Nuclear Potential Energy Surface Research Articles

Macroscopic-Microscopic Fission Yields

We utilize the macroscopic-microscopic approach to fission to calculate nascent fragment distributions. Assuming strongly damped shape motion, we run many iterations of a Metropolis random walk across nuclear potential-energy surfaces to obtain sufficient scission statistics. Our nuclear potential surfaces consist of a macroscopic energy from the Finite-Range Liquid-Drop Model (FRLDM) and microscopic terms that arise from the single-particle spectra. We compare our predictions for two major actinides to experimental data. We present global trends from this modeling that manifest as a function of mass number of the fissioning species. We discuss the impact of fission yield modeling on nucleosynthetic outcomes.

Including vibrational effects in magnetic circular dichroism spectrum calculations in the framework of excited state dynamics.

In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4- and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements.

General Analytical Nuclear Forces and Molecular Potential Energy Surface from Full Configuration Interaction Quantum Monte Carlo.

The full configuration interaction quantum Monte Carlo (FCIQMC) is a state-of-the-art stochastic electronic structure method, providing a methodology to compute FCI-level state energies of molecular systems within a quantum chemical basis. However, especially to probe dynamics at the FCIQMC level, it is necessary to devise more efficient schemes to produce nuclear forces and potential energy surfaces (PES) from FCIQMC. In this work, we derive the general formula for nuclear forces from FCIQMC, and clarify different contributions of the total force. This method to obtain FCIQMC forces eliminates previous restrictions and can be used with frozen core approximation and free selection of orbitals, making it promising for more efficient nuclear forces calculations. After some numerical checks of this procedure on the binding curve of N2 molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of the water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H2O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.

Improvements to the macroscopic-microscopic approach of nuclear fission

The well established macroscopic-microscopic (mac-mic) description of nuclear fission enables the prediction of fission fragment yields for a broad range of fissioning systems. In this work, we present several key enhancements to this approach. We improve upon the microscopic sector of nuclear potential energy surfaces by magnifying the resolution of the Lipkin-Nogami equations and strengthening the Strutinsky procedure, thus reducing spurious effects from the continuum. We further present a novel deterministic method for calculating fission dynamics under the assumption of strongly damped nucleonic motion. Our technique directly determines the evolution of the scissioned shape distribution according to the number of random walk steps rather than the statistical accumulation of fission events. We show that our new technique is equivalent to the Metropolis random walk pioneered over the past decade by Randrup and colleagues. It further improves upon it, as we remove the need for altering the nuclear landscape via a biased potential. With our final improvement, we calculate fission fragments mass and charge distributions using particle number projection, which affords the simultaneous calculation of both mass and charge yield distributions. Fission fragments are thus calculated from the quantum mechanical $A$-body states of the potential energy surface rather than the collective mass asymmetry variable ($\alpha_{\rm g}$) of the Finite-Range Liquid-Drop Model (FRLDM) used in past work. We highlight the success of our enhancements by predicting the odd-even staggering and the charge polarization for the neutron-induced fission of ${}^{233}$U and ${}^{235}$U.

Primary fission fragment mass yields across the chart of nuclides

We have calculated a complete set of primary fission fragment mass yields, $Y(A)$, for heavy nuclei across the chart of nuclides, including those of particular relevance to the rapid neutron capture process ($r$ process) of nucleosynthesis. We assume that the nuclear shape dynamics are strongly damped which allows for a description of the fission process via Brownian shape motion across nuclear potential-energy surfaces. The macroscopic energy of the potential was obtained with the Finite-Range Liquid-Drop Model (FRLDM), while the microscopic terms were extracted from the single-particle level spectra in the fissioning system by the Strutinsky procedure for the shell energies and the BCS treatment for the pairing energies. For each nucleus considered, the fission fragment mass yield, $Y(A)$, is obtained from 50,000 -- 500,000 random walks on the appropriate potential-energy surface. The full mass and charge yield, $Y(Z,A)$, is then calculated by invoking the Wahl systematics. With this method, we have calculated a comprehensive set of fission-fragment yields from over 3,800 nuclides bounded by $80\leq Z \leq 130$ and $A\leq330$; these yields are provided as an ASCII formatted database in the supplemental material. We compare our yields to known data and discuss general trends that emerge in low-energy fission yields across the chart of nuclides.

