Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings.

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

High-level ab initio evidence of bipyramidal Cu5 clusters as fluxional Jahn-Teller molecules.

The front cover artwork is provided by María Pilar de Lara-Castells, Head of the AbinitFot Group at IFF-CSIC (Madrid), Coordinator of the National Project "COSYES", and Chair of the COST Action CA21101 "COSY", and Alexander O. Mitrushchenkov from the Université Paris-Est. The image shows the connection between the Jahn-Teller effect featured by bypiramidal Cu5 clusters and the property of fluxionality. Cover design by Katarzyna Krupka. Read the full text of the Research Article at 10.1002/cphc.202300317.

High-level ab initio evidence of bipyramidal Cu5 clusters as fluxional Jahn-Teller molecules.

Novel highly selective synthesis techniques have enable the production of atomically precise monodisperse metal clusters (AMCs) of subnanometer size. These AMCs exhibit 'molecule-like' structures that have distinct physical and chemical properties, significantly different from those of nanoparticles and bulk material. In this work, we study copper pentamer Cu5 clusters as model AMCs by applying both density functional theory (DFT) and high-level (wave-function-based) ab initio methods, including those which are capable of accounting for the multi-state multi-reference character of the wavefunction at the conical intersection (CI) between different electronic states and augmenting the electronic basis set till achieving well-converged energy values and structures. After assessing the accuracy of a high-level multi-multireference ab initio protocol for the well-known Cu3 case, we apply it to demonstrate that bypiramidal Cu5 clusters are distorted Jahn-Teller (JT) molecules. The method is further used to evaluate the accuracy of single-reference approaches, finding that the coupled cluster singles and doubles and perturbative triples CCSD(T) method delivers the results closer to our ab initio predictions and that dispersion-corrected DFT can outperform the CCSD method. Finally, we discuss how JT effects and, more generally, conical intersections, are intimately connected to the fluxionality of AMCs, giving them a 'floppy' character that ultimately facilitates their interaction with environmental molecules and thus enhances their functioning as catalysts.

Stability and Reversible Oxidation of Sub-Nanometric Cu5 Metal Clusters: Integrated Experimental Study and Theoretical Modeling.

Sub-nanometer metal clusters have special physical and chemical properties, significantly different from those of nanoparticles. However, there is a major concern about their thermal stability and susceptibility to oxidation. In situ X-ray Absorption spectroscopy and Near Ambient Pressure X-ray Photoelectron spectroscopy results reveal that supported Cu5 clusters are resistant to irreversible oxidation at least up to 773 K, even in the presence of 0.15 mbar of oxygen. These experimental findings can be formally described by a theoretical model which combines dispersion-corrected DFT and first principles thermochemistry revealing that most of the adsorbed O2 molecules are transformed into superoxo and peroxo species by an interplay of collective charge transfer within the network of Cu atoms and large amplitude "breathing" motions. A chemical phase diagram for Cu oxidation states of the Cu5 -oxygen system is presented, clearly different from the already known bulk and nano-structured chemistry of Cu.

Mini Review: Quantum Confinement of Atomic and Molecular Clusters in Carbon Nanotubes.

We overview our recent developments on a computational approach addressing quantum confinement of light atomic and molecular clusters (made of atomic helium and molecular hydrogen) in carbon nanotubes. We outline a multi-scale first-principles approach, based on density functional theory (DFT)-based symmetry-adapted perturbation theory, allowing an accurate characterization of the dispersion-dominated particle-nanotube interaction. Next, we describe a wave-function-based method, allowing rigorous fully coupled quantum calculations of the pseudo-nuclear bound states. The approach is illustrated by showing the transition from molecular aggregation to quasi-one-dimensional condensed matter systems of molecular deuterium and hydrogen as well as atomic 4He, as case studies. Finally, we present a perspective on future-oriented mixed approaches combining, e.g., orbital-free helium density functional theory (He-DFT), machine-learning parameterizations, with wave-function-based descriptions.

Nonadiabatic Effects in the Molecular Oxidation of Subnanometric Cu5 Clusters.

