N2, were calculated on this intermolecular potential surface. The computed dissociation energies D0 are 144.91 cm-1, 146.50 cm-1, 152.29 cm-1, and 154.64 cm-1 for (o)-NH3-(o)-N2, (o)-NH3-(p)-N2, (p)-NH3-(o)-N2, and (p)-NH3-(p)-N2, respectively. Guided by these calculations, the pure rotational transitions of the NH3-N2 van der Waals complex were observed in the frequency range of 13-27 GHz using the chirped-pulse Fourier-transform MW technique. A complicated hyperfine structure due to three quadrupole 14N nuclei was partly resolved and examined for all four nuclear spin isomers of the complex. Newly obtained data definitively established the K values (the projection of the angular momentum J on the intermolecular axis) for the lowest states of the different NH3-N2 nuclear spin isomers.

Study of neutron induced fission of actinides in a macroscopic-microscopic model

The macroscopic-microscopic (MM) model, as a powerful theoretical tool for the understanding of nuclear fission mechanism, is deemed to be a so impressive theoretical method that its calculated results would quantitatively predict the fission observables in the near future. This paper reviews our recent progress in the theoretical calculations of the five-dimensional (5D) potential energy surfaces (PESs) and the fission fragment mass distributions for the neutron induced fission of actinides within the framework of the MM model along with the random walking method and Langevin model. Firstly, we use the 5D generalized Lawrence shape and three quadrature surfaces parameterizations as the shape descriptions, the Lublin-Strasbourg Drop model for the macroscopic energy and the folded-Yukawa model as the single-particle potential. A new method to use a two-center oscillator basis in calculating Hamiltonian matrix on any kind of shape description is presented. Then, the advanced search algorithms are developed and used in searching for the optimal fission path, fission saddles and other structure information on a 5D PES surface. The method of random walks on 5D PESs is used to calculate the fission fragment mass distributions for the 235U(n,f) reaction. Finally, three-dimensional Langevin model with a constraint on the heavy fragment deformation are applied to study the fragment mass distributions for 14 MeV neutron-introduced fissions of uranium isotopes.

236U Multi-modal Fission Paths on a Five-dimensional Deformation Surface**Supported by the Major Research plan of National Natural Science of China under Grant No. 11790324, the National Key Research and Development Program of China under Grant Nos. 2016YY0200804 and 2017YFF0206205, and the National Magnetic Confinement Fusion Science Program of China under Grant Nos. 2013GB106004 and 2012GB-101003 and the National Natural Science

In this paper, we develop a new path search algorithm which considers all the degrees of freedom and apply it on our calculated five-dimensional potential energy surface (PES) of 236U. Asymmetric and symmetric fission paths and barriers are obtained.

Collisional Excitation and Weak Maser Action of Interstellar Methanimine.

The inelastic cross sections and rate coefficients for the rotational excitation of methanimine (CH2NH) by cold H2 have been determined quantum mechanically based on a new highly correlated five-dimensional potential energy surface. This surface was fitted to more than 60 000 ab initio points with a root-mean-square error of ∼1-2 cm-1 in the region of the potential well whose depth is -374.0 cm-1. The rotationally inelastic rate coefficients have been combined with spectroscopic data to generate the nonequilibrium spectrum of CH2NH toward the interstellar molecular cloud Sgr B2(N). The transition 110 → 111 at 5.29 GHz is found to be inverted, and the predicted weak maser emission spectrum is in excellent agreement with new observations performed with the 100 m Green Bank Telescope.

High-dimensional wave packet dynamics from first principles: Photodissociation of water on TiO2-rutile (110)

Through solving the time-dependent Schrödinger equation for the nuclear motion, quantum dynamical simulations of the water/TiO2-rutile (110) system were performed. Five-dimensional potential energy surfaces (PES) for the electronic ground and an excited state previously calculated on CASSCF (Complete Active Space Self-Consistent Field) level of theory served as the starting point for our investigations [J. Mitschker, T. Klüner, Phys. Chem. Chem. Phys. 17 (2015) 268–275]. Through investigating the motion of the water molecule by a selected series of three- and four-dimensional simulations, a precise picture of the photodissociation mechanism is obtained. Furthermore, calculations of photodissociation probabilities reveal the most favoured pathway for a complete dissociation of the adsorbate including the excitation and relaxation process as well as temperature effects.

Intermolecular configurations dominated by quadrupole-quadrupole electrostatic interactions: explicit correlation treatment of the five-dimensional potential energy surface and infrared spectra for the CO-N2 complex.