The Los Alamos fission yield evaluation pipeline

The nuclear data team at Los Alamos National Laboratory has undertaken a campaign to construct new fission yield evaluation. Significant advances have been made on a number of fronts. Nuclear potential energy surfaces can now be generated with the newly developed MicMac code based off the Finite Range Liquid-Drop Model (FRLDM). This model can be incorporated into the Los Alamos de-excitation framework codes BeOH and CGMF to perform modeling of prompt, independent (IFY) and cumulative (CFY) fission yields that take into account prompt and beta-delayed neutrons and photons consistent with decay data. This is in stark contrast to what exists in evaluated nuclear data libraries today, where only a few incident energy points are used with limited physical insights and no consistency between IFY, CFY and decay data. We highlight the latest progress with application of neutron-induced fission of 235 U and 239 Pu.

Shape-coexistence Studies in the Ni Isotopic Chain by Using the Selectivity of Different Reaction Mechanisms

We report on the investigation of the shape coexistence phenomenon in the Ni isotopic chain, from A = 62 to A = 66, by using γ-ray spectroscopy techniques and different reaction mechanisms, such as sub-Coulomb barrier transfer reactions and thermal-neutron capture. Our aim is to understand, from the microscopic point of view, the appearance of nuclear deformation in Ni isotopes at low excitation energy. A series of experiments was performed at the Tandem Accelerator Laboratory in Bucharest, at ALTO IPN-Orsay and at the ILL reactor in Grenoble. Various mean-field theoretical approaches, as well as recent state-of-the-art Monte Carlo Shell Model (MCSM) calculations, predict in 66Ni a deep secondary prolate minimum in the nuclear potential energy surface at spin zero, resulting in a hindered electromagnetic decay towards the spherical ground state (i.e., with an E2 transition probability less than 1 W.u.). This has been confirmed in the first experiment performed in Bucharest. Less pronounced prolate minima, at higher excitation energies, are also expected in lighter neutron-rich Ni isotopes, from state-of-the-art Monte Carlo Shell Model (MCSM) calculations. Preliminary results are discussed for 62Ni and 64Ni, in comparison with theory predictions.

Benchmarking DFT-D Dispersion Corrections for Anharmonic Vibrational Frequencies and Harmonic Scaling Factors.

Improvements in the form of the DFT-D empirical dispersion corrections to hybrid density functional theory are shown to have made corrections sufficiently accurate to improve the calculation of both anharmonic frequencies and scaled harmonic vibrational frequencies across a wide range of commonly tested molecules. The Becke-Johnson damping function is noted as being particularly versatile across the molecules tested, and the B3LYP-D3M(BJ) and B3LYP-D3(CSO) methods are found to be the most widely applicable. Dispersion corrections are shown to be important for accurately describing carbon-hydrogen bond stretching vibrations, and standard triple-dipole based three-body terms are found to cause large errors in these anharmonic frequencies. Preliminary results also indicate that there is a cancellation of error at this level of theory when using smaller finite difference step sizes to calculate anharmonic derivatives of the nuclear potential energy surface.

Adaptive Dimensional Decoupling for Compression of Quantum Nuclear Wave Functions and Efficient Potential Energy Surface Representations through Tensor Network Decomposition.

We present an approach to reduce the computational complexity and storage pertaining to quantum nuclear wave functions and potential energy surfaces. The method utilizes tensor networks implemented through sequential singular value decompositions. Two specific forms of tensor networks are considered to adaptively compress the data in multidimensional quantum nuclear wave functions and potential energy surfaces. In one case the well-known matrix product state approximation is used whereas in another case the wave function and potential energy surface space is initially partitioned into "system" and "bath" degrees of freedom through singular value decomposition, following which the individual system and bath tensors (wave functions and potentials) are in turn decomposed as matrix product states. We postulate that this leads to a mean-field version of the well-known projectionally entangled pair state known in the tensor networks community. Both formulations appear as special cases of more general higher order singular value decompositions known in the mathematics literature as Tucker decomposition. The networks are then used to study the hydrogen transfer step in the oxidation of isoprene by peroxy and hydroxy radicals. We find that both networks are extremely efficient in accurately representing quantum nuclear eigenstates and potential energy surfaces and in computing inner products between quantum nuclear eigenstates and a final-state basis to yield product side probabilities. We also present formal protocols that will be useful to perform explicit quantum nuclear dynamics.

An Algorithm of Constructing Potential Energy Surfaces for Nuclear Particle--Hole Excited Configurations

We discuss and illustrate a computer-designed algorithm allowing to construct the nuclear potential energy surfaces generated by a mean field Hamiltonian H(α) as functions of the ensemble of nuclear deformation variables α for multi-particle multi-hole excited configurations. The algorithm in question serves to eliminating the undesired effect of the so-called avoided crossing mechanism, a consequence of the well known property referred to as Landau-Zener non-crossing rule.

Quantum-Mechanical Prediction of the Averaged Structure, Anharmonic Vibrational Frequencies, and Intensities of the H2O···trans-HONO Complex and Comparison with the Experiment.

