Can a Single Molecule of Water be Completely Isolated Within the Subnano-Space Inside the Fullerene C60Cage? A Quantum Chemical Prospective

Probing the Electric Field Response of a Water Molecule Confined in Small Carbon Nanocages: A Density Functional Theory Investigation

We consider a water molecule under tight confinement in the small-sized fullerenes (C28 ${_{28} }$ , C30 ${_{30} }$ , C32 ${_{32} }$ ) within the density functional theory (DFT) calculations with suitable exchange-correlation functionals. Such nanoscopic molecular cages provide an ideal setup to study their characteristic properties not present in the condensed phase. The water molecule entirely loses its feature of typical water when it is confined in small fullerenes of size equal to C30 ${_{30} }$ or smaller, in which the asymmetric O-H stretching vibration occurs at a lower wavenumber than the symmetric stretching. We study the response of the confined water molecule to the applied electric fields in terms of change in geometrical parameters, NMR spin-spin coupling constants, dipole moment, HOMO-LUMO (HL) gap, and vibrational frequency shift. The electric field shielding property of small-sized fullerene cages is explored and found to be strongly correlated with the HL gap. Since the electric field modulates the gap to decrease generally, shielding efficiency varies with field strength, thereby making large fields better shielded than small fields for the small penetration factor at large fields. The results that hold significance for technological applications are discussed.

Fullerenes containing water molecules: a study of reactive molecular dynamics simulations

A different technique was used to investigate fullerenes encapsulating a polar guest species. By reactive molecular dynamics simulations, three types of fullerenes were investigated on a gold surface: an empty C60, a single H2O molecule inside C60 (H2O@C60), and two water molecules inside C60 ((H2O)2@C60). Our findings revealed that despite the free movement of all fullerenes on gold surfaces, confined H2O molecules within the fullerenes result in a distinct pattern of motion in these systems. The (H2O)2@C60 complex had the highest displacement and average velocity, while C60 had the lowest displacement and average velocity. The symmetry of molecules and the polarity of water seem to be crucial in these cases. ReaxFF simulations showed that water molecules in an H2O molecule, H2O@C60, and (H2O)2@C60 have dipole moments of 1.76, 0.42, and 0.47 D, respectively. A combination of the non-polar C60 and polar water demonstrated a significant reduction in the dipole moment of H2O molecules due to encapsulation. The dipole moments of water molecules agreed with those in other studies, which can be useful in the development of biocompatible and high-efficiency nanocars.

H2O·HF@C70: Encapsulation Energetics and Thermodynamics

This report deals with the quantum-chemical evaluation of the energetics and thermodynamics of the simultaneous encapsulation of HF and H2O by the IPR (isolated pentagon rule) C70 fullerene cage, yielding H2O·HF@C70 species which were synthesized and characterized recently, thus further expanding the family of fullerene endohedrals with non-metallic encapsulates. The structures were optimized at the DFT (density functional theory) M06-2X/6-31++G** level. The encapsulation energetics were further refined by the advanced B2PLYPD/6-31++G** and B2PLYPD/6-311++G** methods. After enhancement of the B2PLYPD/6-311++G** encapsulation energy for the BSSE and steric corrections, the encapsulation energy gain was obtained, as 26 kcal/mol. The equilibrium encapsulation thermodynamics were described using the M06-2X/6-31++G** partition functions. The results correspond to our previous evaluations for the water dimer encapsulation by C84 cages.

