Closed-shell System Research Articles

Entanglement coupled cluster theory: Exact spin-adaptation.

We present a novel framework for spin-adapted coupled cluster theory. The approach exploits the entanglement of an open-shell molecule with electrons in a non-interacting bath. Together, the molecule and the bath form a closed-shell system, and electron correlation can be included using the standard spin-adapted closed-shell coupled cluster formalism. A projection operator, which enforces conditions on the electrons in the bath, is used to obtain the desired state of the molecule. This entanglement coupled cluster theory is outlined, and proof-of-concept calculations for doublet states are reported. The approach is further extendable to open-shell systems with other values of the total spin.

Bottom-up design and assembly with superatomic building blocks

Constructing specific structures from the bottom up with artificial units is an important interdisciplinary topic involving physics, chemistry, materials, and so on. In this work, we theoretically demonstrated the feasibility of using superatoms as building blocks to assemble a complex at atomic-level precision. By using a series of actinide-based endohedral metallofullerene (EMF) superatoms that can form one, two, three and four chemical bonds, a planar complex with intra- and inter-molecular interactions was assembled on the Au(111) surface. This complex is composed of two parts, containing ten and eight superatoms, respectively. The electronic structure analysis shows that the electron density inside each part is connected and the closed-shell electronic arrangement system is designed. There is also an obvious van der Waals boundary by physical adsorption between the two parts, and a stable complex is formed. Since this complex is realized by the first-principles calculations of quantum mechanics, our results help not only achieve atomic-level precision construction with artificial superatomic units but also maintain atomic-level functional properties.

Signature of Au as a Halogen.

Gold, although chemically inert in its bulk state, is reactive at the nanoscale and, in small clusters, even behaves like a hydrogen atom. Using a photoelectron spectroscopy experiment and first-principles theory, we show that Au also behaves like a halogen in small clusters. This is evident not only in strong resemblance between the photoelectron spectra of Au2F- and AuF2- but also in Au exhibiting one of the signature properties of halogens, its ability to form superhalogens with electron affinities higher than that of any halogen atom. For example, the electron affinity (EA) of Au2F- is 4.17 eV, while AuF2-, a known superhalogen, has an EA of 4.47 eV. Of particular interest is Au2F2, which, in spite of being a closed-shell system, is a pseudohalogen with an EA of 3.3 ± 0.1 eV. Here, one of the Au atoms behaves like a halogen, making Au2F2 mimic the property of AuF3.

Redefined vacuum approach and gauge-invariant subsets in two-photon-exchange diagrams for a closed-shell system with a valence electron

The two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In contrast to other methods, the redefined vacuum approach enables the identification of eight gauge-invariant subsets and, thus, efficiently checks the consistency of the obtained results. The gauge invariance of found subsets is demonstrated both analytically (for an arbitrary state) as well as numerically for 2s, 2p1/2, and 2p3/2 valence electrons in Li-like ions. Identifying gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, e.g., three-photon exchange, where the fragmentation on simpler subsets is crucial for its successful calculation.

Anionic Boron- and Carbon-Based Hetero-Diradicaloids Spanned by a p-Phenylene Bridge.

Herein we report the synthesis and characterization of anionic boron- and carbon-based Kekulé diradicaloids spanned by a p-phenylene bridge. In contrast to Thiele's hydrocarbon, a closed-shell singlet system, they show an appreciable population of the triplet state at room temperature, as evidenced by both NMR and EPR spectroscopy. Moreover, en route to these anionic boron- and carbon-based hetero-diradicaloids, the formation of an isolable diamino(4-diarylboryl-phenyl)methyl radical was observed.

Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction scheme: An extension to the study of open-shell systems.