A thorough understanding of the intermolecular configurations of van der Waals complexes is a great challenge due to their weak interactions, floppiness and anharmonic nature. Although high-resolution microwave or infrared spectroscopy provides one of the most direct and precise pieces of experimental evidence, the origin and key role in determining such intermolecular configurations of a van der Waals system strongly depend on its highly accurate potential energy surface (PES) and a detailed analysis of its ro-vibrational wavefunctions. Here, a new five-dimensional potential energy surface for the van der Waals complex of CO-N2 which explicitly incorporates the dependence on the stretch coordinate of the CO monomer is generated using the explicitly correlated couple cluster (CCSD(T)-F12) method in conjunction with a large basis set. Analytic four-dimensional PESs are obtained by the least-squares fitting of vibrationally averaged interaction energies for v = 0 and v = 1 to the Morse/Long-Range potential mode (VMLR). These fits to 7966 points have root-mean-square deviations (RMSD) of 0.131 cm-1 and 0.129 cm-1 for v = 0 and v = 1, respectively, with only 315 parameters. Energy decomposition analysis is carried out, and it reveals that the dominant factor in controlling intermolecular configurations is quadrupole-quadrupole electrostatic interactions. Moreover, the rovibrational levels and wave functions are obtained for the first time. The predicted infrared transitions and intensities for the ortho-N2-CO complex as well as the calculated energy levels for para-N2-CO are in good agreement with the available experimental data with RMSD discrepancies smaller than 0.068 cm-1. The calculated infrared band origin shift associated with the fundamental band frequency of CO is -0.721 cm-1 for ortho-N2-CO which is in excellent agreement with the experimental value of -0.739 cm-1. The agreement with experimental values validates the high quality of the PESs and enhances our confidence to explain the observed mystery lines around 2163 cm-1.

Potential energy and dipole moment surfaces for HF@C60: Prediction of spectral and electric response properties.

We present a five-dimensional potential energy surface (PES) for the HF@C60 system computed at the DF-LMP2/cc-pVTZ level of theory. We also calculated a five-dimensional dipole moment surface (DMS) based on DFT(PBE0)/cc-pVTZ calculations. The HF and C60 molecules are considered rigid with bond length rHF = 0.9255 Å (gas phase ground rovibrational state geometry). The C60 geometry is of Ih symmetry. The ab initio points were fitted to obtain a PES in terms of bipolar spherical harmonics. The minimum of the PES corresponds to a geometry where the center of mass of HF is located 0.11 Å away from the center of the cage with an interaction energy of -6.929 kcal/mol. The DMS was also represented in terms of bipolar spherical harmonics. The PES was used to calculate the rotation-translation bound states of HF@C60, and good agreement was found relative to the available experimental data [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] except for the splitting of the first rotational excitation levels. We propose an empirical adjustment to the PES in order to account for the experimentally observed symmetry breaking. The form of that effective PES is additive. We also propose an effective Hamiltonian with an adjusted rotational constant in order to quantitatively reproduce the experimental results including the splitting of the first rotational state. We use our models to compute the molecular volume polarizability of HF confined by C60 and obtain good agreement with experiment.

Theoretical study of HCN-water interaction: five dimensional potential energy surfaces.

A new five-dimensional potential energy surface is calculated at the coupled-cluster CCSD(T) level of theory for the HCN-water system, treating both monomers as rigid rotors. The associated methodology, which combines extensive ab initio calculations of moderate accuracy (CCSD(T)/AVDZ) and a fitting procedure involving a much lower angular coverage with more accurate ab initio calculations (CCSD(T)/CBS), is described in detail. This methodology provides a time-saving approach to compute quantitatively accurate potential energy surfaces with reasonable computational effort. Our potential reproduces the main features reported in the literature, and will allow us to perform the first quantum and semi-classical simulations of the collisional dynamic on this system.

Study of five-dimensional potential-energy surfaces for actinide isotopes by the macroscopic-microscopic method

In this work, the nuclear potential-energy of the deformed nuclei as a function of shape coordinates is calculated in a five-dimensional (5D) parameter space of the axially symmetric generalized Lawrence shapes, on the basis of the macroscopic-microscopic method. The liquid-drop part of the nuclear energy is calculated according to the Myers-Swiatecki model and the Lublin-Strasbourg-drop (LSD) formula. The Woods-Saxon and the folded-Yukawa potentials for deformed nuclei are used for the shell and pairing corrections of the Strutinsky-type. The pairing corrections are calculated at zero temperature, T, related to the excitation energy. The eigenvalues of Hamiltonians for protons and neutrons are found by expanding the eigen-functions in terms of harmonic-oscillator wave functions of a spheroid. Then the BCS pair is applied on the smeared-out single-particle spectrum. By comparing the results obtained by different models, the most favorable combination of the macroscopic-microscopic model is known as the LSD formula with the folded-Yukawa potential. Potential-energy landscapes for actinide isotopes are investigated based on a grid of more than 4,000,000 deformation points and the heights of static fission barriers are obtained in terms of a double-humped structure on the full 5D parameter space. In order to locate the ground state shapes, saddle points, scission points and optimal fission path on the calculated 5D potential-energy surface, the falling rain algorithm and immersion method are designed and implemented. The comparison of our results with available experimental data and others' theoretical results confirms the reliability of our calculations.