Unraveling the Origin of Symmetry Breaking in H2 O@C60 Endofullerene Through Quantum Computations

We explore the origin of the anomalous splitting of the 101 levels reported experimentally for the H2 O@C60 endofullerene, in order to give some insight about the physical interpretations of the symmetry breaking observed. We performed fully-coupled quantum computations within the multiconfiguration time-dependent Hartree approach employing a rigorous procedure to handle such computationally challenging problems. We introduce two competing physical models, and discuss the observed unconventional quantum patterns in terms of anisotropy in the interfullerene interactions, caused by the change in the off-center position of the encapsulated water molecules inside the cage or the uniaxial C60 -cage distortion, arising from noncovalent bonding upon water's encapsulation, or exohedral fullerene perturbations. Our results show that both scenarios could reproduce the experimentally observed rotational degeneracy pattern, although quantitative agreement with the available experimental rotational levels splitting value has been achieved by the model that considers an uniaxial elongation of the C60 -cage. Such finding supports that the observed symmetry breaking could be mainly caused by the distortion of the fullerene cage. However, as nuclear quantum treatments rely on the underlying interactions, a decisive conclusion hinges on the availability of their improved description, taken into account both endofullerene and exohedral environments, from forthcoming highly demanding electronic structure many-body interaction studies.

First principles molecular dynamics calculations of the mechanical properties of endofullerenes containing noble gas atoms or small molecules

The mechanical properties of endofullerenes have been investigated by performing compression tests using finite temperature first principles molecular dynamics calculations. We considered various X@C₆₀ systems, with X a single noble gas atom (He, Ne, Ar, Kr, or Xe), small molecules (H₂O, CH₄), or small helium clusters. In the absence of compression, it is observed that there is no or at best a negligible effect of X on the properties of C₆₀. The compression simulations revealed several original findings. First, the influence of X on the stiffness of X@C₆₀ can be quantified, although it is at most 12% for the studied cases. Next, both energy and contact force variations as a function of strain are demonstrated to depend on X. However, this is not the case for the yield strain and for the failure mechanism of the C₆₀ shell. Finally, it is shown that the X@C₆₀ compression could bring X to be in a high stress state. In the specific cases of H₂O and CH₄ molecules, a mechanism of stress assisted dissociation is observed.

Chemical shielding of H2O and HF encapsulated inside a C60 cage

Molecular surgery provides the opportunity to study relatively large molecules encapsulated within a fullerene cage. Here we determine the location of an H₂O molecule isolated within an adsorbed buckminsterfullerene cage, and compare this to the intrafullerene position of HF. Using normal incidence X-ray standing wave (NIXSW) analysis, coupled with density functional theory and molecular dynamics simulations, we show that both H₂O and HF are located at an off-centre position within the fullerene cage, caused by substantial intra-cage electrostatic fields generated by surface adsorption of the fullerene. The atomistic and electronic structure simulations also reveal significant internal rotational motion consistent with the NIXSW data. Despite this substantial intra-cage interaction, we find that neither HF or H₂O contribute to the endofullerene frontier orbitals, confirming the chemical isolation of the encapsulated molecules. We also show that our experimental NIXSW measurements and theoretical data are best described by a mixed adsorption site model.

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational-rotational-vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H2O@C60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n-mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H2O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H2O@C60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest-host interactions.

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.

Infrared spectroscopy of an endohedral water in fullerene

An infrared absorption spectroscopy study of the endohedral water molecule in a solid mixture of H₂O@C₆₀ and C₆₀ was carried out at liquid helium temperature. From the evolution of the spectra during the ortho-para conversion process, the spectral lines were identified as para-H₂O and ortho-H₂O transitions. Eight vibrational transitions with rotational side peaks were observed in the mid-infrared: ω₁, ω₂, ω₃, 2ω₁, 2ω₂, ω₁ + ω₃, ω₂ + ω₃, and 2ω₂ + ω₃. The vibrational frequencies ω₂ and 2ω₂ are lower by 1.6% and the rest by 2.4%, as compared to those of free H₂O. A model consisting of a rovibrational Hamiltonian with the dipole and quadrupole moments of H₂O interacting with the crystal field was used to fit the infrared absorption spectra. The electric quadrupole interaction with the crystal field lifts the degeneracy of the rotational levels. The finite amplitudes of the pure v₁ and v₂ vibrational transitions are consistent with the interaction of the water molecule dipole moment with a lattice-induced electric field. The permanent dipole moment of encapsulated H₂O is found to be 0.50 ± 0.05 D as determined from the far-infrared rotational line intensities. The translational mode of the quantized center-of-mass motion of H₂O in the molecular cage of C₆₀ was observed at 110 cm^-1 (13.6 meV).