This work proposes to describe open-shell molecules or radicals using the framework of the doubly occupied configuration interaction (DOCI) treatments, so far limited to closed-shell system studies. The proposal is based on considering molecular systems in singlet states generated by adding extra hydrogen atoms located at infinite distance from the target radical system. The energy of this radical is obtained by subtracting the energies of the dissociated hydrogen atoms from that provided by the two-electron reduced density matrix corresponding to the singlet state system in the DOCI space, which is variationally calculated by imposing a set of N-representability conditions. This method is numerically assessed by describing potential energy curves and reduced density matrices in selected ionic and neutral open-shell systems in the doublet spin symmetry ground state.

Synthesis and Characterization of the Highly Unstable Metalloid Cluster Ag64 (Pn Bu3 )16 Cl6.

The reduction of (nBu3P)AgCl with LiBH(sBu)3 in toluene gives the metalloid silver cluster Ag64(PnBu3)16Cl6 (1) as dark red, temperature‐ and light‐sensitive single crystals in high yield. 1 is the largest structurally characterized metalloid silver cluster exhibiting chlorine and phosphine substituents only. The silver atoms in 1 show an overall brick‐shape arrangement, where structural resemblance to the close‐packed fcc and hcp structures is realized. Within 1 a 58 electron closed shell system is present. The light sensitivity renders 1 as a model compound for the primary seeds of the photo process, whereby this sensitivity, together with the high‐yield synthesis show that 1 is a perfect starting compound for further investigations like silver‐plating processes.

A DFT Study of the Modulation of the Antiaromatic and Open-Shell Character of Dibenzo[a,f]pentalene by Employing Three Strategies: Additional Benzoannulation, BN/CC Isosterism, and Substitution.

Dibenzo[a,f]pentalene ([a,f]DBP) is a highly antiaromatic molecule having appreciable open-shell singlet character in its ground state. In this work, DFT calculations at the B3LYP/6-311+G(d,p) level of theory were performed to explore the efficiency of three strategies, that is, BN/CC isosterism, substitution, and (di)benzoannulation of [a,f]DBP, in controlling its electronic state and (anti)aromaticity. To evaluate the type and extent of the latter, the harmonic oscillator model of aromaticity (HOMA) and aromatic fluctuation (FLU) indices were used, along with the nucleus-independent chemical shift NICS-XY-scan procedure. The results suggest that all three strategies could be employed to produce either the closed-shell system or open-shell species, which may be in the singlet or triplet ground state. Triplet states have been characterized as aromatic, which is in accordance with Baird's rule. All the singlet states were found to have weaker global paratropicity than [a,f]DBP. Additional (di)benzo fusion adds local aromatic subunit(s) and mainly retains the topology of the paratropic ring currents of the basic molecule. The substitution of two carbon atoms by the isoelectronic BN pair, or the introduction of substituents, results either in the same type and very similar topology of ring currents as in the parent compound, or leads to (anti)aromatic and nonaromatic subunits. The triplet states of all the examined compounds are also discussed.

Ligand stabilization of manganocene dianions - in defiance of the 18-electron rule.

Manganocene [Mn(C5H5)2], a 17-electron system, is expected to have a high electron affinity, as addition of an extra electron would make it a closed-shell 18-electron system. Surprisingly, it has a very low electron affinity of only 0.28 eV. Combined with its high ionization potential of around 7.0 eV, manganocene, therefore, should not be eager to either donate or accept an electron. We show that this property can be fundamentally altered with the proper choice of ligands, even though the total electron count remains the same. For example, the electron affinities of manganocene-derivatives Mn[C5(CN)5]2 and Mn[C5(BO)5]2, created by replacing H with CN or BO, are found to be 4.78 eV and 4.85 eV, respectively, making these species superhalogens. The power of the ligands is further demonstrated by studying the stability of their di-anions. Note that [Mn(C5X5)2]2- (X = H, CN, BO) di-anions, with 19-electrons, have one electron more than necessary to satisfy the 18-electron rule for stability. This factor, combined with the unavoidable repulsion between the two extra electrons, should destabilize [Mn(C5X5)2]2-. While that is the case for [Mn(C5H5)2]2-, we show that both Mn[C5(CN)5]22- and Mn[C5(BO)5]22- are stable against auto-detachment of the second electron by 0.7 eV and 0.38 eV, respectively. These results, based on first-principles calculations, demonstrate that ligand-manipulation can be used as an effective strategy to design and synthesize new materials with novel and tailored properties.

