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Lower bounds to energy eigenvalues in perturbation theory ground state, studying lower bounds to ground state energies of helium-like ions
Quantum theory of thermogalvanomagnetic phenomena in metals and semiconductors
We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.
The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MCPDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. Herein, the analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMCPDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.
In density functional theory, each self-consistent field (SCF) nonlinear step updates the discretized Kohn-Sham orbitals by solving a linear eigenvalue problem. The concept of pseudodiagonalization is to solve this linear eigenvalue problem approximately, and specifically utilizing a method involving a small number of Jacobi rotations that takes advantage of the good initial guess to the solution given by the approximation to the orbitals from the previous SCF iteration. The approximate solution to the linear eigenvalue problem can be very rapid, particularly for those steps near SCF convergence. Here, we adapt pseudodiagonalization to finite-temperature and metallic systems, where partially-occupied orbitals must be individually resolved with some accuracy. We apply pseudodiagonalization to the subspace eigenvalue problem that arises in Chebyshev-filtered subspace iteration. In tests on metallic and other systems for a range of temperatures, we show that pseudodiagonalization achieves similar rates of SCF convergence to exact diagonalization.
The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear–electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear–electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (H 2 O) 27 where all 54 protons are treated quantum mechanically. Furthermore, this study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.
Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.
Adsorption of n-nonane/1-hexanol (C9/C6OH) mixtures into the lamellar phase formed by a 50/50 w/w triethylene glycol mono-n-decyl ether (C10E3)/water system was studied using configurational-bias Monte Carlo simulations in the osmotic Gibbs ensemble. The interactions were described by the Shinoda–Devane–Klein coarse-grained force field. Prior simulations probing single-component adsorption indicated that C9 molecules preferentially load near the center of the bilayer increasing the bilayer thickness, whereas C6OH molecules are more likely to be found near the interface of the polar and non-polar moieties swelling the bilayer in the lateral dimension. Here, we extend this work to binary C9/C6OH adsorption to probe whether the difference in the spatial preferences may lead to a synergistic effect and enhanced loadings for the mixture. Comparing loading trends and the thermodynamics of binary adsorption to unary adsorption reveals that C9–C9 interactions lead to the largest enhancement, whereas C9–C6OH and C6OH–C6OH interactions are less favorable for this bilayer system. As a result, ideal adsorbed solution theory yields satisfactory predictions of the binary loading.
Gold and gold-silver alloys can be active and selective oxidation catalysts. Previous work has suggested that O 2 dissociation occurs at bimetallic step sites on gold-silver alloys, but the site responsible for the rest of the reaction steps has not been studied. As a first step in gaining insight into this issue, in this work we investigated the adsorption of oxygen and other oxidation intermediates on the (111) and (211) facets of gold-silver alloys using density functional theory. Oxygen and silver coverage effects were analyzed, and different model structures were compared. We also examined the energy barriers for the diffusion of atomic oxygen to gain insight into O migration and spillover. On (111) surfaces, O adsorption is much stronger at low O coverage (less than 0.22 ML), while on (211) surfaces O is strongly bound at both high and low O coverage. O diffusion across the step is faster than diffusion along the step. Ag stabilizes O, both when directly bound to it and when in an adjacent site. Ag also reduces repulsive O-O interactions at low O coverage. Our calculated reaction barriers for O-assisted CH 3 O dehydrogenation suggest that reaction is faster on steps than on terraces. Overall, our findings suggest that spillover of O from Ag-rich steps to Au-rich terraces does not occur, and that oxidation reactions on gold-silver alloys occurs on step sites. More specifically, oxidation likely occurs either on Ag-rich step sites or on Au-rich step sites that are adjacent to Ag-rich step sites.
In order to assess the role of a metal substrates on the thermal chemistry of adsorbed acetamidinate metalorganic compounds, we have studied the surface chemistry of copper(I)–N,N'-dimethylacetamidinate on Ni(110) using density functional theory and contrasted it with similar calculations we previously carried out on Cu(110). At low coverages, it was found that, in its most stable configuration, the molecular adsorption of copper(I)–N,N'-dimethylacetamidinate dimers occurs with the Cu atoms occupying surface hollow sites. In this work, the ligands reorient away from those metal centers, and the N atoms develop new direct bonds with surface Ni atoms. However, this configuration is not stable and decomposes by losing both ligands to the surface. In the final state, the two ligands bind via their N atoms to Ni sites one lattice space away from the sites where the Cu atoms remain, with their molecular planes perpendicular to that of the surface. This is in contrast with what happens in the case of adsorption on Cu(110), where the Cu atoms from the metalorganic complex still occupy hollow sites but where only one of the ligands breaks away and binds directly to the surface; the other remains on top of the two Cu ions. In terms of the energetics of adsorption and decomposition, the reactions on Ni(110) are much more exothermic than on Cu(110). Further analysis of the distribution of charge within the adsorbates shows a minor reduction of the Cu atoms of the dimer upon interaction with the surface; full reduction to metallic copper is complete only when both ligands have fully migrated to their new Ni surface sites.
Due to the large lattice mismatch between gold and nickel, gold–nickel surface alloys can form unique nonstoichiometric overlayer structures characterized by a moiré pattern and subsurface defects. For this work, we performed density functional theory (DFT) calculations to study the adsorption of molecular oxygen, atomic hydrogen, and atomic carbon on a gold–nickel(111) surface alloy with 0.46 monolayer gold randomly distributed in the surface layer. We observed six distinct adsorption structures for molecular oxygen characterized by intramolecular stretching frequencies of <700, 729, 795, 857, 929, and 1004 cm –1 , which describe well the experimentally observed high-resolution electron energy-loss spectra. Surface atomic hydrogen adsorption is associated with adsorbate–surface modes in the ∼1000 cm –1 range, while subsurface hydrogen can have features as low as ∼400 cm –1 . We observed a unique adsorption structure for atomic carbon inside the surface dislocation loop defect, which explains the experimentally observed low carbon-surface mode at ∼340 cm –1 . Our study sheds light on the unique adsorption properties of the gold–nickel surface alloys and helps with rationalizing vibrational frequency experimental studies for this system.
The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. Here, in this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.
Full potential energy curves, electronic configurations, spectroscopic parameters, dipole moments, and energetics of ground and excited electronic states of TaB and WB were studied using MRCI, MRCI+Q, CCSD(T), and DFT levels of theory.
Nuclear reaction data required for astrophysics and applications is incomplete, as not all nuclear reactions can be measured or reliably predicted. Neutron-induced reactions involving unstable targets are particularly challenging, but often critical for simulations. In response to this need, indirect approaches, such as the surrogate reaction method, have been developed. Nuclear theory is key to extract reliable cross sections from such indirect measurements. We describe ongoing efforts to expand the theoretical capabilities that enable surrogate reaction measurements. We focus on microscopic predictions for charged-particle inelastic scattering, uncertainty-quantified optical nucleon-nucleus models, and neural-network enhanced parameter inference.
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To create a community of scholars with a deep understanding of TDDFT and excited state methods, both their capabilities and limitations, and how they can be used to model the excited state properties and charge transfer in materials and molecules, we are planning the third iteration of a summer school and workshop focusing on theory and applications of TDDFT, Excited States, and Excited State Dynamics to be offered in the summer of 2023. The two iterations of the US-based school that we previously organized have been very successful with overwhelmingly positive feedback. There is a high level of engagement, enthusiasm, and active participation and networking amongst the students of the school and the scientists of the workshop.
Asymptotic formulas for elastic cylindrical shells and analysis of Kirchhoff-Love theory
Differential equations and their relationships to dynamic systems and control theory, with bibliographies