Rotational Transitions in the N2 + Ion Induced by Collisions with Helium Atoms in Cold Helium Plasmas. A Quasiclassical Trajectory Study.

Cross-sections of state-to-state rotational transitions in electronically ground-state 14 N 2 + ${{\rm{N}}_2^ + }$ (X2 Σ g + ${{\Sigma }_{g}^{+}}$ ) ions induced by collisions with 4 He atoms have been calculated using a quasiclassical trajectory method and a set of artificial neural networks representing the N 2 + ${{\rm{N}}_2^ + }$ /He potential energy surface. The training points for the neural networks have been calculated at a MCSCF (multi-configuration self-consistent field)/aug-cc-pVQZ level. A broad range of the N 2 + ${{\rm{N}}_2^ + }$ /He collision energy has been considered ( E c o l l ≤ 100 ${{E}_{{\rm c}{\rm o}{\rm l}{\rm l}}\le 100}$  eV) and the efficiency of vibrational transitions in the N 2 + ${{\rm{N}}_2^ + }$ ion has also been analyzed. It has been found that vibrational transitions are negligible with respect to rotational transitions up to E c o l l ≈ 10 ${{E}_{{\rm c}{\rm o}{\rm l}{\rm l}}\approx 10}$  eV and that above this energy, both rotational and vibrational transitions in N 2 + ${{\rm{N}}_2^ + }$ are marginal in the N 2 + ${{\rm{N}}_2^ + }$ /He collisions.

Electronic Structure of Pentagonal Carbon Nanocones: An ab Initio Study.

In this work, we investigate the electronic structure of a particular class of carbon nanocones having a pentagonal tip and C5v symmetry. The ground-state nature of the wave function for these structures can be predicted by the recently proposed generalized Hückel rule that extends the original Hückel rule for annulenes to this class of carbon nanocones. In particular, the structures here considered can be classified as closed-shell or anionic/cationic closed-shells, depending on the geometric characteristics of the cone. The goal of this work is to assess the relationship between the electronic configuration of these carbon nanocones and their ability to gain or lose an electron as well as their adsorption capability. For this, the geometry of these structures in the neutral or ionic forms, as well as systems containing either one lithium or fluorine atom, was optimized at the DFT/B3LYP level. It was found that the electron affinity, ionization potential, and the Li or F adsorption energy present an intimate connection to the ground-state wave function character predicted by the generalized Hückel rule. In fact, a peculiar oscillatory energy behavior was discovered, in which the electron affinity, ionization energy, and adsorption energies oscillate with an increase in the nanocone size. The reasoning behind this is that if the anion is closed-shell, then the neutral nanocone will turn out to be a good electron acceptor, increasing the electron affinity and lithium adsorption energy. On the other hand, in the case of a closed-shell cation, this means that the neutral nanocone will easily lose an electron, leading to a smaller ionization potential and higher fluorine adsorption energy.

Multilayer Graphtriyne Membranes for Separation and Storage of CO2: Molecular Dynamics Simulations of Post-Combustion Model Mixtures.

The ability to remove carbon dioxide from gaseous mixtures is a necessary step toward the reduction of greenhouse gas emissions. As a contribution to this field of research, we performed a molecular dynamics study assessing the separation and adsorption properties of multi-layered graphtriyne membranes on gaseous mixtures of CO2, N2, and H2O. These mixtures closely resemble post-combustion gaseous products and are, therefore, suitable prototypes with which to model possible technological applications in the field of CO2 removal methodologies. The molecular dynamics simulations rely on a fairly accurate description of involved force fields, providing reliable predictions of selectivity and adsorption coefficients. The characterization of the interplay between molecules and membrane structure also permitted us to elucidate the adsorption and crossing processes at an atomistic level of detail. The work is intended as a continuation and a strong enhancement of the modeling research and characterization of such materials as molecular sieves for CO2 storage and removal.

Toward a Generalized Hückel Rule: The Electronic Structure of Carbon Nanocones.

In this work, we investigate a particular class of carbon nanocones, which we name graphannulenes, and present a generalized Hückel rule (GHR) that predicts the character of their ground state based on simply the three topological indices that uniquely define them. Importantly, this rule applies to both flat and curved systems, encompassing a wide variety of known structures that do not satisfy the "classic" 4n + 2 rule such as coronene, corannulene, and Kekulene. We test this rule at the Hückel level of theory for a large number of systems, including structures that are convex and flat, with a saddle-like geometry, and at the CASSCF level of theory for a selected representative subset. All the performed calculations support the GHR that we propose in this work.

Tuning the magnetic properties of beryllium chains.

