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Carbon diffusion in molten uranium: an ab initio molecular dynamics study
In this work we used ab initio molecular dynamics (AIMD) within the framework of density functional theory (DFT) and the projector-augmented wave (PAW) method to study carbon diffusion in liquid uranium at temperatures above 1600 K. The electronic interactions of carbon and uranium were described using the local density approximation (LDA). The self-diffusion of uranium based on this approach is compared with literature computational and experimental results for liquid uranium. The temperature dependence of carbon and uranium diffusion in the melt was evaluated by fitting the resulting diffusion coefficients to an Arrhenius relationship. We found that the LDA calculated activation energy for carbon was nearly twice that of uranium: 0.55±0.03 eV for carbon compared to 0.32±0.04 eV for uranium. Structural analysis of the liquid uranium-carbon system is also discussed.
Emergent Sp(3,$\mathbb{R}$) Dynamical Symmetry in the Nuclear Many-Body System from an Ab Initio Description
Ab initio nuclear theory provides not only a microscopic framework for quantitative description of the nuclear many-body system, but also a foundation for deeper understanding of emergent collective correlations. In this work, a symplectic Sp(3, $\mathbb{R}$) $\supset$ U(3) dynamical symmetry is identified in ab initio predictions, from a no-core configuration interaction approach, and found to provide a qualitative understanding of the spectrum of 7 Be. Low-lying states form an Elliott SU(3) spectrum, while an Sp(3, $\mathbb{R}$) excitation gives rise to an excited rotational band with strong quadrupole connections to the ground state band.
Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.
Ab initio electronic structure of quasi-two-dimensional materials: A “native” Gaussian–plane wave approach
Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is “native” to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory — density functional theory, GW approximation and Bethe-Salpeter equation — are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.
An analysis of hydrated proton diffusion in ab initio molecular dynamics
A detailed understanding of the inherently multiscale proton transport process raises a number of scientifically challenging questions. For example, there remain many (partially addressed) questions on the molecular mechanism for long-range proton migration and the potential for the formation of long-lived traps giving rise to burst-and-rest proton dynamics. Using results from a sizeable collection of ab initio molecular dynamics (AIMD) simulations (totaling ∼2.7 ns) with various density functional approximations (Becke-Lee-Yang-Parr (BLYP), BLYP–D3, Hamprecht-Cohen-Tozer-Handy, B3LYP) and temperatures (300–330 K), equilibrium and dynamical properties of one excess proton and 128 water molecules are studied. Two features in particular (concerted hops and weak hydrogen-bond donors) are investigated to identify modes in the system that are strongly correlated with the onset of periods of burst-and-rest dynamics. The question of concerted hops seeks to identify those time scales over which long-range proton transport can be classified as a series of sequential water hopping events or as a near-simultaneous concerted process along compressed water wires. The coupling of the observed burst-and-rest dynamics with motions of a fourth neighboring water molecule (a weak hydrogen-bond donor) solvating the protonated water molecule is also investigated. The presence (absence) of hydrogen bonds involving this fourth water molecule before and after successful proton hopping events is found to be strongly correlated with periods of burst (rest) dynamics (and consistent with pre-solvation concepts). By analyzing several realizations of the AIMD trajectories on the 100-ps time scale, convergence of statistics can be assessed. For instance, it was observed that the probability for a fourth water molecule to approach the hydronium, if not already proximal at the beginning of the lifetime of the hydronium, is very low, indicative of the formation of stable void regions. Furthermore, the correlations of the neighboring water atoms are identified as the fourth water approaches the hydronium. Finally, the temperature effects on structural and dynamical properties are studied.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Communication: Towards ab initio self-energy embedding theory in quantum chemistry
The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green’s function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.
