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In this contribution, we report on recent progress in coupled-cluster simulations of open-shell atomic nuclei using interactions consistently derived from chiral effective field theory. In particular, we compare different coupled-cluster approaches by computing binding energies and electric dipole polarizabilities in medium-mass calcium isotopes.
Hammett substituent constants (σ), which quantify the electronic effects of functional groups, are widely used for predicting the properties of organic compounds and investigating reaction mechanisms. While these values have been obtained for a wide range of closed-shell substituents, measurements of analogous values for open-shell substituents are rare due to challenges associated with their short lifetimes. Here, in this report, we developed a combined experimental and computational approach for quantifying the electronic properties of open-shell substituents based on changes in nitrile vibrational frequencies (ν(C≡N)). By coupling pulse radiolysis and time-resolved infrared spectroscopy (PR-TRIR), we measured ν(C≡N) IR bands of 30 para - and meta -substituted benzonitriles bearing C-, N-, and S-centered radicals. A linear scaling relationship was obtained between these experimental values and values obtained from DFT calculations. Using these computed values, two different Hammett constants, σ m , and σ p + , were determined for a series of C-, N-, O-, S-, Si-, and B-centered radicals. The differences between σm and σp+ values enable the separate evaluation of inductive and resonance effects in these open-shell substituents. The results suggest that there are three classes of radicals: one is electron withdrawing (σ m , σ p + > 0), one is electron donating (σm, σp+ < 0), and one is inductively withdrawing but resonance donating (σ m > 0, σ p + < 0). Our study represents a general approach to the analysis of the electronic properties of open-shell species and has potential applications in a wide range of molecular processes involving free radical intermediates.
Open-shell π-conjugated systems have emerged as promising molecular wires that can sustain unusually high low-bias conductance over tens of nanometers. However, predictive design rules remain limited because near-degeneracy and spin polarization give rise to correlated electronic states that are not reliably captured by standard density functional theory and Landauer transport descriptions. Here, we establish physically transparent design rules for long-range, weakly length-dependent charge transport based on the interplay between bond-length alternation and electron–electron interactions. Using a fully correlated transport framework that combines density matrix renormalization group calculations with nonequilibrium Green’s function embedding, we show that weak dimerization maintains spatially extended edge states, while moderate on-site interaction stabilizes open-shell character without excessively separating transport-relevant resonances. This balance yields zero-bias transmission that is largely insensitive to molecular length, providing a route to connect chemically tunable structure to correlated transport beyond mean-field descriptions.
A grand challenge in molecular electronics is the development of molecular materials that can facilitate efficient longrange charge transport. Research spanning more than two decades has been fueled by the prospects of creating a new generation of miniaturized electronic technologies based on molecules whose synthetic tunability offers tailored electronic properties and functions unattainable with conventional electronic materials. However, current design paradigms produce molecules that exhibit off-resonant transport under low bias, which limits the conductance of molecular materials to unsatisfactorily low levels several orders of magnitude below the conductance quantum 1 G 0 and often results in an exponential decay in conductance with length. Here, we demonstrate a chemically robust, air-stable, and highly tunable molecular wire platform comprised of open-shell donor−acceptor macromolecules that exhibit remarkably high conductance close to 1 G 0 over a length surpassing 20 nm under low bias, with no discernible decay with length. Single-molecule transport measurements and ab initio calculations show that the ultralong-range resonant transport arises from extended π-conjugation, a narrow bandgap, and diradical character, which synergistically enables excellent alignment of frontier molecular orbitals with the electrode Fermi energy. The implementation of this long-sought-after transport regime within molecular materials offers new opportunities for the integration of manifold properties within emerging nanoelectronic technologies.