In this work we explore the effect of confining beryllium chains inside carbon nanotubes. Linear Ben systems are characterized by two states originating from the presence of edge orbitals localized at the chain extremities. The two spins occupying these orbitals are, in the gas phase, antiferromagnetically coupled, with the magnetic coupling J decaying exponentially as a function of increasing length of the chain. When inserted into narrow carbon nanotubes, the linear geometry is found to be more stable than the more compact cluster conformation favored for the isolated case: the lack of space inside the cavity prevents the chain from folding. Most importantly, the presence of the surrounding nanotube not only preserves the linear structure of Ben, but affects its magnetic properties too. In particular it was found that the magnetic coupling between the ground and the first excited state can be modulated according to the nanotube diameter as well as the chain length, and our calculations suggest a possible direct relationship between these parameters and J. This behavior can be exploited to engineer a composite Ben@CNT system with the magnetic coupling tuned by construction, with interesting potential applications.

Distributed Gaussian orbitals for the description of electrons in an external potential.

In this work, we demonstrate the viability of using distributed Gaussian orbitals as a basis set for the calculation of the properties of electrons subjected to an external potential. We validate our method by studying one-electron systems for which we can compare to exact analytical results. We highlight numerical aspects that require particular care when using a distributedGaussian basis set. In particular, we discuss the optimal choice for the distance between two neighboring Gaussian orbitals. Finally, we show how our approach can be applied to many-electron problems.

The Electronic Structure of Beryllium Chains.

We present an ab initio theoretical study of quasi one-dimensional beryllium chains, Be N, from an electronic structure perspective for N = 3, 4,···, 12. In particular, linear and cyclic systems were compared by using high-quality coupled-cluster formalism. Both linear and cyclic species were found to be local minima on the corresponding potential energy surface, for all the considered values of N. The linear geometry is the most stable one only in the case of Be4. Several indicators (energy gap, position spread tensor, locality of the molecular orbitals) clearly show that both linear and cyclic one-dimensional structures, unlike three-dimensional bulk beryllium, have a covalent insulating nature.

Signatures of Wigner localization in one-dimensional systems.

We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.

N⁻3 azide anion confined inside finite-size carbon nanotubes.

In this work, the confinement of an N[Formula: see text] azide anion inside finite-size single-wall zigzag and armchair carbon nanotubes of different diameters has been studied by wave function and density functional theory. Unrelaxed and relaxed interaction energies have been computed, resulting in a favorable interaction between the guest and host system. In particular, the largest interaction has been observed for the confinement in an armchair (5,5) carbon nanotube, for which a natural population analysis as well as an investigation based on the molecular electrostatic potential has been carried out. The nature of the interaction between the two fragments appears to be mainly electrostatic, favored by the enhanced polarizability of the nanotube wall treated as a finite system and passivated by hydrogen atoms. The results obtained are promising for possible applications of this complex as a starting point for the stabilization of larger polynitrogen compounds, suitable as a high-energy density material.

Increasing Radical Character of Large [n]cyclacenes Unveiled by Wave Function Theory.

We have investigated the radicality and the vertical singlet-triplet energy gap of [n]cyclacenes (cyclic polyacenes) as a function of the system size for n even, from 6 to 22. The calculations are performed using the complete active space self-consistent field method and second-order n-electron valence perturbation theory. We present a systematic way for the selection of the active space in order to have a balanced description of the wave function as the size of the system increases. Moreover, we provide didactic insight into the failure of an approach based on a minimal active space. We find that the ground state is an open-shell singlet and its multireference character increases progressively with n. The singlet-triplet gap decreases as a function of the system size and approaches a finite positive value for the limit n → ∞. Finally, an analysis based on the one-particle reduced density matrix suggests a polyradical character for the largest cyclacenes.

The Spin-Partitioned Total-Position Spread Tensor: An Application To Diatomic Molecules.

The spin partition (SP) of the total-position spread (TPS) tensor is applied to the case of a few light diatomic molecules at full configuration interaction (FCI) level. It appears that the SP-TPS tensor gives informations that are complementary with respect to the corresponding spin-summed (SS) quantity. The spin-summed total position-spread tensor (SS-TPS, Λ) is defined as the second moment cumulant of the total position operator, and the SP-TPS is its partition in equal (Λαα+ßß) and different spin (Λαß+ßα) contributions. Then, the SS-TPS allows description of the molecule charge mobility, while the SP-TPS allows description of the spin delocalization. The most relevant Cartesian-component for both tensors (SS-TPS and SP-TPS) is the component along the chemical bond (Λ(∥)), and it was found that its behavior was related to the type of interaction involved. For covalent bonds the SP-TPS has a squared growth when the bond is stretched, while for ionic bonds there exists a faster-than-linear growth after the avoided-crossing between the covalent and the ionic states. Other exotic bonds, like He2 and Be2, were also considered, and a particular spin delocalization was able to describe the different character of the two weakly bonded molecules, and specially the multireference character of the wave function along the dissociative potential energy curve.

