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.

Gas-phase and solid-state electronic structure analysis and DFT benchmarking of HfCO.

Ab initio multi-reference configuration interaction (MRCI) and coupled cluster singles doubles and perturbative triples [CCSD(T)] levels of theory were used to study ground and excited electronic states of HfCO. We report potential energy curves, dissociation energies (De), excitation energies, harmonic vibrational frequencies, and chemical bonding patterns of HfCO. The 3Σ- ground state of HfCO has an 1σ22σ21π2 electron configuration and a ∼30 kcal mol-1 dissociation energy with respect to its lowest-energy fragments Hf(3F) + CO(X1Σ+). We further evaluated the De of its isovalent HfCX (X = S, Se, Te, Po) series and observed that they increase linearly from the lighter HfCO to the heavier HfCPo with the dipole moment of the CX ligand. The same linear relationship was observed for TiCX and ZrCX. We utilized the CCSD(T) benchmark values of De, excitation energy, and ionization energy (IE) values to evaluate density functional theory (DFT) errors with 23 exchange-correlation functionals spanning GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, and double-hybrid functional families. The global GGA hybrid B3LYP and range-separated hybrid ωB97X performed well at representing the ground state properties of HfCO (i.e., De and IE). Finally, we extended our DFT analysis to the interaction of a CO molecule with a Hf surface and observed that the surface chemisorption energy and the gas-phase molecular dissociation energy are very similar for some DFAs but not others, suggesting moderate transferability of the benchmarks on these molecules to the solid state.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands.

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations.

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf-O or Hf-B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X4Σ-) and HfO(X1Σ+) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (De) from HfO to HfPo and the singlet-triplet energy gap (ΔES-T) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange-correlation functionals spanning multiple rungs of "Jacob's ladder." When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

Molecular-level electrocatalytic CO2 reduction reaction mediated by single platinum atoms.

The activation and transformation of H2O and CO2 mediated by electrons and single Pt atoms is demonstrated at the molecular level. The reaction mechanism is revealed by the synergy of mass spectrometry, photoelectron spectroscopy, and quantum chemical calculations. Specifically, a Pt atom captures an electron and activates H2O to form a H-Pt-OH- complex. This complex reacts with CO2via two different pathways to form formate, where CO2 is hydrogenated, or to form bicarbonate, where CO2 is carbonated. The overall formula of this reaction is identical to a typical electrochemical CO2 reduction reaction on a Pt electrode. Since the reactants are electrons and isolated, single atoms and molecules, we term this reaction a molecular-level electrochemical CO2 reduction reaction. Mechanistic analysis reveals that the negative charge distribution on the Pt-H and the -OH moieties in H-Pt-OH- is critical for the hydrogenation and carbonation of CO2. The realization of the molecular-level CO2 reduction reaction provides insights into the design of novel catalysts for the electrochemical conversion of CO2.

Ground and Electronically Excited States of Main-Group-Metal-Doped B20 Double Rings.

Ab initio coupled-cluster, electron propagator, and Møller-Plesset second-order perturbation theory calculations are utilized to analyze the low-lying electronic states of several metal-doped B20. In the ground state, the presently focused AB20/EB20 (A = Li, Na, and K; E = Mg and Ca) consist of charge-separated A+B20-/E2+B202- frameworks. The excited electronic states of AB20 and EB20+ were analyzed by computing the vertical electron attachment energies (VEAEs) of AB20+ and EB202+. In several excited states, the radical electron is predominantly localized on the B20 frames, which are counterparts of the low-lying states of bare B20-. A variety of basis sets were tested on obtaining VEAEs, and the aug-cc-pVDZ/A,E d-aug-cc-pVDZ/B combination provided the best accuracy-efficiency compromise on them. Furthermore, this work analyzes the Rydberg-like excited states of AB20 and EB20+ and will serve as a guide for future studies on similar metal-doped boron systems.

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 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.

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 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.

Radical abstraction vs. oxidative addition mechanisms for the activation of the S-H, O-H, and C-H bonds using early transition metal oxides.

Quantum chemical calculations are performed to study the S-H, O-H, and C-H bond activation of H2S, H2O, and CH4 by bare and ligated ZrO+ and NbO+ units. These representative oxides bear low energy oxo and higher energy oxyl units. S-H and C-H bonds are readily activated by metal oxyl states (radical mechanism), but the O-H bond is harder to activate with either the oxyl or oxo states. Our results suggest that known practices for the C-H bond activation can be applied to S-H, but not to O-H bonds. The identified trends are rationalized in terms of the HS-H, HO-H, and H3C-H dissociation energies to the homolytic or heterolytic fragments. We also found that these dissociation energies drop to about half after coordination of H2S or H2O to the metal oxide unit. In addition, chlorine ligands are shown to stabilize the higher energy oxyl states of the transition metal oxygen unit enhancing the reactivity of the formed complexes.