Locating hydrides is crucial in organometallic chemistry but difficult to do accurately using X-ray diffraction. Electron diffraction has been proposed as a way to overcome this problem but has not been systematically compared to neutron diffraction and to quantum crystallography (Hirshfeld atom refinement, HAR) to test this hypothesis. Here, we present a comparative analysis of methods for a terminal cobalt hydride complex by comparing a single-crystal neutron diffraction reference structure to results from single-crystal X-ray diffraction with and without Hirshfeld atom refinement (HAR, NoSpherA2), density functional theory (DFT), and electron diffraction (3D-ED/MicroED) refined under kinematical and dynamical formalisms. Conventional X-ray diffraction gives lower precision than neutron diffraction as expected. Despite expected improvements, HAR gives systematic deviation from the neutron benchmark. Interestingly, optimized DFT equilibrium geometries are closer to the neutron value than the value from HAR. On the other hand, electron diffraction with a high-quality data set coupled with dynamical refinement localizes the hydride in difference maps and gives excellent agreement with the neutron data. Dynamical refinement is crucial, as kinematical refinement does not allow assignment of a hydride peak. This cross-modal comparison defines the conditions under which 3D-ED/MicroED delivers high-precision metal–hydride distances for this open-shell cobalt hydride.
We extend the spherical coupled-cluster ab initio method for open-shell nuclei where two nucleons are removed from a shell subclosure. Following the recent implementation of the two-particle-attached approach [Phys. Rev. C 110, 044306 (2024)], we focus on the two-particle-removed method. Using the equations-of-motion framework, we address both nuclear structure and dipole response functions by coupling coupled-cluster theory with the Lorentz integral transform technique. We perform calculations using chiral interactions, including three-nucleon forces, and estimate many-body uncertainties by comparing different coupled-cluster truncation schemes. Here, we validate our approach by studying ground-state energies, excited states, and electric dipole polarizabilities in the oxygen and calcium isotopic chains. For binding energies and selected low-lying excited states, we achieve an accuracy comparable to that of the established closed-shell coupled-cluster theory and generally agree with experiment. Finally, we underestimate experimental data for electric dipole polarizabilities, particularly in calcium isotopes.
The dynamics of reactive atoms at surfaces are centrally important to areas such as heterogeneous catalysis, corrosion, materials degradation in extreme environments, and plasma etching. Remarkably detailed understanding of dynamical processes at surfaces has been extracted from scattering molecules and inert atoms under well-defined conditions. However, traditional techniques for generating beams of reactive atoms often result in impure mixtures, broad energy distributions, and poorly defined contributions of metastable electronically excited atoms. In this perspective article, we review the state-of-the-art in reactive atom surface scattering with a focus on experiments performed under controlled conditions on well-defined surfaces. We highlight a new technique for controlled state-to-state scattering of polyelectronic atoms from surfaces, based on vacuum ultraviolet photolysis and state-selective ion imaging. The new capabilities provide an avenue for research into the underexplored area of excited state and spin selective chemical dynamics at surfaces.
The electronic structure of the gold nanoparticle-titanium dioxide (AuNP-TiO 2 ) heterojunction plays a critical role for charge transfer and recombination dynamics that underpin its photocatalytic function. However, building a representative model to capture the key physics remains a significant challenge. Here, we investigate the influence of the AuNP size and shape, as well as oxygen vacancy (V O ) defects at the anatase-phase TiO 2 (101) surface and the temperature of the heterojunction, on its interfacial electronic properties. Using density functional theory (DFT), we compare the closed-shell Au 20 and open-shell Au 19 clusters interfaced with pristine and V O defect TiO 2 surfaces. We find that the presence of a V O defect transforms pure TiO 2 from a p-type to an n-type semiconductor, reversing the interfacial band bending from downward to upward. For the heterosystem, density of states (DOS) analysis shows that V O minimally affects the open-shell Au 19 -TiO 2 system, but it significantly alters the closed-shell Au 20 -TiO 2 system, converting it from p-type to n-type at the Γ-point at 0 K. Furthermore, ab initio molecular dynamics (AIMD) simulations at 300 K reveal significant thermal fluctuations in AuNP positions relative to the TiO 2 surface. These fluctuations result in dynamic variations in the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in all systems studied: Au 19 NP-Pristine TiO 2 , Au 20 NP-Pristine TiO 2 , Au 19 NP-V O defect TiO 2 , and Au 20 NP-V O defect TiO 2 . Complementary Bader charge analysis performed at both 0 K and finite-temperature AIMD snapshots supports the emergence of an upward band bending and the formation of a Schottky barrier at the V O containing heterojunctions. Notably, we find that at finite temperature, an Au atom can dynamically passivate the V O , leading to a pronounced widening of the HOMO-LUMO gap in the AuNP-V O defect TiO 2 heterojunctions. Our computational findings underscore the pivotal role of the V O defect and thermal effects in modulating interfacial band alignment, electronic states, and HOMO-LUMO gaps, providing insights for designing Au-TiO 2 heterojunctions with tailored electronic properties.