Why Do Silver Trimers Intercalated in DNA Exhibit Unique Nonlinear Properties That Are Promising for Applications?

Our investigation of one-photon absorption (OPA) and nonlinear optical (NLO) properties such as two-photon absorption (TPA) of silver trimer intercalated in DNA based on TDDFT approach allowed us to propose a mechanism responsible for large TPA cross sections of such NLO-phores. We present a concept that illustrates the key role of quantum cluster as well as of nucleotide bases from the immediate neighborhood. For this purpose, different surroundings consisting of guanine-cytosine and adenine-thymine such as (GCGC) and (ATAT) have been investigated that are exhibiting substantially different values of TPA cross sections. This has been confirmed by extending the immediate surroundings as well as using the two-layer quantum mechanics/molecular mechanics (QM/MM) approach. We focus on the cationic closed-shell system and illustrate that the neutral open-shell system shifts OPA spectra into the NIR regime, which is suitable for applications. Thus, in this contribution, we propose novel NLO-phores inducing large TPA cross sections, opening the route for multiphoton imaging.

Excitonic effects and optical spectra of graphene nanoflakes

By solving the Bethe-Salpeter equation within the Hartree-Fock formalism, we study the optical spectra, optical gap, quasi-particle gap, exciton binding energy, and wave function of a closed-shell graphene system. With the excitonic effects fully taken into account, we find that all peaks of optical spectrum are blueshifted to higher photon energy with either the enhancement of the long-range Coulomb interactions or the suppression of the short-range Coulomb interactions but are redshifted to lower photon energy due to the increased size and decreased confinement. Remarkably, the region of a much higher relative probability for an electron resides mainly around the geometrical center of the structure, whereas the hole strongly localizes in the peripheral region of the geometric center. Our results are found to agree well with both recent experimental and theoretical works.

H2 Oxidation Mediated by Au1-Doped Vanadium Oxide Cluster Cation AuV2O5+: A Comparative Study with AuCe2O4.

To clarify the relationship between the type of the oxide support and the activity of the gold-doped oxide clusters toward H2 oxidation, a suitable closed-shell system AuV2O5+ is chosen to have a comparative study with AuCe2O4+, the first closed-shell cluster that is reactive toward H2 oxidation. The reaction of AuV2O5+ with H2 was characterized by mass spectrometry and density functional theory calculations. The AuV2O5+ cluster is reactive toward H2 leading to the major product of V2O5H2+ (+ Au), whereas the product of AuV2O4+ (+ H2O) is completely absent in the experiment. This is in sharp contrast with the similar reaction system of AuCe2O4+ with H2, in which the formation of H2O was experimentally evidenced. Theoretical calculations revealed that the distinct reaction behaviors between AuV2O5+ and AuCe2O4+ can be attributed to the gold-metal bond strength, which plays an important role in anchoring the gold atom. The weaker Au-V bond promotes the evaporation of Au, which has a negative effect on the total oxidation of H2 to H2O. This comparative study provides molecular-level mechanisms to understand the important roles of the gold-metal bond in the oxidation of hydrogen molecule over metal oxide supports.

Influence of a graphene surface on the first steps of the hydrogenation of a coronene molecule

The first steps of the hydrogenation of a coronene molecule deposited on a graphene surface is investigated using Density Functional Theory including a van Der Waals functional. Binding energies and geometries are calculated. The role of the surface is determined by comparing hydrogenation reactions in the gas phase and on the surface. The radical product of the H with a closed-shell system is more stable on the surface. The closed-shell product of the H with a radical species is more stable in the gas phase. This can be interpreted in terms of electronic and geometrical properties of these hydrogenated species.