Metastable Dianions and Dications

A theoretical study of metastable dianions and dications has been carried out at the CCSD(T)//MP2 level. MX₃ ^2- and LX₄ ^2- (M=Li and Na, L=Be and Mg, X=F and Cl) have been considered as dianions, M₃ X²⁺ (M=Li and Na, X=F and Cl), YH₃ ²⁺ and ZH₄ ²⁺ (Y=F and Cl and Z=O, S) as dications. Minima structures are found in all cases, but they are less stable than the corresponding dissociated pair of mono-ions. The dissociation profile of the molecules in two mono-ions has been explored showing in all cases a maximum that prevent their spontaneous dissociation. The strength and nature of the chemical bond in the dianions and dications have been analyzed with the QTAIM, NBO and LMOEDA method and compared to the corresponding monoanions and monocations.

Does Oxygen Feature Chalcogen Bonding?

Using the second-order Møller-Plesset perturbation theory (MP2), together with Dunning's all-electron correlation consistent basis set aug-cc-pVTZ, we show that the covalently bound oxygen atom present in a series of 21 prototypical monomer molecules examined does conceive a positive (or a negative) σ-hole. A σ-hole, in general, is an electron density-deficient region on a bound atom M along the outer extension of the R-M covalent bond, where R is the reminder part of the molecule, and M is the main group atom covalently bonded to R. We have also examined some exemplar 1:1 binary complexes that are formed between five randomly chosen monomers of the above series and the nitrogen- and oxygen-containing Lewis bases in N2, PN, NH3, and OH2. We show that the O-centered positive σ-hole in the selected monomers has the ability to form the chalcogen bonding interaction, and this is when the σ-hole on O is placed in the close proximity of the negative site in the partner molecule. Although the interaction energy and the various other 12 characteristics revealed from this study indicate the presence of any weakly bound interaction between the monomers in the six complexes, our result is strongly inconsistent with the general view that oxygen does not form a chalcogen-bonded interaction.

C70 Fullerene Cage as a Novel Catalyst for Efficient Proton Transfer Reactions between Small Molecules: A Theoretical study

When acids are supplied with an excess electron (or placed in an Ar or the more polarizable N₂ matrix) in the presence of species such as NH₃, the formation of ion-pairs is a likely outcome. Using density functional theory and first-principles calculations, however, we show that, without supplying an external electron or an electric field, or introducing photo-excitation and -ionization, a single molecule of HCl or HBr in the presence of a single molecule of water inside a C₇₀ fullerene cage is susceptible to cleavage of the σ-bond of the Brønsted-Lowry acid into X⁻ and H⁺ ions, with concomitant transfer of the proton along the reaction coordinate. This leads to the formation of an X⁻···⁺HOH₂ (X = Cl, Br) conjugate acid-base ion-pair, similar to the structure in water of a Zundel ion. This process is unlikely to occur in other fullerene derivatives in the presence of H₂O without significantly affecting the geometry of the carbon cage, suggesting that the interior of C₇₀ is an ideal catalytic platform for proton transfer reactions and the design of related novel materials. By contrast, when a single molecule of HF is reacted with a single molecule of H₂O inside the C₇₀ cage, partial proton transfers from HF to H₂O is an immediate consequence, as recently observed experimentally. The geometrical, energetic, electron density, orbital, optoelectronic and vibrational characteristics supporting these observations are presented. In contrast with the views that have been advanced in several recent studies, we show that the encaged species experiences significant non-covalent interaction with the interior of the cage. We also show that the inability of current experiments to detect many infrared active vibrational bands of the endo species in these systems is likely to be a consequence of the substantial electrostatic screening effect of the cage.