Ab initio pressure-dependent reaction kinetics of methyl propanoate radicals
The unimolecular dissociation and isomerization kinetics of the three methyl propanoate (MP) radicals, CH 3 CH 2 C(=O)O$\dot{C}$H 2 (MP-m), CH 3 $\dot{C}$HC(=O)OCH 3 (MP-α), and $\dot{C}$H 2 CH 2 C(=O)OCH 3 (MP-β), are theoretically investigated using high-level ab initio methods and the Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Stationary-point energies are obtained using the coupled cluster singles and doubles with perturbative triples correction (CCSD(T)), multi-reference singles and doubles configuration interaction (MRSDCI) with the Davidson-Silver (DS) correction, and multi-reference averaged coupled pair functional (MRACPF2) theories. The isomerization barriers between the three radicals are predicted to be generally lower than the corresponding bond dissociation channels, leading to a strongly coupled reaction system in subsequent kinetics studies. The phenomenological temperature- and pressure-dependent rate coefficients are computed using the RRKM/ME theory over a temperature range of 500 to 2000 K and at a pressure range of 0.01 atm to the high-pressure limit, which are then fitted to modified Arrhenius expressions. The β-scission rate coefficients of MP-α to CH 3 CHC(=O) and CH 3 $\dot{O}$ are predicted to be the smallest because of its highest activation energy among all studied unimolecular reactions channels. Analysis of branching fractions shows that both MP-m and MP-α radicals mainly decompose to the bimolecular products CH 3 CH 2 $\dot{C}$(=O) and H 2 CO, whereas the MP-β radical primarily decomposes via cleavage of a C–C bond to form C 2 H 4 and CH 3 O$\dot{C}$(=O). The isomerization channels dominate at low temperatures, the branching fractions of which decrease with increasing temperature and become very minor at about 2000 K. Our accurate rate coefficients and branching fractions help to illuminate the unique combustion properties of MP.
Ab initio molecular dynamics simulation of Nd3+ incorporation in calcite
Trivalent rare-earth elements (REEs) readily incorporate in Ca-bearing minerals such as calcite (CaCO3), a phenomenon with important implications for the use of REEs as biogeochemical tracers as well as for environmental remediation. Despite substantial efforts, determining the incorporation modes of trivalent REEs in calcite has remained challenging due to their presence in multiple coordination environments. This is particularly problematic for the interpretation of extended X-ray absorption fine structure (EXAFS) spectroscopy. In this work, ab initio molecular dynamics (AIMD) simulations of Nd3+ incorporated in calcite were performed to resolve its incorporation modes. Nd3+ and Ca2+ have very similar ionic radii but the additional positive charge requires a charge compensation scheme (CCS). Five CCSs were considered in AIMD simulations, and the resulting atomic trajectories were then used to compute EXAFS spectra for direct fitting to a published experimental spectrum. The results of the fits indicated that Nd3+ incorporates at the Ca2+ site in calcite in a mixture of six- and seven-fold coordination environments and through three main incorporation modes: associated with a protonated nearest-neighbor Ca2+ vacancy, incorporated as NdOH2+, and charge compensated by a remote species (on the spatial scale probed by EXAFS). The incorporation of Nd3+ in calcite via multiple modes was consistent with previous work, but the AIMD-EXAFS approach allowed for resolving the nature, proportion, and structure of the different coordination environments.
The interaction of reactants, intermediates and products with Cu ions in Cu-SSZ-13 NH3 SCR catalysts: An energetic and ab initio X-ray absorption modeling study