Economical Doubly Electron-Attached Equation-of-Motion Coupled-Cluster Methods with an Active-Space Treatment of Three-Particle-One-Hole and Four-Particle-Two-Hole Excitations.

The previously developed active-space doubly electron-attached (DEA) equation-of-motion (EOM) coupled-cluster (CC) method with up to four-particle-two-hole (4p-2h) excitations [Shen, J.; Piecuch, P. J. Chem. Phys. 2013, 138, 194102], which utilizes the idea of applying a linear electron-attaching operator to the CC ground state of an (N - 2)-electron closed-shell system to generate ground and excited states of the N-electron open-shell species of interest, has been extended to a considerably less expensive model, in which both 3p-1h and 4p-2h terms rather than 4p-2h contributions only are selected using active orbitals. As illustrated by the calculations involving low-lying singlet and triplet states of methylene, trimethylenemethane, cyclobutadiene, and cyclopentadienyl cation and bond breaking in F2, the proposed DEA-EOMCC method with the active-space treatment of 3p-1h and 4p-2h excitations and its lower-level counterpart neglecting 4p-2h contributions are capable of accurately reproducing the results obtained using their considerably more expensive parent counterparts with a full treatment of 3p-1h and full or active-space treatment of 4p-2h excitations.

Elastic response of the atomic nucleus in gauge space: Giant Pairing Vibrations

Due to quantal fluctuations, the ground state of a closed shell system $ A_{0}$ can become virtually excited in a state made out of the ground state of the neighbour nucleus $ \vert gs(A_0+2) \rangle $ ( $ \vert gs(A_0-2) \rangle $ ) and of two uncorrelated holes (particles) below (above) the Fermi surface. These $ J^{\pi} = 0^{+}$ pairing vibrational states have been extensively studied with two-nucleon transfer reactions. Away from closed shells, these modes eventually condense, leading to nuclear superfluidity and thus to pairing rotational bands with excitation energies much smaller than $ \hbar\omega_{0}$ , the energy separation between major shells. Pairing vibrations are the plastic response of the nucleus in gauge space, in a similar way in which low-lying quadrupole vibrations, i.e. surface vibrations with energies much smaller than $ \hbar\omega_{0}$ whose eventual condensation leads to quadrupole deformed nuclei, provide an example of the plastic nuclear response in 3D space. While much is known, in particular concerning its damping, regarding the counterpart of quadrupole plastic modes, i.e. regarding the giant quadrupole resonances (GQR), $ J^{\pi} = 2^{+}$ elastic response of the nucleus with energies of the order of $ \hbar\omega_{0}$ , little is known regarding this subject concerning pairing modes (giant pairing vibrations, GPV). Consequently, the recently reported observation of L = 0 resonances, populated in the reactions 12C(18O,16O)14C and 13C(18O,16O)15C and lying at an excitation energy of the order of $ \hbar\omega_{0}$ , likely constitutes the starting point of a new field of research, that of the study of the elastic response of nuclei in gauge space. Not only that, but also the fact that the GPV have likely been serendipitously observed in these light nuclei when it has failed to show up in more propitious nuclei like Pb, provides unexpected and fundamental insight into the relation existing between basic mechanisms --Landau, doorway, compound damping-- through which giant resonances acquire a finite lifetime, let alone the radical difference regarding these phenomena displayed by correlated (ph) and (pp) modes.

Investigation of Praseodymium Fluorides: A Combined Matrix-Isolation and Quantum-Chemical Study.

The chemistry of the lanthanides is mostly dominated by compounds in the oxidation state +III. Only few compounds of Ce, Pr, and Tb are known with the metal in the +IV oxidation state. Removal of the last f-electron on praseodymium +IV would lead to a closed-shell system with formal oxidation state V. In this work we investigated the stability of the PrF5 molecule by theory and matrix-isolation techniques through the reaction of laser-ablated praseodymium atoms with fluorine in excess of neon, argon, krypton, or neat fluorine. Besides the known PrF3 molecule, unreported IR bands for PrF4 could be observed, and there is evidence for the formation of PrF and PrF2 but not for the formation of PrF5.