Calculated fission-fragment yield systematics in the region74≤Z≤94and90≤N≤150

Background: In the seminal experiment by Schmidt et al. [Nucl. Phys. A 665, 221 (2000)] in which fission-fragment charge distributions were obtained for 70 nuclides, asymmetric distributions were seen above nucleon number $A\ensuremath{\approx}226$ and symmetric ones below. Because asymmetric fission had often loosely been explained as a preference for the nucleus to always exploit the extra binding of fragments near $^{132}\mathrm{Sn}$ it was assumed that all systems below $A\ensuremath{\approx}226$ would fission symmetrically because available isotopes do not have a proton-to-neutron $Z/N$ ratio that allows division into fragments near $^{132}\mathrm{Sn}$. But the finding by Andreyev et al. [Phys. Rev. Lett. 105, 252502 (2010)] did not conform to this expectation because the compound system $^{180}\mathrm{Hg}$ was shown to fission asymmetrically. It was suggested that this was a new type of asymmetric fission, because no strong shell effects occur for any possible fragment division.Purpose: We calculate a reference database for fission-fragment mass yields for a large region of the nuclear chart comprising 987 nuclides. A particular aim is to establish whether $^{180}\mathrm{Hg}$ is part of a contiguous region of asymmetric fission, and if so, its extent, or if not, in contrast to the actinides, there are scattered smaller groups of nuclei that fission asymmetrically in this area of the nuclear chart.Methods: We use the by now well benchmarked Brownian shape-motion method and perform random walks on the previously calculated five-dimensional potential-energy surfaces. The calculated shell corrections are damped out with energy according to a prescription developed earlier.Results: We have obtained a theoretical reference database of fission-fragment mass yields for 987 nuclides. These results show an extended region of asymmetric fission with approximate extension $74\ensuremath{\le}Z\ensuremath{\le}85$ and $100\ensuremath{\le}N\ensuremath{\le}120$. The calculated yields are highly variable. We show 20 representative plots of these variable features and summarize the main aspects of our results in terms of ``nuclear-chart'' plots showing calculated degrees of asymmetry versus $N$ and $Z$.Conclusions: Experimental data in this region are rare: only ten or so yield distributions have been measured, some with very limited statistics. We agree with several measurements with higher statistics. Regions where there might be differences between our calculated results and measurements lie near the calculated transition line between symmetric and asymmetric fission. To draw more definite conclusions about the accuracy of the present implementation of the Brownian shape-motion approach in this region experimental data, with reliable statistics, for a fair number of suitably located additional nuclides are clearly needed. Because the nuclear potential-energy structure is so different in this region compared to the actinide region, additional experimental data together with fission theory studies that incorporate additional, dynamical aspects should provide much new insight.

Photodesorption of water from rutile(110): ab initio calculation of five-dimensional potential energy surfaces of ground and excited electronic states and wave packet studies.

In this paper, we report on our results concerning the interaction of water with titanium dioxide in its rutile modification. The (110) surface is modelled by an embedded Ti9O18Mg7(14+) cluster. We present up to five-dimensional potential energy surfaces for the water molecule on this surface and include the dissociation of one hydrogen atom. The electronic ground state as well as one electronically excited state is included. To deal with the multi-configurational character of the wave function, we use the complete active space self-consistent field (CASSCF) approach. The resulting potential energy surfaces are fitted by means of an artificial neural network. As a first example of quantum dynamical studies based on our potential surfaces, we present results on the photodesorption of water from rutile(110).

Intermolecular potential energy surface and thermophysical properties of the CH4-N2 system.

A five-dimensional potential energy surface (PES) for the interaction of a rigid methane molecule with a rigid nitrogen molecule was determined from quantum-chemical ab initio calculations. The counterpoise-corrected supermolecular approach at the CCSD(T) level of theory was utilized to compute a total of 743 points on the PES. The interaction energies were calculated using basis sets of up to quadruple-zeta quality with bond functions and were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites for methane and five sites for nitrogen was fitted to the interaction energies. The PES was validated by calculating the cross second virial coefficient as well as the shear viscosity and binary diffusion coefficient in the dilute-gas limit for CH4-N2 mixtures. An improved PES was obtained by adjusting a single parameter of the analytical potential function in such a way that quantitative agreement with the most accurate experimental values of the cross second virial coefficient was achieved. The transport property values obtained with the adjusted PES are in good agreement with the best experimental data.