Electronic structure analysis and DFT benchmarking of Rydberg-type alkali-metal-crown ether, -cryptand, and -adamanzane complexes

Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me2-1.1.1, and 36Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3)2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6-2.0 eV) and hence these complexes belong to the superalkali category. The ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3)2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

Ground and excited electronic structures of electride and alkalide units: The cases of Metal-Tren, -Azacryptand, and -TriPip222 complexes

A systematic electronic structure analysis was conducted for M(L)n molecular electrides and their corresponding alkalide units M(L)n @M' (M/M' = Na, K; L = Tren, Azacryptand, TriPip222; n = 1, 2). All complexes belong to the "superalkali" category due to their low ionization potentials. The saturated molecular electrides display M+ (L)n - form with a greatly diffuse quasispherical electron cloud. They were identified as "superatoms" considering the contours of populating atomic-type molecular orbitals. The observed superatomic Aufbau order of M(Tren)2 is 1S, 1P, 1D, 1F, 2S, 2P, and 1G and it is consistent with those of M(Azacryptand) and M(TriPip222) up to the analyzed 1F level. Their excitation energies decrease gradually moving from M(Tren)2 to M(Azacryptand) and to M(TriPip222). The studied alkalide complexes carry [M(L)n ]+ @M'- ionic structure and their dissociation energies vary in the sequence of K(L)n @Na > Na(L)n @Na > K(L)n @K > Na(L)n @K. Similar to molecular electrides, the anions of alkalide units occupy electrons in diffuse Rydberg-like orbitals. In this work, excited states of [M(L)n @M']0/+/- and their trends are also analyzed.

A two-electron reducing reaction of CO2 to an oxalate anion: a theoretical study of delocalized (presolvated) electrons in Al(CH3)n(NH3)m, n = 0-2 and m = 1-6, clusters

Presolvated electron possibility in three oxidation states of aluminum - Al(0), Al(I), and Al(II) - has been theoretically investigated for the Al + 6NH3, Al(CH3) + 5NH3, and Al(CH3)2 + 4NH3 reactions. It has been shown that the metal center adopts a tetrahedral shape for its most stable geometric structure, irrespective of the degree of Al oxidation states. Using different analysis techniques (highest occupied molecular orbital shapes, spin density distributions, and electron delocalization ranges), we showed that presolvated (delocalized) electrons are only formed in the Al(CH3)2(NH3)p coordination complexes when 2 ≤ p ≤ 4. It has also been evidenced that these delocalized electrons being powerful reducing agents allowed two CO2 molecules to be captured and form an oxalate ion in close contact with the [Al2(CH3)2(CH2)2(NH3)4]2+ dication core.

A fresh perspective on metal ammonia molecular complexes and expanded metals: opportunities in catalysis and quantum information

Recent advances in our comprehension of the electronic structure of metal ammonia complexes have opened avenues for novel materials with diffuse electrons. These complexes in their ground state can host peripheral "Rydberg" electrons which populate a hydrogenic-type shell model imitating atoms. Aggregates of such complexes form the so-called expanded or liquid metals. Expanded metals composed of d- and f-block metal ammonia complexes offer properties, such as magnetic moments and larger numbers of diffuse electrons, not present for alkali and alkaline earth (s-block) metals. In addition, tethering metal ammonia complexes via hydrocarbon chains (replacement of ammonia ligands with diamines) yields materials that can be used for redox catalysis and quantum computing, sensing, and optics. This perspective summarizes the recent findings for gas-phase isolated metal ammonia complexes and projects the obtained knowledge to the condensed phase regime. Possible applications for the newly introduced expanded metals and linked solvated electrons precursors are discussed and future directions are proposed.

Ab Initio Calculations on the Ground and Excited Electronic States of Thorium-Ammonia, Thorium-Aza-Crown, and Thorium-Crown Ether Complexes

Positively charged metal-ammonia complexes are known to host peripheral, diffuse electrons around their molecular skeleton. The resulting neutral species form materials known as expanded or liquid metals. Alkali, alkaline earth, and transition metals have been investigated previously in experimental and theoretical studies of both the gas and condensed phase. This work is the first ab initio exploration of an f-block metal-ammonia complex. The ground and excited states are calculated for Th^0-3+ complexes with ammonia, crown ethers, and aza-crown ethers. For Th³⁺ complexes, the one valence electron Th populates the metal's 6d or 7f orbitals. For Th^0-2+, the additional electrons prefer occupation of the outer s- and p-type orbitals of the complex, except Th(NH₃)₁₀, which uniquely places all four electrons in outer orbitals of the complex. Although thorium coordinates up to ten ammonia ligands, octa-coordinated complexes are more stable. Crown ether complexes have a similar electronic spectrum to ammonia complexes, but excitations of electrons in the outer orbitals of the complex are higher in energy. Aza-crown ethers disfavor the orbitals perpendicular to the crowns, attributed to the N-H bonds pointing along the plane of the crowns.