Copper-exchanged SSZ-13 (Cu-SSZ-13) provides excellent catalytic activity and hydrothermal stability in the selective catalytic reduction (SCR) of NOx by using NH3 as a reductant. In this contribution, we compare the most likely positions for Cu with a single charge compensating Al atom (ZCu), including the effect of the adsorption of reactants, intermediates and products of a NH3 SCR reaction by using first-principles calculations based on density functional theory. We find that the 6-membered ring (6MR) site is the most energetically favorable while the 8-membered ring (8MR) sites are less favorable with energy differences about 0.5 eV with respect to the 6MR site. Upon molecular adsorption, the energy differences between Cu in the 8MR and 6MR sites decreases and almost disappears, which means that the thermodynamic stability of ZCu with molecularly adsorbed species is nearly identical for Cu in different sites. Considering more complicated scenarios of NO (or CO) adsorption, we find that the co-adsorption of 2 NO (or 2 CO) molecules weakens their interaction with Cu, as well as their co-adsorption with OH and H2O. The X-ray absorption near edge structure (XANES) of Cu in Cu-SSZ-13 under different conditions was also modeled from first principles. We find that the pre-edge feature in the K-edge XANES of Cu in clean Cu-SSZ-13 with Cu in a 8MR site is induced by a 1s to 4s transition while there is no pre-edge peak when Cu is in a 6MR site. Molecular adsorption onto Cu in a 6MR or a 8MR site results in the same K-edge XANES. When NO is adsorbed onto Cu in SSZ-13, we find that the origin of the small pre-edge peak in the K-edge XANES lies in a 1s to 3d electron transition. On the other hand, when CO or N2 is adsorbed onto an isolated Cu atom in SSZ-13, a transition from the 1s state to the hybridized state of 3d and 4p results in a pre-edge peak in the K-edge of the XANES spectrum. It is also found that the edge position and intensity of the maximum peak of Cu K-edge XANES depend on the Cu locations and the adsorbed molecules. By studying the Cu K-edge XANES of ZCu with adsorption of species of different oxidizing power, we conclude that a higher oxidation state of Cu will result in a higher energy edge position in the Cu K-edge XANES. These results are expected to greatly aid our understanding of Cu-SSZ-13 SCR catalysts. This work was supported by institutional funds provided to JSM from the Voiland School of Chemical Engineering and Bioengineering. Financial support was also provided by the National Science Foundation GOALI program under contract Nos. CBET-1258717, CBET-1258715 and CBET-1258690. We thank Prof. Fabio Ribeiro, Mr. Atish Parekh, Prof. W. F. Schneider, Mr. Christopher Paolucci, Mr. Trunjoyo Anggara and Prof. Jeff Miller for stimulating discussions on the modeling of the XANES spectrum and Ms. Alyssa Hensley for her comments on the manuscript. J.Sz. acknowledges the financial support of this work by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program. A portion of the computer time for the computational work was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at PNNL. PNNL is a multi-program national laboratory operated for the US DOE by Battelle.
AXISYMMETRIC AB INITIO CORE-COLLAPSE SUPERNOVA SIMULATIONS OF 12-25 M{sub Sun} STARS
We present an overview of four ab initio axisymmetric core-collapse supernova simulations employing detailed spectral neutrino transport computed with our CHIMERA code and initiated from Woosley and Heger progenitors of mass 12, 15, 20, and 25 M{sub Sun }. All four models exhibit shock revival over {approx}200 ms (leading to the possibility of explosion), driven by neutrino energy deposition. Hydrodynamic instabilities that impart substantial asymmetries to the shock aid these revivals, with convection appearing first in the 12 M{sub Sun} model and the standing accretion shock instability appearing first in the 25 M{sub Sun} model. Three of the models have developed pronounced prolate morphologies (the 20 M{sub Sun} model has remained approximately spherical). By 500 ms after bounce the mean shock radii in all four models exceed 3000 km and the diagnostic explosion energies are 0.33, 0.66, 0.65, and 0.70 Bethe (B = 10{sup 51} erg) for the 12, 15, 20, and 25 M{sub Sun} models, respectively, and are increasing. The three least massive of our models are already sufficiently energetic to completely unbind the envelopes of their progenitors (i.e., to explode), as evidenced by our best estimate of their explosion energies, which first become positive at 320, 380, and 440 ms after bounce. By 850 ms the 12 M{sub Sun} diagnostic explosion energy has saturated at 0.38 B, and our estimate for the final kinetic energy of the ejecta is {approx}0.3 B, which is comparable to observations for lower mass progenitors.