The total position-spread tensor: spin partition.

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains Hn (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.

The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains.

The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.

Partly saturated polyacene structures: a theoretical study.

Planar molecular edifices obtained by joining polyacene fragments (polyacene stripes) are investigated at tight-binding (i.e., with a Hückel Hamiltonian) and ab initio level. For this kind of system, it is known that the presence of 60-degree angles between two stripes of the polyacene molecular skeleton induces the formation of singly occupied molecular orbitals, whose combination gives rise to quasi-degenerate electronic states. In particular, two types of convex polygons having a unique side length (rhombuses and triangles) are considered in this work. It is shown that the saturation via hydrogen atoms of the apical carbons located on outer borders of the 60-degree angles increases the number of quasi-degenerate orbitals, and hence the maximal multiplicity of the low-lying states of the system. Our tight-binding and ab initio (CAS-CI, NEVPT2) calculations indicate that the spin multiplicity of these molecular structures is in systematical accord with the Ovchinnikov rule.

Beryllium dimer: a bond based on non-dynamical correlation.

The bond nature in beryllium dimer has been theoretically investigated using high-level ab initio methods. A series of ANO basis sets of increasing quality, going from sp to spdf ghi contractions, has been employed, combined with HF, CAS-SCF, CISD, and MRCI calculations with several different active spaces. The quality of these calculations has been checked by comparing the results with valence Full-CI calculations, performed with the same basis sets. It is shown that two quasi-degenerated partly occupied orbitals play a crucial role to give a qualitatively correct description of the bond. Their nature is similar to that of the edge orbitals that give rise to the quasi-degenerated singlet-triplet states in longer beryllium chains.

The Total Position Spread in mixed-valence compounds: A study on the H4+ model system.

The behavior of the Total Position Spread (TPS) tensor, which is the second moment cumulant of the total position operator, is investigated in the case of a mixed-valence model system. The system consists of two H2 molecules placed at a distance D. If D is larger than about 4 bohr, the singly ionized system shows a mixed-valence character. It is shown that the magnitude of the TPS has a strong peak in the region of the avoided crossing. We believe that the TPS can be a powerful tool to characterize the behavior of the electrons in realistic mixed-valence compounds.

Surprising electronic structure of the BeH- dimer: a full-configuration-interaction study.

The electronic structure of the beryllium hydride anion, BeH(-), was investigated at valence full-configuration-interaction (FCI) level, using large cc-pV6Z basis sets. It appears that there is a deep change of the wave function nature as a function of the internuclear distance: the ion structure goes from a weakly bonded Be···H(-) complex, at long distance, to a rather strongly bonded system (more than 2 eV) at short distance, having a (:Be-H)(-) Lewis structure. In this case, it is the beryllium atom that formally bears the negative charge, a surprising result in view of the fact that it is the hydrogen atom that has a larger electronegativity. Even more surprisingly, at very short distances the average position of the total electronic charge is close to the beryllium atom but on the opposite side with respect to the hydrogen position.

Behavior of the Position-Spread Tensor in Diatomic Systems.

The behavior of the Position-Spread Tensor (Λ) in a series of light diatomic molecules (either neutral or negative ions) is investigated at a Full Configuration Interaction level. This tensor, which is the second moment cumulant of the total position operator, is invariant with respect to molecular translations, while its trace is also rotationally invariant. Moreover, the tensor is additive in the case of noninteracting subsystems and can be seen as an intrinsic property of a molecule. In the present work, it is shown that the longitudinal component of the tensor, Λ∥, which is small for internuclear distances close to the equilibrium, tends to grow if the bond is stretched. A maximum is reached in the region of the bond breaking, then Λ∥ decreases and converges toward the isolated-atom value. The degenerate transversal components, Λ⊥, on the other hand, usually have a monotonic growth toward the atomic value. The Position Spread is extremely sensitive to reorganization of the molecular wave function, and it becomes larger in the case of an increase of the electron mobility, as illustrated by the neutral-ionic avoided crossing in LiF. For these reasons, the Position Spread can be an extremely useful property that characterizes the nature of the wave function in a molecular system.

A theoretical study of closed polyacene structures.

The electronic structure of planar molecular edifices obtained by joining polyacene fragments (polyacene stripes) is investigated at tight-binding and ab initio levels. It is shown that the presence of 60° angles in the molecular skeleton induces the formation of singly-occupied molecular orbitals, whose combination gives rise to quasi-degenerate electronic states. The ab initio investigation requires therefore the use of CAS-SCF and MR-PT approaches. The three types of possible convex polygons having a unique side length (hexagons, rhombuses and triangles) have been considered in this work. The spin multiplicity of these quasi-flat molecular structures is found to be in systematical accord with the Ovchinnikov rule.