Simultaneous Functionalization of Methane and Carbon Dioxide Mediated by Single Platinum Atomic Anions.

Mass spectrometric analysis of the anionic products of interaction among Pt-, methane, and carbon dioxide shows that the methane activation complex, H3C-Pt-H-, reacts with CO2 to form [H3C-Pt-H(CO2)]-. Two hydrogenation and one C-C bond coupling products are identified as isomers of [H3C-Pt-H(CO2)]- by a synergy between anion photoelectron spectroscopy and quantum chemical calculations. Mechanistic study reveals that both CH4 and CO2 are activated by the anionic Pt atom and that the successive depletion of the negative charge on Pt drives the CO2 insertion into the Pt-H and Pt-C bonds of H3C-Pt-H-. This study represents the first example of the simultaneous functionalization of CH4 and CO2 mediated by single atomic anions.

Be-Be Bond in Action: Lessons from the Beryllium-Ammonia Complexes [Be(NH3)0-4]20,2.

High-level electronic structure calculations are performed to elucidate the Be-Be chemical bond in the (NH3)nBe-Be(NH3)n species for n = 0-4. We show that the Be2 bond is explained as a resonance between two Lewis structures, where one beryllium atom donates an electron pair to the second one, and vice versa. The presence of ammonia ligands enhances the stability of this bond considerably. The ∼2.5 kcal/mol binding energy of Be2 becomes ∼30 kcal/mol for [Be(NH3)1-3]2 because of their more polarizable electron pairs. The larger Be(NH3)4 complex has been classified as a solvated electron precursor in the past and has an electron pair in the periphery of a Be(NH3)42+ core occupying a diffuse s-type orbital. The analogy of Be(NH3)4 to Be reflects into the electronic structure of their dimers. The two systems have identical bonding patterns and low-lying electronic states. The ground state binding energy of [Be(NH3)4]2 is 3 times larger than Be2, and its excitation energies are considerably lower by a factor of 3. We also studied the dimers of the cationic Be(NH3)n+ species, and we found that the Coulombic repulsion is counterbalanced by the formation of a single covalent bond in the cases of n = 1, 2 forming stable dicationic [(NH3)nBe-Be(NH3)n]2+ systems, unlike Be22+. We believe that our numerical results will allow the identification and characterization of these exotic species and their solid state (beryllium liquid metals) analogues in future experiments.

Geometric and electronic structure analysis of calcium water complexes with one and two solvation shells.

Neutral and cationic calcium water complexes are studied by means of high-level quantum calculations. Both the geometric and electronic structure of these species is investigated. We study complexes with up to eight water molecules in the first solvation sphere of calcium Ca(H2O)n=1-80,+, and examine their stability with respect to Ca(H2O)n-k@kH2O0,+, where a number k of water molecules resides at the second solvation shell. For the cationic species, we find that five water molecules readily attach to calcium and the sixth water molecule goes to the second shell. The hexa-coordinated calcium core is restored after the addition of a seventh water molecule. For neutral species, zero-point energy corrections are critical in stabilizing structures with water ligands directly bound to calcium for up to six water ligands. The (one or two) valence electrons of Ca+ and Ca are displaced gradually from the valence space of calcium to the periphery of the complex forming solvated electron precursors (SEPs). For example, in the ground state of Ca(H2O)6+ one electron occupies an s-type diffuse peripheral orbital, which can be promoted to higher energy p-, d-, f-, g-atomic-type orbitals (1s, 1p, 1d, 2s, 1f, 2p, 2d, 1g, 3s) in the excited states of the system. Finally, we considered the effect of a complete second solvation shell using the Ca(H2O)6+@12H2O cluster, which is shown to have significantly lower excitation energies compared to the Ca(H2O)6+.

Ab initio investigation of the ground and excited states of RuO+,0,- and their reaction with water.

High-level quantum chemical calculations on RuO0,± elucidate the electronic structure of their low-lying electronic states. For thirty-two states, we report the electronic configurations, bond lengths, vibrational frequencies, spin-orbit splittings, and excitation energies. The electronic states of RuO can be generated from those of RuO+ by adding one electron to the σ non-bonding orbital closely resembling the 5s atomic orbital of Ru. The ground states for RuO and RuO- are clearly identified as 5Δ and 4Δ, but the two states (4Δ and 2Π) compete for RuO+. The difficulty of calculations is revealed by our small binding energies compared to the experimental values. In addition, we studied the reaction of the three species with water in their ground and selected low-lying electronic states. We found a consistent decrease of the activation energy barriers and higher exothermicity as we add electrons to the system. RuO- is found to facilitate the reaction for both kinetic and thermodynamic reasons.