The geometrical parameters, the frequencies, and absolute intensities of vibrational transitions of H2O···trans-HONO hydrogen-bonded complex are calculated using the approach earlier tested in calculations of isolated molecules of nitrous acid and complexes of this acid with ammonia. The equilibrium nuclear configuration and potential energy and dipole moment surfaces are calculated by the MP2/aug-cc-pVTZ method with the basis set superposition error taken into account. The fundamental transition frequencies and intensities of the complex are first obtained in the harmonic approximation, and then the energy values, vibrational wave functions, and transition frequencies and intensities are determined from variational solutions of one- to four-dimensional anharmonic equations. The results obtained are compared with the data calculated in the same approximation for an isolated trans-HONO molecule and the NH3···trans-HONO complex. The average discrepancy between the anharmonic frequency values and five available experimental data is 15 cm-1. Three absorption bands of trans-HONO with the highest intensity are recommended for detecting the presence of H2O···trans-HONO.

Differential evolution algorithm for global optimizations in nuclear physics

We explore the applicability of the differential evolution algorithm in finding the global minima of three typical nuclear structure physics problems: the global deformation minimum in the nuclear potential energy surface, the optimization of mass model parameters and the lowest eigenvalue of a nuclear Hamiltonian. The algorithm works very effectively and efficiently in identifying the minima in all problems we have tested. We also show that the algorithm can be parallelized in a straightforward way.

Anharmonic exciton dynamics and energy dissipation in liquid water from two-dimensional infrared spectroscopy.

Water's extended hydrogen-bond network results in rich and complex dynamics on the sub-picosecond time scale. In this paper, we present a comprehensive analysis of the two-dimensional infrared (2D IR) spectrum of O-H stretching vibrations in liquid H2O and their interactions with bending and intermolecular vibrations. By exploring the dependence of the spectrum on waiting time, temperature, and laser polarization, we refine our molecular picture of water's complex ultrafast dynamics. The spectral evolution following excitation of the O-H stretching resonance reveals vibrational dynamics on the 50-300 fs time scale that are dominated by intermolecular delocalization. These O-H stretch excitons are a result of the anharmonicity of the nuclear potential energy surface that arises from the hydrogen-bonding interaction. The extent of O-H stretching excitons is characterized through 2D depolarization measurements that show spectrally dependent delocalization in agreement with theoretical predictions. Furthermore, we show that these dynamics are insensitive to temperature, indicating that the exciton dynamics alone set the important time scales in the system. Finally, we study the evolution of the O-H stretching mode, which shows highly non-adiabatic dynamics suggestive of vibrational conical intersections. We argue that the so-called heating, commonly observed within ∼1 ps in nonlinear IR spectroscopy of water, is a nonequilibrium state better described by a kinetic temperature rather than a Boltzmann distribution. Our conclusions imply that the collective nature of water vibrations should be considered in describing aqueous solvation.

Anharmonic Calculation of the Structure, Vibrational Frequencies, and Intensities of the NH3···cis-HONO and NH3···cis-DONO Complexes.

The geometrical parameters, the frequencies, and absolute intensities for transitions between vibrational states of NH3···cis-HONO and NH3···cis-DONO hydrogen-bonded complexes are calculated using the approach earlier tested in calculations of isolated molecules of nitrous acid and the NH3···trans-HONO and NH3··trans-DONO complexes. Vibrational wave functions and energy values of the complexes are derived from variational solutions of anharmonic equations in one to four dimensions. The equilibrium nuclear configuration and potential energy surfaces are calculated by the MP2/aug-cc-pVTZ method with the basis set superposition error taken into account. Comparison of the obtained results with the analogous data calculated in the same approximation for isolated cis- and trans-HONO (DONO) molecules and the NH3···trans-HONO (DONO) complexes provides information about the changes in the spectroscopic and geometrical parameters of nitrous acid upon cis-trans transition, H/D substitution, and H-bond formation.

Differences in the Vibrational Dynamics of H(2)O and D(2)O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water.

Water's ability to donate and accept hydrogen bonds leads to unique and complex collective dynamical phenomena associated with its hydrogen-bond network. It is appreciated that the vibrations governing liquid water's molecular dynamics are delocalized, with nuclear motion evolving coherently over the span of several molecules. Using two-dimensional infrared spectroscopy, we have found that the nuclear motions of heavy water, D2O, are qualitatively different than those of H2O. The nonlinear spectrum of liquid D2O reveals distinct O-D stretching resonances, in contrast to H2O. Furthermore, our data indicates that condensed-phase O-D vibrations have a different character than those in the gas phase, which we understand in terms of weakly delocalized symmetric and antisymmetric stretching vibrations. This difference in molecular dynamics reflects the shift in the balance between intra- and intermolecular couplings upon deuteration, an effect which can be understood in terms of the anharmonicity of the nuclear potential energy surface.