In actinide chemistry, the formal number of open-shell 5f electrons, n open , is a well-defined quantity with an integer value. The effective 5f occupation, n f , additionally takes donation and back-donation into account, generally has a non-integer value, and has varying numerical definitions. The present study explores the important distinction between n f and n open in actinide chemistry with the example of PuO2, by using electronic structure methods with a relativistic Hamiltonian in combination with experimental Pu M 5 -edge high-energy-resolution X-ray absorption and emission spectroscopic data. The total donation to the metal in PuO 2 is between 3.1 and 2.4 electrons, depending on the type of calculation, most of which is to the Pu 6d and 5f shells. The donation into 5f is sensitive to the approximations in the electronic structure model but likely amounts to 1.6/0.8 electrons when the diffuse regions of the 5f shell are included/excluded. Valence band resonant inelastic X-ray scattering experiments demonstrate that Pu 5f electron density is present in the valence band; thus, there is a clear experimental signature of covalent bonding in PuO 2 . Pu M 5 -edge and M 3 -edge high-energy-resolution X-ray absorption near-edge structures for Pu 3+ and Pu 4+ in an aqueous solution are compared to PuO 2 , showing that Pu in PuO 2 has an nf closer to Pu 4+ (aq).
Solid-state 239 Pu NMR spectra of crystalline PuO 2 have been recorded over temperatures from 11 to 295 K with better than part per thousand resolution. These experiments represent the first independent detection of 239 Pu NMR in PuO 2 since the original report by Yasuoka and co-workers and extend the NMR observations to higher temperatures where recent theoretical explanations of the enigmatic magnetism and electronic structure of PuO 2 may be evaluated. The sensitivity achieved in these experiments was sufficient to measure the sinusoidal dependence of the NMR signal amplitude on the radiofrequency pulse length, which allows the determination of the nuclear g factor and magnetic moment of 239 Pu. These results demonstrate the use of NMR with an open-shell f element to explore subtle magnetic effects in plutonium materials of both technological and scientific significance.
We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn 2+ and the tetrahedral Mn(II)O 4 6– complex.
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.
To follow up on the unexpectedly good performance of several coupled-cluster models with approximate inclusion of 3-body clusters we performed a more complete assessment of the 3CC method for accurate computational thermochemistry in the standard HEAT framework. New spin-integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-ζ basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean absolute errors in cc-pVDZ {3CC, CCSDT, and CCSD(T)} electronic (per valence electron) and atomization energies relative to the CCSDTQ reference for the HEAT data set, were {24, 70, 122} μE h /e and {0.46, 2.00, 2.58} kJ/mol, respectively. The mean absolute errors in the complete-basis-set limit {3CC, CCSDT, and CCSD(T)} atomization energies relative to the HEAT model reference, were {0.52, 2.00, and 1.07} kJ/mol, The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post- CCSD(T) thermochemistry applications, as well as the preferred alternative to CCSDT in general.
A coherent vibrational wavepacket is launched and manipulated in the symmetric stretch (a1) mode of CBr 4 , by impulsive stimulated Raman scattering (ISRS) from nonresonant 400 nm laser pump pulses with various peak intensities on the order of tens of 10 12 W/cm 2 . Extreme ultraviolet (XUV) attosecond transient absorption spectroscopy (ATAS) records the wavepacket dynamics as temporal oscillations in XUV absorption energy at the bromine M 4,5 3d 3/2,5/2 edges around 70 eV. The results are augmented by nuclear timedependent Schrödinger equation simulations. Slopes of the (Br 3d 3/2,5/2 ) –1 10a 1 * core-excited state potential energy surface (PES) along the a 1 mode are calculated to be –9.4 eV/Å from restricted open-shell Kohn–Sham calculations. Using analytical relations derived for the small-displacement limit and the calculated slopes of the core-excited state PES, a deeper insight into the vibrational dynamics is obtained by retrieving the experimental excursion amplitude of the vibrational wavepacket and the amount of population transferred to the vibrational first-excited state as a function of pump-pulse peak intensity. Experimentally, the results show that XUV ATAS is capable of resolving oscillations in the XUV absorption energy on the order of a few to tens of meV with tens of femtosecond time precision. This corresponds to change in C–Br bond length on the order of 10 –4 to 10 –3 Å. The results and the analytic relationships offer a clear physical picture, on multiple levels of understanding, of how the pump-pulse peak intensity controls the vibrational dynamics launched by nonresonant ISRS in the small-displacement limit.