Interactions between a water molecule and C60 in the endohedral fullerene H2O@C60

A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bačić et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.

Fully Coupled Quantum Treatment of Nanoconfined Systems: A Water Molecule inside a Fullerene C60

We implemented a systematic procedure for treating the quantal rotations by including all translational and vibrational degrees of freedom for any triatomic bent molecule in any embedded or confined environment, within the MCTDH framework. Fully coupled quantum treatments were employed to investigate unconventional properties in nanoconfined molecular systems. In this way, we facilitate a complete theoretical analysis of the underlying dynamics that enables us to compute the energy levels and the nuclear spin isomers of a single water molecule trapped in a C₆₀ fullerene cage. The key point lies in the full 9D description of both nuclear and electronic degrees of freedom, as well as a reliable representation of the guest-host interaction. The presence of occluded impurities or inhomogeneities due to noncovalent interactions in the interfullerene environment could modify aspects of the potential, causing significant coupling between otherwise uncoupled modes. Using specific n-mode model potentials, we obtained splitting patterns that confirm the effects of symmetry breaking observed by experiments in the ground ortho-H₂O state. Further, our investigation reveals that the first rotationally excited states of the encapsulated ortho- and para-H₂O have also raised their 3-fold degeneracy. In view of the complexity of the problem, our results highlight the importance of accurate and computational demanding approaches for building up predictive models for such nanoconfined molecules.

Probing the interaction between the encapsulated water molecule and the fullerene cages in H2O@C60- and H2O@C59N. Chem Sci 2018;9:5666-5671. [PMID: 30062000 PMCID: PMC6050629 DOI: 10.1039/c8sc01031e]

We report a high-resolution photoelectron imaging study of cryogenically-cooled H2O@C60- and H2O@C59N- endohedral fullerene anions. The electron affinity (EA) of H2O@C60 is measured to be 2.6923 ± 0.0008 eV, which is 0.0088 eV higher than the EA of C60, while the EA of H2O@C59N is measured to be 3.0058 eV ± 0.0007 eV, which is 0.0092 eV lower than the EA of C59N. The opposite shifts are found to be due to the different electrostatic interactions between the encapsulated water molecule and the fullerene cages in the two systems. There is a net coulombic attraction between the guest and host in H2O@C60-, but a repulsive interaction in H2O@C59N-. We have also observed low-frequency features in the photoelectron spectra tentatively attributed to the hindered rotational excitations of the encapsulated H2O molecule, providing further insights into the guest-host interactions in H2O@C60- and H2O@C59N-.

Sigma-hole carbon-bonding interactions in carbon-carbon double bonds: an unnoticed contact

In this manuscript, we combine high-level ab initio calculations on some small complexes and a CSD survey to analyze the existence of unprecedented noncovalent carbon bonds in X₂C[double bond, length as m-dash]CH₂Y systems (Y = electron-rich atom or group). The methylene group is usually seen as a weak hydrogen bond donor when interacting with an electron-rich atom. However, we demonstrate that when the electron-rich atom is located equidistant from the two H atoms and along the C[double bond, length as m-dash]C bond a σ-hole noncovalent carbon-bonding interaction is established, instead of a bifurcated hydrogen bond, as derived from Atoms-in-Molecules (AIM) and Natural bond orbital (NBO) analyses. The physical nature of the interaction has been analyzed using the Symmetry Adapted Perturbation Theory (SAPT) method. The results indicate that electrostatics is very important followed by either the induction or dispersion terms in anionic and neutral complexes, respectively. In addition the CSD analysis reveals the existence of such interactions, giving reliability to our calculations, which are much more numerous for neutral than for anionic Y systems.

Can an entirely negative fluorine in a molecule, viz. perfluorobenzene, interact attractively with the entirely negative site(s) on another molecule(s)? Like liking like!

The study presents the possibility for the formation of attractive intermolecular interactions between various entirely negative Lewis bases, leading to the formation of the thirteen isolated binary complexes examined.