Gold-gold bonding: the key to stabilizing the 19-electron ternary phases LnAuSb (Ln = La-Nd and Sm).

We report a new family of ternary 111 hexagonal LnAuSb (Ln = La-Nd, Sm) compounds that, with a 19 valence electron count, has one extra electron compared to all other known LnAuZ compounds. LaAuSb, CeAuSb, PrAuSb, NdAuSb, and SmAuSb crystallize in the YPtAs-type structure, and have a doubled unit cell compared to other LnAuZ phases as a result of the buckling of the Au-Sb honeycomb layers to create interlayer Au-Au dimers. The dimers accommodate the one excess electron per Au and thus these new phases can be considered Ln2(3+)(Au-Au)(0)Sb2(3-). Band structure, density of states, and crystal orbital calculations confirm this picture, which results in a nearly complete band gap between full and empty electronic states and stable compounds; we can thus present a structural stability phase diagram for the LnAuZ (Z = Ge, As, Sn, Sb, Pb, Bi) family of phases. Those calculations also show that LaAuSb has a bulk Dirac cone below the Fermi level. The YPtAs-type LnAuSb family reported here is an example of the uniqueness of gold chemistry applied to a rigidly closed shell system in an unconventional way.

Communication: generalization of Koopmans' theorem to optical transitions in the Hubbard model of graphene nanodots.

Koopmans' theorem implies that the Hartree-Fock quasiparticle gap in a closed-shell system is equal to its single-particle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closed-shell graphene system within the Hubbard model is equal to its tight-binding single-particle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interaction, and thus, both become small when only on-site Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and single-particle gaps of the graphene systems.

Computation of Chemical Shifts for Paramagnetic Molecules: A Laboratory Experiment for the Undergraduate Curriculum

A computational experiment investigating the 1H and 13C nuclear magnetic resonance (NMR) chemical shifts of molecules with unpaired electrons has been developed and implemented. This experiment is appropriate for an upper-level undergraduate laboratory course in computational, physical, or inorganic chemistry. The chemical shift range for paramagnetic systems differs substantially from the well-known range of diamagnetic compounds. Students carried out density functional theory calculations of the chemical shifts of an organic radical and a related closed-shell system. This simple exercise illustrated that a single unpaired electron may result in dramatically different chemical shifts. Organometallic systems were also considered. The chemical shifts of the closed shell molecule ferrocene were compared to those of vanadocene and nickelocene, which afford three and two unpaired electrons, respectively. A natural bonding orbital (NBO) analysis was employed to study the electronic structure of NiCp2.

Remarks on the exact energy functional for fermions: an analysis using the Löwdin partitioning technique

A comparison model based in the Löwdin partitioning technique is used to analyse the differences between the wave function and density functional models. This comparison model provides a tool, the Löwdin function f (E), to understand the structure of both theories and its discrepancies in terms of the subjacent mathematical structure and the necessary conditions of variationality required for the energy functional. It is argued that density functional theory (DFT) can be compared to the wave function theory (WFT) using the expressions of f (E) at E = 0. The WFT provides an explicit form of the exact energy functional for a fermion system from the full configuration interaction approach. The DFT can be seen as a special case of Löwdin function that does not satisfy all variational conditions on ρ(r) and also on the EXC[ρ] term. This analysis shows that ignoring the restrictions imposed by the spin and space symmetry requirements of the solutions when making a variational calculation implies that the correlations expressed by the ρ(r) function will be inconsistent with a γ1(r1; r′1) function derivable from a spin and space symmetry adapted wave function Ψ(r1s1, …, rnsn), even for a closed-shell system (i.e. an energy minimum that will exhibit the phenomenon of ‘overcorrelation’). The comparison scheme also provides a new insight on the variational requirements in order to achieve a consistent description of the molecular electronic structure of both ground and excited states. Some numerical results are reported.