The COLUMBUS program system provides the tools for performing high-level multireference (MR) computations, including the multireference configuration interaction (MRCI) method and its multireference averaged quadratic coupled cluster (MR-AQCC) extension, allowing computations on a wide range of fascinating atomic and molecular systems, including the treatment of open-shells and complicated excited state phenomena. The inclusion of spin−orbit coupling (SOC) directly within the MRCI step enables the description of systems containing heavy elements, such as lanthanides and actinides, whose properties are strongly influenced by SOC. Analytic energy gradients and nonadiabatic couplings at the correlated MRCI level provide the foundation for a variety of dynamics studies, giving insight into ultrafast photochemistry. New and ongoing method developments in COLUMBUS include the computation of spin densities, improved descriptions of ionic states, enhancements to the AQCC method, and the porting of COLUMBUS to graphical processing units (GPUs). New external interfaces enable an enhanced description of electronic resonances and molecules in strong laser fields. This work highlights these new developments while providing a detailed account of the diverse applications of COLUMBUS in recent years.
The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.
Au nanoparticle (NP)/TiO 2 heterojunction is a representative system to study interfacial charge transfer in photocatalysis and photovoltaics, where suppressing recombination from TiO 2 to Au can enhance hot carrier extraction. We apply real-space constrained density functional theory (CDFT) with Marcus theory to quantify charge recombination time scales across Au/TiO 2 . This approach enables direct control and visualization of charge-separated states, aligning with site-specific probes like time-resolved X-ray photoelectron spectroscopy (trXPS). We find that the charge-separated state features a bipolaron, with recombination dominated by TiO 2 LUMO to Au HOMO transitions, primarily at interfacial Au sites. Marcus rate predictions are benchmarked with surface hopping methods, quantifying differences in time scales and computational efficiency. Lastly, we examine how the Au cluster size affects the free energy change (ΔG) and reorganization energy (λ), explaining trends in closed-shell systems and highlighting challenges for open-shell extrapolations. Overall, CDFT + Marcus theory provides efficient, mechanistically transparent interfacial charge transfer modeling, and we clearly defined its applicability and limitation.
The synthesis of molecules with strong coupling between electronic and nuclear spins represents an important challenge in molecular quantum information science. Here, we report the synthesis and characterization of the divalent lutetium metallocene complexes Lu(Cp Me 5 )(Cp iPr 5 ) (Cp Me 5 = pentamethylcyclopentadienyl; Cp iPr 5 = pentaisopropylcyclopentadienyl), Lu(Cp iPr 4 Et ) 2 (Cp iPr 4 Et = ethyltetraisopropylcyclopentadienyl), and Lu(Cp iPr 4 ) 2 (Cp iPr 4 = tetraisopropylcyclopentadienyl). The molecular structures of these complexes, as determined through singlecrystal X-ray diffraction, feature a common bent sandwich geometry, with average Cp–Lu–Cp angles ranging from 159.9° to 152.6°. Analysis of continuous-wave electron paramagnetic resonance (EPR) spectra for the complexes reveals nearly isotropic g tensors with only a slight deviation from that of a free electron. Moreover, an extremely large splitting of the eight-line spectra indicates the presence of strong hyperfine coupling, and simulations provide isotropic hyperfine coupling constants of A iso = 4.38, 4.30, and 4.17 GHz across the series, where the value of A iso is found to decrease as the Cp–Lu–Cp angle becomes more acute. Notably, these values are the largest yet observed for any lanthanide complex. Moreover, EPR and computational analysis show that the large values of A iso stem from large s-orbital character up to 41.2% in the corresponding singly occupied molecular orbitals. To our knowledge, this degree of s-character in a molecular orbital is the largest yet reported for an open-shell isolable complex. These results outline a general strategy toward the isolation of paramagnetic molecules with strong hyperfine coupling and highly isotropic doublet electronic ground states.