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At least 37 records · Page 2

Some Aspects of the Implementation of Double Group Symmetry and Electron Correlation in Molecular 4-Component Calculations

The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.

Dyall, Kenneth G.↗

Electronic structure of Li 1,2,3 +,0,– and nature of the bonding in Li 2,3 +,0,–

Abstract The current study of the small lithium molecules Li 2 +,0,− and Li 3 +,0,− focuses on the nature of the bonding in these molecules as well as their structures and energetics (bond energies, ionization energies, and electron affinities). Valence CASSCF (2s,2p) calculations incorporate nondynamical electron correlation in the calculations, while the corresponding multireference configuration interaction and coupled cluster calculations incorporate dynamical electron correlation. Treatment of nondynamical correlation is critical for properly describing the Li 2,3 +,0,− molecules as well as the Li − anion with dynamical correlation, in general, only fine‐tuning the predictions. All lithium molecules and ions are bound, with the Li 3 + and Li 2 + ions being the most strongly bound, followed by Li 3 − , Li 2 , Li 2 − and Li 3 . The minimum energy structures of Li 3 +,0,− are, respectively, an equilateral triangle, an isosceles triangle, and a linear structure. The results of SCGVB calculations are analyzed to obtain insights into the nature of the bonding in these molecules. An important finding of this work is that interstitial orbitals, a concept first put forward by McAdon and Goddard in 1985, play an essential role in the bonding of all lithium molecules considered here except for Li 2 . The interstitial orbitals found in the Li 3 +,0 molecules likely give rise to the non‐nuclear attractors/maxima observed in these molecules.

Chemistry↗

Pump and ionizing-probe dynamics in a simultaneous treatment of electronic and nuclear motion in LiH

The dissociative single ionization of the LiH molecule using a two-color UV-UV pump-probe scheme is simulated in ab initio calculations demonstrating how the dynamics initiated on intermediate Rydberg states of diatomic molecules can be imaged by such experiments. The theoretical treatment combines nuclear motion with highly correlated descriptions of electronic continua and bound electronic states. Nuclear dynamics on Rydberg states are only weakly reflected by changes in photoelectron energies ejected by time-delayed ionizing pulses if the Rydberg potential curves parallel those of the ion states being produced. However, coincidence measurements guided by knowledge of the photoionization amplitudes as a function of internuclear distance can still reveal intermediate-state dynamics in pump-probe experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. In conclusion, we compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantification of electron correlation for approximate quantum calculations

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

Chemistry↗

Nuclear charge radii of Na isotopes: Interplay of atomic and nuclear theory

The accuracy of atomic theory calculations limits the extraction of nuclear charge radii from isotope shift measurements of odd-proton nuclei. For Na isotopes, though precise spectroscopic measurements have existed for more than half a century, calculations by different methods offer a wide range of values. Here, we present accurate atomic calculations to reliably extract the Na charge radii. By combining experimental matter radii with nuclear coupled-cluster calculations based on nucleon-nucleon and three-nucleon forces, we constrain the parameters obtained from the atomic calculations. Furthermore, this study guides atomic theory and highlights the importance of using accurate atomic and nuclear computations in our understanding of the size of light nuclei.

20 ≤ A ≤ 38↗

Electron Correlation in 4-Component Relativistic Calculations

The full 4-component Dirac-Coulomb equation can nowadays be used in molecular calculations, The first step in solving this relativistic many-electron equation usually consists of solving the closed or open-shell Diarc-Fock equations. Like in non-relativistic calculations the outcome does not account for the effects of electron correlation. This can in principle be remedied by developing relativistic variants of electron correlation methods like Configuration Interaction or Coupled Cluster. In this talk the differences and similarities of such relativistic approaches as compared to non-relativistic methods will be reviewed. Results of Configuration Interaction calculations on the PtH molecule and on the MeF(sub 6, sup 2-) (Me= Co, Rh, Ir) complexes will be presented to give an impression of the kind of results that currently can be obtained.

Visscher, Luuk↗

The Generality of the GUGA MRCI Approach in COLUMBUS for Treating Complex Quantum Chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using isotope shift for testing nuclear theory: The case of nobelium isotopes

We calculate field isotope shifts for nobelium atoms using nuclear charge distributions which come from different nuclear models.We demonstrate that comparing calculated isotope shifts with experiment can serve as a testing ground for nuclear theories. It also provides a way of extracting parameters of nuclear charge distribution beyond nuclear root mean square (rms) radius, e.g., parameter of quadrupole deformation β. The measurements of at least two atomic transitions is needed to disentangle the contributions of the changes in deformation and nuclear rms radius into field isotopic shift. We argue that a previous interpretation of the isotope measurements in terms of δ < r 2 > between 252,254 No isotopes should be amended when nuclear deformation is taken into account. As a result, we calculate isotope shifts for other known isotopes and for hypothetically metastable isotope 286 No for which the predictions of nuclear models differ substantially.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optical telecommunications-band clock based on neutral titanium atoms

Here, we propose an optical clock based on ultranarrow transitions in neutral titanium, which exhibit small blackbody radiation and quadratic Zeeman shifts and have wavelengths in the S-, C-, and L-telecommunications fiber bands, allowing for integration with robust laser technology. We calculate relevant properties using a high-precision relativistic hybrid method that combines configuration interaction and coupled-cluster approaches. To identify magic wavelengths, we have completed the largest-to-date direct dynamical polarizability calculations. Finally, we identify challenges that arise from magnetic dipole-dipole interactions and describe an approach to overcome them. A telecommunications-band atomic frequency standard will aid the deployment of optical clock networks and clock comparisons over long distances.