The electronic structure of subnanometric clusters, far off the bulk regime, is still dominated by molecular characteristics. The spatial arrangement of the notoriously undercoordinated metal atoms is strongly coupled to the electronic properties of the system, which makes this class of materials particularly interesting for applications including luminescence, sensing, bioimaging, theranostics, energy conversion, catalysis, and photocatalysis. Opposing a common rule of thumb that assumes an increasing chemical reactivity with smaller cluster size, Cu5 clusters have proven to be exceptionally resistant to irreversible oxidation, i.e., the dissociative chemisorption of molecular oxygen. Besides providing reasons for this behavior in the case of heavy loading with molecular oxygen, we investigate the competition between physisorption and molecular chemisorption from the perspective of nonadiabatic effects. Landau-Zener theory is applied to the Cu5(O2)3 complex to estimate the probability for a switching between the electronic states correlating the neutral O2 + Cu5(O2)2 and the ionic O2- + (Cu5(O2)2)+ fragments in a diabatic representation. Our work demonstrates the involvement of strong nonadiabatic effects in the associated charge transfer process, which might be a common motive in reactions involving subnanometric metal structures.

On the Accuracy of Mean-Field Spin-Orbit Operators for 3d Transition-Metal Systems.

We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2.

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement. The goal is to address Fermi-Dirac and Bose-Einstein nuclear spin statistics on an equal footing and to deliver excited states with a similar accuracy to that of the ground state, implementing ab initio-derived potential models as well. The method is applied to clusters of up to four (three) 4He atoms and para-H2 molecules (3He atoms) inside a single-walled (1 nm diameter) carbon nanotube. Due to spin symmetry effects, the bound states energy landscape as a function of the angular momentum around the tube axis becomes much more complex and rich as the number of 3He atoms increase compared to the spinless 4He and para-H2 counterparts. Four bosonic 4He and para-H2 particles form pyramidal-like structures which are more compact as the particle mass and the strength of the inter-particle interaction increases. They feature stabilization of the collective rotational motion as bosonic quantum rings bearing persistent rotational motion and superfluid flow. Our results are brought together with two key experimental findings from the group of Jan-Peter Toennies: (1) the congestion of spectral profiles in doped 3He droplets as opposed to the case of 4He droplets (S. Gebenev, J. P. Toennies and A. F. Vilesov, Science, 1998, 279, 2083); (2) the onset of microscopic superfluidity in small doped clusters of para-H2 molecules (S. Grebenev, B. G. Sartakov, J. P. Toennies and A. F. Vilesov, Science, 2000, 289, 1532), but at the reduced dimensionality offered by the confinement inside carbon nanotubes.

From Molecular Aggregation to a One-Dimensional Quantum Crystal of Deuterium Inside a Carbon Nanotube of 1 nm Diameter.

The quantum motion of clusters of up to four deuterium molecules under confinement in a single-wall (1 nm diameter) carbon nanotube is investigated by applying a highly accurate full quantum treatment of the most relevant nuclear degrees of freedom and an ab initio-derived potential model of the underlying dispersion-dominated intermolecular interactions. The wave functions and energies are calculated using an ad hoc-developed discrete variable representation (DVR) numerical approach in internal coordinates, with the space grid approaching a few billion grid points. We unambiguously demonstrate the formation of a solid-like pyramidal one-dimensional chain structure of molecules under the cylindrical nanotube confinement. The onset of solid-like packing is explained by analyzing the potential minima landscape. The stabilization of collective rotational motion through "rigid rotations" of four deuterium molecules provides conclusive evidence for the onset of a quantum solid-like behavior resembling that of quantum rings featuring persistent current (charged particles) or persistent flow (neutral particles).

The Molpro quantum chemistry package.

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

On the Stability of Cu5 Catalysts in Air Using Multireference Perturbation Theory.