Tuning the conductance of H2O@C60 by position of the encapsulated H2O

The change of conductance of single-molecule junction in response to various external stimuli is the fundamental mechanism for the single-molecule electronic devices with multiple functionalities. We propose the concept that the conductance of molecular systems can be tuned from inside. The conductance is varied in C₆₀ with encapsulated H₂O, H₂O@C₆₀. The transport properties of the H₂O@C₆₀-based nanostructure sandwiched between electrodes are studied using first-principles calculations combined with the non-equilibrium Green’s function formalism. Our results show that the conductance of the H₂O@C₆₀ is sensitive to the position of the H₂O and its dipole direction inside the cage with changes in conductance up to 20%. Our study paves a way for the H₂O@C₆₀ molecule to be a new platform for novel molecule-based electronics and sensors.

Transport properties of the H2O@C60-dimer-based junction

Theoretical predictions play an important role in finding potential applications in molecular electronics. Fullerenes have a number of potential applications, and the charge flow from a single C60 molecule to another becomes more versatile and more interesting after doping. Here, we report the conductance of two H2O@C60 molecules in series order and how the number of encapsulated water molecules influences the transport properties of the junction. Encapsulating an H2O molecule into one of the C60 cages increases the conductance of the dimer. Negative differential resistance is found in the dimer systems, and its peak-to-valley current ratio depends on the number of encapsulated H2O molecules. The conductance of the C60 dimer and the H2O@C60 dimer is two orders of magnitude smaller than that of the C60 monomer. Furthermore, we demonstrate that the conductance of the molecular junctions based on the H2O@C60 dimer can be tuned by moving the encapsulated H2O molecules. The conductance is H2O-position dependent. Our findings indicate that H2O@C60 can be used as a building block in C60-based molecular electronic devices and sensors.

Ligand(s)-to-metal charge transfer as a factor controlling the equilibrium constants of late first-row transition metal complexes: revealing the Irving–Williams thermodynamical series

Ligand(s)-to-metal charge transfer obtained from QTAIM charges unravel the Irving–William series for the equilibrium constants of late first-row bivalent metal ions.

Unusual bonding modes of perfluorobenzene in its polymeric (dimeric, trimeric and tetrameric) forms: entirely negative fluorine interacting cooperatively with entirely negative fluorine

The Laplacian of the charge density plot for the tetramer of perfluorobenzene, displaying the attraction between entirely negative fluorine atoms, as well as the windmill type intermolecular topology between those atoms.

Significant evidence of C⋯O and C⋯C long-range contacts in several heterodimeric complexes of CO with CH3–X, should one refer to them as carbon and dicarbon bonds!

An illustrated example of a ‘dicarbon bond’ formed between a pair of two carbon atoms of the OC⋯CH₃–Cl₃intermolecular complex, one corresponding to the methylated carbon in 1,1,1-trichloro-ethane (CH₃–Cl₃) and one to the carbon in the carbon dioxide (CO) molecule.

Fullerene nanoarchitectonics: from zero to higher dimensions

The strategic design of nanostructured materials, the properties of which could be controlled across different length scales and which, at the same time, could be used as building blocks for the construction of devices and functional systems into new technological platforms that are based on sustainable processes, is an important issue in bottom-up nanotechnology.Such strategic design has enabled the fabrication of materials by using convergent bottom-up and top-down strategies. Recent developments in the assembly of functional fullerene (C60) molecules, either in bulk or at interfaces, have allowed the production of shape-controlled nano-to-microsized objects that possess excellent optoelectronic properties, thus enabling the fabrication of optoelectronic devices. Because fullerene molecules can be regarded as an ideal zero-dimensional (0D) building units with attractive functions, the construction of higher-dimensional objects, that is, 1D, 2D, and 3D nanomaterials may realize important aspects of nanoarchitectonics. This Focus Review summarizes the recent developments in the production of nanostructured fullerenes and techniques for the elaboration of fullerene nanomaterials into hierarchic structures.