74 ATOMIC AND MOLECULAR PHYSICS↗

Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the standard model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden 2 S 1/2 → 2 F 7/2 octupole transition of trapped 168,170, 172, 174, 176 Yb ions. When combined with previous measurements in Yb + and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240σ. Furthermore, the trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with 4.3σ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Relativistic and correlation effects in the photoionization dynamics of oganesson ( Z = 118): Spin-orbit-interaction-activated interchannel coupling effects

High-Z atoms are excellent laboratories to study the combination of relativistic and many-electron correlation effects in electronic structure and dynamics. In the present work, the relativistic-random-phase approximation at different levels of truncation is employed to explore the final-state correlation effects in the photoelectron dynamics of the heaviest known element in the Periodic Table: oganesson (Og) with Z = 118. Here, the focus of this work is to illustrate the relativistic effects resulting from coupling different photoionization channels arising from spin-orbit split subshells, termed the spin-orbit-interaction-activated interchannel coupling effect. Comparison with the photoelectron dynamics of Rn on a qualitative level is also carried out, since Og is a homologue of Rn. The photoelectron dynamics of 7p, 7s, and 6d subshells are investigated and differences between Og and Rn, due to enhanced relativistic effects, are investigated.

74 ATOMIC AND MOLECULAR PHYSICS↗

Oscillate and renormalize: Fast phonons reshape the Kondo effect in flat-band systems

Here, we examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency 𝜔 0 ≪ 𝑈/2, the onsite Coulomb scale 𝑈/2), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong-coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling 𝛼* when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast (𝜔 0 ≳ 𝑈/2), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively 𝑈 eff due to phonon-mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

Anderson impurity model↗

Accurate ab initio calculations which demonstrate a 3Pi(u) ground state for Al2

The computational requirements for accurately describing the spectroscopic constants for all three candidates for the ground state of Al2 are determined. Full CI(FCI) calculations are used to calibrate approximate methods of including the electron correlation. CASSCF/MRCI calculations which accurately reproduce the FCI results in the valence DZ + 2d Gaussian basis are carried to chemical accuracy by using extensive one-particle basis sets. The effect of 2s and 2p correlation and relativistic effects are considered as well as the valence 3s and 3p correlation. Several excited states are also considered. It is shown that the computed vibrational frequency of the (2) 3Pi(g) state and the Franck-Condon factors for the (1) 3Pi(u) - (2) 3Pi(g) transition are consistent with the spectrum obtained by Douglas et al. (1983) and Abe and Kolb (1983). It is therefore concluded that the ground state is 3Pi(u).

Bauschlicher, Charles W., Jr.↗

Energetics of the protonation of CO - Implications for the observation of HOC(+) in dense interstellar clouds

A number of molecular species on the H3CO(+) energy hypersurface is examined. Ab initio molecular orbital theory is used to determine the structures and relative energetics of the two isomers of HCO(+) and HOC(+) together with the affinity of CO for protonation at either end. The proton affinities of H2 and H2CO are also examined. The calculations are performed using large basis sets and include the effects of electron correlation. The calculated vibrational frequencies are used to correct for zero point energy differences. The results show that the proton affinities of H2 and CO to form HOC(+) are within 1 kcal of each other. The calculations demonstrate that there is no thermodynamic driving force to form HOC(+) in collisions of H3(+) with CO, and that the formation of HCO(+) in such collisions is very exoergic. A plausible mechanism is suggested to explain the differences observed between the laboratory and the interstellar medium.

Dixon, D.↗

Angle-resolved nonresonant two-photon single ionization of argon using 9.3-eV photons produced via high-order harmonic generation

Here we present an experimental study on the photoionization dynamics of nonresonant one-color two-photon single valence ionization of neutral argon atoms. Using 9.3-eV photons produced via high harmonic generation and a three-dimensional momentum imaging spectrometer, we detect the photoelectrons and ions produced from nonresonant two-photon ionization in coincidence. Photoionization from the $3p$ orbital produces a photoelectron scattering wave function with $p$- and $f$-partial-wave components, which interfere and result in a photoelectron angular distribution with peak amplitude perpendicular to the vacuum ultraviolet polarization. The comparison between the present results and the two previous sets of theoretical calculations [Phys. Rev. A 44, 324 (1991), and J. Phys. B: At. Mol. Phys. 16, 2737 (1983)] indicates that electron-electron correlation contributes appreciably to the two-photon ionization dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