Ab Initio Reaction Kinetics of CH 3 O$\dot{C}$(=O) and $\dot{C}$H 2 OC(=O)H Radicals
The dissociation and isomerization kinetics of the methyl ester combustion intermediates methoxycarbonyl radical (CH3O$\dot{C}$(=O)) and (formyloxy)methyl radical ($\dot{C}$H2OC(=O)H) are investigated theoretically using high-level ab initio methods and Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Geometries obtained at the hybrid density functional theory (DFT) and coupled cluster singles and doubles with perturbative triples correction (CCSD(T)) levels of theory are found to be similar. We employ high-level ab initio wave function methods to refine the potential energy surface: CCSD(T), multireference singles and doubles configuration interaction (MRSDCI) with the Davidson–Silver (DS) correction, and multireference averaged coupled-pair functional (MRACPF2) theory. MRSDCI+DS and MRACPF2 capture the multiconfigurational character of transition states (TSs) and predict lower barrier heights than CCSD(T). The temperature- and pressure-dependent rate coefficients are computed using RRKM/ME theory in the temperature range 300–2500 K and a pressure range of 0.01 atm to the high-pressure limit, which are then fitted to modified Arrhenius expressions. Dissociation of CH3O$\dot{C}$(=O) to $\dot{C}$H3 and CO2 is predicted to be much faster than dissociating to CH3$\dot{O}$ and CO, consistent with its greater exothermicity. Isomerization between CH3O$\dot{C}$(=O) and $\dot{C}$H2OC(=O)H is predicted to be the slowest among the studied reactions and rarely happens even at high temperature and high pressure, suggesting the decomposition pathways of the two radicals are not strongly coupled. The predicted rate coefficients and branching fractions at finite pressures differ significantly from the corresponding high-pressure-limit results, especially at relatively high temperatures. Finally, because it is one of the most important CH3$\dot{O}$ removal mechanisms under atmospheric conditions, the reaction kinetics of CH3$\dot{O}$ + CO was also studied along the PES of CH3O$\dot{C}$(=O); the resulting kinetics predictions are in remarkable agreement with experiments.
Communication: GAIMS—Generalized Ab Initio Multiple Spawning for both internal conversion and intersystem crossing processes
Full multiple spawning is a formally exact method to describe the excited-state dynamics of molecular systems beyond the Born-Oppenheimer approximation. However, it has been limited until now to the description of radiationless transitions taking place between electronic states with the same spin multiplicity. This Communication presents a generalization of the full and ab initio multiple spawning methods to both internal conversion (mediated by nonadiabatic coupling terms) and intersystem crossing events (triggered by spin-orbit coupling matrix elements) based on a spin-diabatic representation. The results of two numerical applications, a model system and the deactivation of thioformaldehyde, validate the presented formalism and its implementation.
Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-state hadron observables using a nonperturbative truncation of QCD's Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.
Which Ab Initio Wave Function Methods Are Adequate for Quantitative Calculations of the Energies of Biradicals? The Performance of Coupled-Cluster and Multi-Reference Methods Along a Single-Bond Dissociation Coordinate
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Effects of boron-nitride substrates on Stone-Wales defect formation in graphene: An ab initio molecular dynamics study
Ab initio molecular dynamics simulations are performed to investigate the effects of a boron nitride (BN) substrate on Stone-Wales (SW) defect formation and recovery in graphene. It is found that SW defects can be created by an off-plane recoil atom that interacts with the BN substrate. A mechanism with complete bond breakage for formation of SW defects in suspended graphene is also revealed for recoils at large displacement angles. In addition, further irradiation can result in recovery of the SW defects through a bond rotation mechanism in both graphene and graphene/BN, and the substrate has little effect on the recovery process. This study indicates that the BN substrate enhances the irradiation resistance of graphene.
Toward spectroscopically accurate global ab initio potential energy surface for the acetylene-vinylidene isomerization
A new full-dimensional global potential energy surface (PES) for the acetylene-vinylidene isomerization on the ground (S{sub 0}) electronic state has been constructed by fitting ∼37 000 high-level ab initio points using the permutation invariant polynomial-neural network method with a root mean square error of 9.54 cm{sup −1}. The geometries and harmonic vibrational frequencies of acetylene, vinylidene, and all other stationary points (two distinct transition states and one secondary minimum in between) have been determined on this PES. Furthermore, acetylene vibrational energy levels have been calculated using the Lanczos algorithm with an exact (J = 0) Hamiltonian. The vibrational energies up to 12 700 cm{sup −1} above the zero-point energy are in excellent agreement with the experimentally derived effective Hamiltonians, suggesting that the PES is approaching spectroscopic accuracy. In addition, analyses of the wavefunctions confirm the experimentally observed emergence of the local bending and counter-rotational modes in the highly excited bending vibrational states. The reproduction of the experimentally derived effective Hamiltonians for highly excited bending states signals the coming of age for the ab initio based PES, which can now be trusted for studying the isomerization reaction.