An ab initio study of the interaction of O2, the most abundant radical and oxidant species in the atmosphere, with a Cu5 cluster, a new generation atomic metal catalyst, is presented. The open-shell nature of the reactant species is properly accounted for by using the multireference perturbation theory, allowing the experimentally confirmed resistivity of Cu5 clusters toward oxidation to be investigated. Approximate reaction pathways for the transition from physisorption to chemisorption are calculated for the interaction of O2 with quasi-iso-energetic trapezoidal planar and trigonal bipyramidal structures. Within the multireference approach, the transition barrier for O2 activation can be interpreted as an avoided crossing between adiabatic states (neutral and ionic), which provides new insights into the charge-transfer process and gives better estimates for this hard to localize and therefore often neglected first intermediate state. For Cu5 arranged in a bipyramidal structure, the O-O bond cleavage is confirmed as the rate-determining step. However, for planar Cu5, the high energy barrier for O2 activation, related to a very pronounced avoided crossing when going from physisorption to chemisorption, determines the reactivity in this case.

Spectroscopy of a rotating hydrogen molecule in carbon nanotubes.

A first-principles study of the spectroscopy of a single hydrogen molecule rotating inside and outside of carbon nanotubes is presented. Density functional theory (DFT)-based symmetry-adapted perturbation theory (SAPT) is applied to analyze the influence of the rotation in the dispersionless and dispersion energy contributions to the adsorbate-nanotube interaction. A potential model for the H2-nanotube interaction is proposed and applied to derive the molecular energy levels of the rotating hydrogen molecule. The SAPT-based analysis shows that a subtle balance between the dispersionless and dispersion contributions is key in determining the angular dependence of the H2-nanotube interaction, which is strongly influenced by the diameter of the carbon nanotubes. As a consequence, the structure of molecular energy levels is very different in wide and narrow nanotubes with the diameter above and below 1 nanometer, respectively. Strong anisotropy effects lead to a rather constrained rotation of molecular hydrogen inside narrow nanotubes.

Ab initio design of light absorption through silver atomic cluster decoration of TiO2.

A first-principles study of the stability and optical response of subnanometer silver clusters Agn (n ≤ 5) on a TiO2(110) surface is presented. First, the adequacy of the vdW-corrected DFT-D3 approach is assessed using the domain-based pair natural orbital correlation DLPNO-CCSD(T) calculations along with the Symmetry-Adapted Perturbation Theory [SAPT(DFT)] applied to a cluster model. Next, using the DFT-D3 treatment with a periodic slab model, we analyze the interaction energies of the atomic silver clusters with the TiO2(110) surface. Finally, the hybrid HSE06 functional and a reduced density matrix treatment are applied to obtain the projected electronic density of states and photo-absorption spectra of the TiO2(110) surface, with and without adsorbed silver clusters. Our results show the stability of the supported clusters, the enhanced light absorbance intensity of the material upon their deposition, and the appearance of intense secondary broad peaks in the near-infrared and the visible regions of the spectrum, with positions depending on the size and shape of the supported clusters. The secondary peaks arise from the photo-induced transfer of electrons from intra-band valence 5s orbitals of the noble-metal cluster to 3d Ti band states of the supporting material.

Quantum confinement of molecular deuterium clusters in carbon nanotubes: ab initio evidence for hexagonal close packing.

An ab initio study of quantum confinement of deuterium clusters in carbon nanotubes is presented. First, density functional theory (DFT)-based symmetry-adapted perturbation theory is used to derive parameters for a pairwise potential model describing the adsorbate-nanotube interaction. Next, we analyze the quantum nuclear motion of N D2 molecules (N < 4) confined in carbon nanotubes using a highly accurate adsorbate-wave-function-based approach, and compare it with the motion of molecular hydrogen. We further apply an embedding approach and study zero-point energy effects on larger hexagonal and heptagonal structures of 7-8 D2 molecules. Our results show a preference for crystalline hexagonal close packing hcp of D2 molecules inside carbon nanotubes even at the cost of a reduced volumetric density within the cylindrical confinement.

Ab Initio Confirmation of a Harpoon-Type Electron Transfer in a Helium Droplet.

An ab initio study of a long-range electron transfer or "harpoon"-type process from Cs and Cs2 to C60 in a superfluid helium droplet is presented. The heliophobic Cs or Cs2 species are initially located at the droplet surface, while the heliophilic C60 molecule is fully immersed in the droplet. First, probabilities for the electron transfer in the gas phase are calculated for reactants with velocities below the critical Landau velocity of 57 m/s to account for the superfluid helium environment. Next, reaction pathways are derived that also include the repulsive contribution from the extrusion of helium upon the approach of the two reactants. Our results are in perfect agreement with recent experimental measurements of electron ionization mass spectroscopy [ Renzler , M. ; et al., J. Chem. Phys. 2016 , 145 , 181101 ], showing a high possibility for the formation of a Cs2-C60 complex inside of the droplet through a direct harpoon-type electron transfer involving the rotation of the molecule but a negligibly low reactivity for atomic Cs.