Electron Presolvation in Tetrahydrofuran-Incorporated Supramolecular Sodium Entities

Alkali metal atoms can repopulate their valence electrons toward solvation due to impact from solvents or microsurroundings and provide the remaining alkali metal cations for coordinating with a variety of specific solvents, forming various electron-expanded complexes or solvated ionic pairs with special interactions. Such special solute-solvent interactions not only affect their electronic structures but also enable the formation of entirely new species. Taking Na(THF)_n (n = 1-6, THF = tetrahydrofuran) and Na₂@THF complexes as typical representatives, density functional theory calculations are carried out to explore the solvation of a sodium atom and its dimer in THF and characterize their complexes as solvent-incorporated supramolecular entities and particularly valence electron presolvation due to their interaction with solvent THF. Electron presolvation is caused by the Pauli repulsion between THF containing a coordinating O atom with a lone pair of electrons and the alkali metal Na or Na₂ containing valence electrons, and THF coordination to them forces their valence electrons to redistribute, which can be easily realized in such solvents. Compared with strongly bound valance electrons of alkali metal atoms, THF coordination enables Na or Na₂ electrons to exhibit much more active states (i.e., the presolvated states) featuring small vertical detachment energies of electrons and distorted diffuse distributions in the frames of the generally structured metal cation complexes, acting as the electron-expanded chemical entities. Furthermore, the degree of electron diffusion and the polarity of the Na-Na bond are proportional to the coordination number (n) and the coordination number difference (Δn) between two Na centers in Na₂@THF. The unique properties of such entities are also discussed. This work offers a theoretical support to the supramolecular entities formed by alkali-metal atoms or their dimers with ligands containing O or N and uncovers the unique electron presolvation phenomena and also enriches our understanding of the novel metal atom complexes.

Superatomic Chelates: The Cases of Metal Aza-Crown Ethers and Cryptands

Li, Na, and Mg⁺-coordinated hexaaza-18-crown-6 ([18]aneN₆) and 1,4,7-triazacyclononane ([9]aneN₃), Li[1.1.1]cryptand, and Na[2.2.2]cryptand species possess a diffuse electron in a quasispherical s-type orbital. They populate expanded p-, d-, f-, and g-shape orbitals in low-lying excited states and hence are identified as "superatoms". By means of quantum calculations, their superatomic shell models are revealed. The observed orbital series of M([9]aneN₃)₂ and M[18]aneN₆ (M = Li, Na, Mg⁺) are identical to the 1s, 1p, 1d, 1f, 2s, and 2p. The electronic spectra of Li[1.1.1]cryptand and Na[2.2.2]cryptand were analyzed up to the 1f¹ configuration, and their transitions were found to occur at lower energies compared to their aza-crown ethers. The introduced superatomic shell models in this work closely resemble the Aufbau principle of "solvated electrons precursors". All reported alkali metal complexes bear lower ionization potentials than any atom in the periodic table; thus, they can also be recognized as "superalkalis".

Ground and excited states analysis of alkali metal ethylenediamine and crown ether complexes

High-level electronic structure calculations are carried out to obtain optimized geometries and excitation energies of neutral lithium, sodium, and potassium complexes with two ethylenediamine and one or two crown ether molecules. Three different sizes of crowns are employed (12-crown-4, 15-crown-5, 18-crown-6). The ground state of all complexes contains an electron in an s-type orbital. For the mono-crown ether complexes, this orbital is the polarized valence s-orbital of the metal, but for the other systems this orbital is a peripheral diffuse orbital. The nature of the low-lying electronic states is found to be different for each of these species. Specifically, the metal ethylenediamine complexes follow the previously discovered shell model of metal ammonia complexes (1s, 1p, 1d, 2s, 1f), but both mono- and sandwich di-crown ether complexes bear a different shell model partially due to their lower (cylindrical) symmetry and the stabilization of the 2s-type orbital. Li(15-crown-5) is the only complex with the metal in the middle of the crown ether and adopts closely the shell model of metal ammonia complexes. Our findings suggest that the electronic band structure of electrides (metal crown ether sandwich aggregates) and expanded metals (metal ammonia aggregates) should be different despite the similar nature of these systems (bearing diffuse electrons around a metal complex).