Aufbau Principle for Diffuse Electrons of Double-Shell Metal Ammonia Complexes: The Case of M(NH3)4@12NH3, M = Li, Be+, B2.

Positively charged or neutral metal ammonia complexes can form molecular species called solvated electron precursors (SEPs) that accommodate peripheral electrons in approximately hydrogenic diffuse orbitals. This work expands the notion of SEPs to metal ammonia complexes wherein a second coordination shell with 12 ammonia molecules is attached to M(NH3)4 (M = Li, Be+, B2+) SEPs via hydrogen bonding. In such complexes, denoted M(NH3)4@12NH3, the 12 outer ammonia molecules displace the peripheral electrons even further away from the first shell of ammonia molecules. We have benchmarked several density functional methods against CCSD(T) results and found that CAM-B3LYP provides the best M(NH3)4@12NH3 structures. The electron attachment energies of the closed-shell cores calculated with electron-propagator methods and the corresponding Dyson orbitals reveal the Aufbau principle for the ground and excited states of M(NH3)4@12NH3 to be 1s, 1p, 1d, 1f, 2s, 2p, 1g, 2d. These orbitals are diffuse and delocalized over the periphery of the second solvation shell.

Carbon monoxide activation by atomic thorium: ground and excited state reaction pathways.

Multi-reference configuration interaction (MRCI) and single reference coupled cluster calculations are performed for the ThCO and OThC isomers. Scalar and spin-orbit relativistic effects are considered through a relativistic pseudopotential and the coupling of MRCI wavefunctions via the Breit-Pauli spin-orbit Hamiltonian. Optimized geometries, excitation energies, and vibrational frequencies are reported for both isomers. Full potential energy profiles are constructed for the Th+CO reaction and the conversion of the produced ThCO to OThC. Linear ThCO was found to be more stable than the highly ionic bent OThC system by about 4 kcal mol-1. The interconversion barrier is estimated to be around 30 kcal mol-1. Our results are in agreement with earlier experimental data for the two isomers. The lowest lying states of Th do not populate f-orbitals and resemble the electronic structure of Ti. Therefore, the ability of the two atoms to activate the C[triple bond, length as m-dash]O bond is compared. OTiC is found to be about 40 kcal mol-1 less stable than TiCO revealing the efficiency of Th and possibly other f-block elements to activate multiple chemical bonds as opposed to d-block metals.

O-H and C-H Bond Activations of Water and Methane by RuO2+ and (NH3)RuO2+: Ground and Excited States.

Investigation of the ground and excited states of RuO2+ is carried out using multireference quantum chemical methodologies. The electronic structure is explored in detail, and accurate spectroscopic constants for 12 states are reported. Although ruthenium belongs to the same group as iron, the ground state of RuO2+ is 1Σ+ with a strong oxo character as opposed to the 3Δ of FeO2+ with primarily oxyl character. To see the effect of the different electronic structure of RuO2+ on the O-H and C-H bond activation processes, we studied its reaction with one water or methane molecule. Reaction energies and activation barriers are given for six low-lying electronic states of singlet, triplet, and quintet spin multiplicities. It is found that the higher-energy quintet state (5Σ+) provides the lowest activation energies and is the same state responsible for the C-H activation for FeO2+ complexes. The reason is attributed to its weaker metal-oxygen bond (longer bond length), which is "prepared" to be activated at the same time with the O-H and C-H bonds. The effect of an ammonia ligand in the chemical activity is also discussed.

Superatomic nature of alkaline earth metal-water complexes: the cases of Be(H2O) and Mg(H2O).

Beryllium- and magnesium-water complexes are shown to accommodate peripheral electrons around their Be2+(H2O)4 and Mg2+(H2O)6 cores in hydrogenic type orbitals. The lowest energy state of these tetra- and hexa-coordinated complexes possess one (cationic species) and two electrons (neutral species) in a pseudo spherical s-orbital, and populate p-, d-, f-, and g-type orbitals in their low-lying excited electronic states. High level quantum chemical calculations are performed to study the electronic structure of these complexes belonging to the category of solvated electrons precursors (SEPs). The observed Aufbau principle is in harmony with the previously introduced series for metal-ammonia complexes. In the current study we are able to expand the previously proposed shell model of SEPs beyond the 2d level. The observed shell model for Mg(H2O)6+ is found to be 1s, 1p, 1d, 2s, 2p, 1f, 2d, 3s, and 1g. The stability of the Be(H2O)0/+m and Mg(H2O)0/+n systems with m = 1-4 and n = 1-6 is also examined and the higher stability of metal-ammonia SEPs over metal-water SEPs is explained in terms of the metal-ligand binding energies, hydrogen bonding, and the activation energy barrier leading to H2 release.