Orbital breathing effects in the computation of x-ray d-ion spectra in solids by ab initio wave-function-based methods.

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d 9 cuprate Li2CuO2, for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d n electronic structures of group VI B to VIII B correlated oxide compounds.

Ab initio ro-vibronic spectroscopy of the Π2 PCS radical and Σ+1PCS- anion.

Near-equilibrium potential energy surfaces have been calculated for both the PCS radical and its anion using a composite coupled cluster approach based on explicitly correlated F12 methods in order to provide accurate structures and spectroscopic properties. These transient species are still unknown and the present study provides theoretical predictions of the radical and its anion for the first time. Since these species are strongly suggested to play an important role as intermediates in the interstellar medium, the rotational and vibrational spectroscopic parameters are presented to help aid in the identification and assignment of these spectra. The rotational constants produced will aid in ground-based observation. Both the PCS radical and the PCS- anion are linear. In the PCS- anion, which has a predicted adiabatic electron binding energy (adiabatic electron affinity of PCS) of 65.6 kcal/mol, the P-C bond is stronger than the corresponding neutral radical showing almost triple bond character, while the C-S bond is weaker, showing almost single bond character in the anion. The PCS anion shows a smaller rotational constant than that of the neutral. The ω3 stretching vibrational frequencies of PCS- are red-shifted from the radical, while the ω1 and ω2 vibrations are blue-shifted with ω1 demonstrating the largest blue shift. The ro-vibronic spectrum of the PCS radical has been accurately calculated in variational nuclear motion calculations including both Renner-Teller (RT) and spin-orbit (SO) coupling effects using the composite potential energy near-equilibrium potential energy and coupled cluster dipole moment surfaces. The spectrum is predicted to be very complicated even at low energies due to the presence of a strong Fermi resonance between the bending mode and symmetric stretch, but also due to similar values of the bending frequency, RT, and SO splittings.

Transferability and accuracy by combining dispersionless density functional and incremental post-Hartree-Fock theories: Noble gases adsorption on coronene/graphene/graphite surfaces.

The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = (3)He, (4)He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6-7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of the combined DFT and post-HF incremental scheme is established for all the noble-gas atoms. With relative deviations smaller than 4% and 11%, good agreement is also achieved by applying the vdW-corrected DFT treatments PBE-D3 and vdW-DF2 for noble-gas atoms heavier than neon.

Nuclear Bound States of Molecular Hydrogen Physisorbed on Graphene: An Effective Two-Dimensional Model.

The interaction potential of molecular hydrogen physisorbed on a graphene sheet is evaluated using the ab initio-based periodic dlDF+Das scheme and its accuracy is assessed by comparing the nuclear bound-state energies supported by the H2(D2/HD)/graphite potentials with the experimental energies. The periodic dlDF+Das treatment uses DFT-based symmetry-adapted perturbation theory on surface cluster models to extract the dispersion contribution to the interaction whereas periodic dispersionless density functional (dlDF) calculations are performed to determine the dispersion-free counterpart. It is shown that the H2/graphene interaction is effectively two-dimensional (2D), with the distance from the molecule center-of-mass to the surface plane and the angle between the diatomic axis and the surface normal as the relevant degrees of freedom. The global potential minimum is found at the orthogonal orientation of the molecule with respect to the surface plane, with an equilibrium distance of 3.17 Å and a binding energy of -51.9 meV. The comparison of the binding energies shows an important improvement of our approach over the vdW-corrected DFT schemes when we are dealing with the very weak H2/surface interaction. Next, the 2D nuclear bound-state energies are calculated numerically. As a cross-validation of the interaction potential, the bound states are also determined for molecular hydrogen on the graphite surface (represented as an assembly of graphene sheets). With the largest absolute deviation being 1.7 meV, the theoretical and experimental energy levels compare very favorably.