Ground and excited electronic structures of metal encapsulated nanocages: the cases of endohedral M@C20H20 (M = K, Rb, Ca, Sr) and M@C36H36 (M = Na, K, Rb)

High-level electronic structure calculations were performed to analyze ground and excited states of neutral and cationic endohedral M@C₂₀H₂₀ (M = K, Rb, Ca, Sr) and M@C₃₆H₃₆ (M = Na, K, Rb). In their ground states, one or two electrons occupy a diffuse atomic s-type orbital, thus 1s¹ and 1s² superatomic electronic configurations are assigned for M = Na, K, Rb and M = Ca, Sr cases, respectively. These species populate 1p-, 1d-, 1f-superatomic orbitals in electronically excited states. The specific superatomic Aufbau model introduced for M@C₂₀H₂₀ (M = K, Rb) is 1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 2f. On the other hand, excited electronic spectra of M@C₂₀H₂₀ (M = Ca, Sr) are rich in multireference characters. Excited states of bigger M@C₃₆H₃₆ molecules were investigated up to the 1d level and the transitions were found to require slightly higher energies compared to M@C₂₀H₂₀. These superatoms possess lower ionization potentials, hence can also be categorized as superalkalis.

Comparison of the Microsolvation of CaX2 (X = F, Cl, Br, I) in Water: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations

To understand the microsolvation of alkaline-earth dihalides in water and provide information about the dependence of solvation processes on different halides, we investigated CaBr₂(H₂O)_n^-, CaI₂(H₂O)_n^-, and CaF₂(H₂O)_n^- (n = 0-6) clusters using size-selected anion photoelectron spectroscopy and conducted theoretical calculations on these clusters and their neutrals. The results are compared with those of CaCl₂(H₂O)_n^-/0 clusters reported previously. It is found that the vertical detachment energies (VDEs) of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^- show a similar trend with increasing cluster size, while the VDEs of CaF₂(H₂O)_n^- show a different trend. The VDEs of CaF₂(H₂O)_n^- are much lower than those of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^-. A detailed probing of the structures shows that a significant increase of the Ca-X distance (separation of Ca²⁺-X^- ion pair) in CaCl₂(H₂O)_n^-/0, CaBr₂(H₂O)_n^-/0, and CaI₂(H₂O)_n^-/0 clusters occurred at about n = 5. However, for CaF₂(H₂O)_n^-/0, no abrupt change of the Ca-F distance with the increasing cluster size has been observed. In CaCl₂(H₂O)₆^-/0, CaBr₂(H₂O)₆^-/0, and CaI₂(H₂O)₆^-/0, the Ca atom coordinates directly with 5 H₂O molecules. However, in CaF₂(H₂O)_n^-/0, the Ca atom coordinates directly with only 2 or 3 H₂O molecules. The similarity or differences in the structures and coordination numbers are consistent with the fact that CaCl₂, CaBr₂, and CaI₂ have similar solubility, while CaF₂ has much lower solubility.

Ground and excited electronic structure analysis of XM4 (X = N, P and M = Li, Na) and their anions

High-level coupled-cluster, electron propagator, and multi-reference ab initio methods are employed to study the ground and excited electronic states of the XM4 (X = N, P and M = Li, Na) series. All XM4 species bear lower ionization potentials and can be classified as superalkalis. In the ground state each possesses a diffuse electron in the periphery. This expanded electron cloud of tetrahedral NLi4, NNa4, and PNa4 molecules is spherical (similar to an s-orbital) and evenly distributed around the XM4+ core. The outer electron is promoted to higher-angular momentum p-, d-, 2s-type orbitals in excited states. Singly occupied molecular orbitals of excited PLi4 are deformed due to its lower C1 symmetry. The aug-cc-pVQZ basis set was found to describe the excited states of XM4 accurately and efficiently. The bound singlet and triplet electronic states of XM4- that possess two peripheral electrons are also analyzed.