Laser-induced electron localization in H₂⁺: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface.

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett., 2010, 105, 123002] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes.

Mixed quantum-classical dynamics on the exact time-dependent potential energy surface: a fresh look at non-adiabatic processes

The exact nuclear time-dependent potential energy surface arises from the exact decomposition of the electronic and nuclear motions, recently presented in [A. Abedi, N.T. Maitra, and E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on nuclear dynamics. We observe that the potential, after the nuclear wave packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorisation of the electron-nuclear wave function is at the basis of the decomposition. In particular, the nuclear part is the true nuclear wave function, solution of a time-dependent Schrödinger equation and leading to the exact many-body density and current density. As a consequence, the Ehrenfest theorem can be extended to the nuclear subsystem and Hamiltonian, as discussed here with an analytical derivation and numerical results.

Ab initio non-adiabatic molecular dynamics

Adiabatic nuclear potential energy surfaces (PESs) defined via the Born-Oppenheimer (BO) approximation are a fundamental concept underlying chemical reactivity theory. For a wide range of excited-state phenomena such as radiationless decay, energy and charge transfer, and photochemical reactions, the BO approximation breaks down due to strong couplings between two or more BO PESs. Non-adiabatic molecular dynamics (NAMD) is the method of choice to model these processes. We review new developments in quantum-classical dynamics, analytical derivative methods, and time-dependent density functional theory (TDDFT) which have lead to a dramatic expansion of the scope of ab initio NAMD simulations for molecular systems in recent years. We focus on atom-centered Gaussian basis sets allowing highly efficient simulations for molecules and clusters, especially in conjunction with hybrid density functionals. Using analytical derivative techniques, forces and derivative couplings can be obtained with machine precision in a given basis set, which is crucial for accurate and stable dynamics. We illustrate the performance of surface-hopping TDDFT for photochemical reactions of the lowest singlet excited states of cyclohexadiene, several vitamin D derivatives, and a bicyclic cyclobutene. With few exceptions, the calculated quantum yields and excited state lifetimes agree qualitatively with experiment. For systems with ∼50 atoms, the present Turbomole implementation allows NAMD simulations with 0.2-0.4 ns total simulation time using hybrid density functionals and polarized double zeta valence basis sets on medium-size compute clusters. We close by discussing open problems and future directions.

On the relationship between molecular state and single electron pictures in simple electrochemical junctions

We consider a molecular conduction junction that comprises a redox molecule bridging between metal electrodes, in the limit of weak coupling and high temperature where electron transport is dominated by Marcus electron transfer kinetics. We address the correspondence between the Marcus description in terms of nuclear potential energy surfaces associated with different charging states of the molecular bridge, and the single electron description commonly used in theories of molecular conduction. The relationship between the energy gap, reorganization energy and activation energy parameters of the Marcus theory and the corresponding energy parameters in the single electron description is elucidated. We point out that while transport in the normal Marcus regime involves activated (therefore relatively slow) transitions between at least two charging states of the molecular bridge, deep in the inverted regime only one of these states is locally stable and transitions into this state are activationless. The relatively slow rates that characterize the normal Marcus transport regime manifest themselves in the appearance of hysteresis in the system transport behavior as a function of gate or bias potentials for relatively slow scan rates of these potentials, but not bistability in the junction conduction behavior. We also consider the limit of fast solvent reorganization that may reflect the response of the electronic environment (electronic polarization of a solvent and of the metal electrodes) to the changing charging state of the bridge. In this limit, environmental reorganization appears as renormalization of the bridge electronic energy levels. We show that the effect of this reorganization on the junction conduction properties is not universal and depends on the particular bridge charging states that are involved in the conduction process.

Energy Dependence of Plutonium Fission-Product Yields

A method is developed for interpolating between and/or extrapolating from two pre-neutron-emission first-chance mass-asymmetric fission-product yield curves. Measured 240Pu spontaneous fission and thermal-neutron-induced fission of 239Pu fission-product yields (FPY) are extrapolated to give predictions for the energy dependence of the n + 239Pu FPY for incident neutron energies from 0 to 16 MeV. After the inclusion of corrections associated with mass-symmetric fission, prompt-neutron emission, and multi-chance fission, model calculated FPY are compared to data and the ENDF/B-VII.1 evaluation. The ability of the model to reproduce the energy dependence of the ENDF/B-VII.1 evaluation suggests that plutonium fission mass distributions are not locked in near the fission barrier region, but are instead determined by the temperature and nuclear potential-energy surface at larger deformation.