Endohedral chemistry of C60-based fullerene cages

Fullerenes have unique chemistry owing to their cage structure, their richness in pi-electrons, and their large polarizabilities. They can trap atoms and small molecules to generate endohedral complexes as superconductors, drug carriers, molecular reactors, and ferroelectric materials. An important goal is to develop effective methods that can affect the behavior of the atoms and small molecules trapped inside the cage. In this paper, the quantum chemical density functional theory was employed to demonstrate that the stability and position of a guest molecule inside the C60 cage can be changed, and its orientation controlled, by modifying the C60 cage shell. The outside attachment of two hydrogen atoms to two adjacent carbon atoms located between two six-membered rings of the C60 cage affects the orientation of the LiF molecule inside and increases the stability of LiF inside the cage by 45%. In contrast, when 60 hydrogen atoms were attached to the outside surface of the C60 cage, thus transforming all C=C double bonds into single bonds, the stability of the LiF inside was reduced by 34%. If two adjacent carbon atoms were removed from C60, the stability of LiF inside this defect C60 was reduced by 41%.     

Methane clathrate: CH(4) quantum rotor state dependent rattling potential

In methane hydrate the dominant peak in the density of states above 3 meV represents a rattling mode of the guest molecule CH(4) in the large ice cages. This mode shifts from 6.7 meV at T=4.5 K to T=30 K to 7.14 meV with conversion of CH(4) guest molecules into the tunneling ground state. The less symmetric angular density distribution PsiPsi(*) in the excited rotational state compared to the ground state allows the methane to fit better in the orientation dependent cage potential surface. This leads to a larger average distance to the cage-forming molecules with a weaker potential and a reduced rattling energy. A two state single particle model with characteristic rattling energies of 5.20 meV for pure T-methane and 7.3 meV for pure A-methane weighted by the population factors can fit the data.     

One and two hydrogen molecules in the large cage of the structure II clathrate hydrate: quantum translation-rotation dynamics close to the cage wall

We have performed a rigorous theoretical study of the quantum translation-rotation (T-R) dynamics of one and two H2 and D2 molecules confined inside the large hexakaidecahedral (5(12)6(4)) cage of the sII clathrate hydrate. For a single encapsulated H2 and D2 molecule, accurate quantum five-dimensional calculations of the T-R energy levels and wave functions are performed that include explicitly, as fully coupled, all three translational and the two rotational degrees of freedom of the hydrogen molecule, while the cage is taken to be rigid. In addition, the ground-state properties, energetics, and spatial distribution of one and two p-H2 and o-D2 molecules in the large cage are calculated rigorously using the diffusion Monte Carlo method. These calculations reveal that the low-energy T-R dynamics of hydrogen molecules in the large cage are qualitatively different from that inside the small cage, studied by us recently. This is caused by the following: (i) The large cage has a cavity whose diameter is about twice that of the small cage for the hydrogen molecule. (ii) In the small cage, the potential energy surface (PES) for H2 is essentially flat in the central region, while in the large cage the PES has a prominent maximum at the cage center, whose height exceeds the T-R zero-point energy of H2/D2. As a result, the guest molecule is excluded from the central part of the large cage, its wave function localized around the off-center global minimum. Peculiar quantum dynamics of the hydrogen molecule squeezed between the central maximum and the cage wall manifests in the excited T-R states whose energies and wave functions differ greatly from those for the small cage. Moreover, they are sensitive to the variations in the hydrogen-bonding topology, which modulate the corrugation of the cage wall.     

C60笼内内陷粒子的运动

研究C60笼内内陷粒子的量力力学运动, 导出运动能量与波函数, 以内陷CO分子为例做了计算, 解释了分子对微波的吸收现象。     

Application of potential constants: Empirical determination of molecular energy components for diatomic molecules

The potential (force) constant of a diatomic molecule is applied to determine the molecular energy components such as the electronic kinetic (T) and electrostatic potential (V) energies. The theoretical framework of the method is constructed from T and V representations of the quantum mechanical virial theorem. To confirm the utility of the method developed here, the calculated molecular energy components of diatomic molecules are compared with available Hartree-Fock data. It is concluded that the present method is simple and powerful for evaluating the molecular energy components of various diatomic molecules.     

Molecular dynamics simulation of liquid trimethylphosphine

Structural and dynamical properties of liquid trimethylphosphine (TMP), (CH(3))(3)P, as a function of temperature is investigated by molecular dynamics (MD) simulations. The force field used in the MD simulations, which has been proposed from molecular mechanics and quantum chemistry calculations, is able to reproduce the experimental density of liquid TMP at room temperature. Equilibrium structure is investigated by the usual radial distribution function, g(r), and also in the reciprocal space by the static structure factor, S(k). On the basis of center of mass distances, liquid TMP behaves like a simple liquid of almost spherical particles, but orientational correlation due to dipole-dipole interactions is revealed at short-range distances. Single particle and collective dynamics are investigated by several time correlation functions. At high temperatures, diffusion and reorientation occur at the same time range as relaxation of the liquid structure. Decoupling of these dynamic properties starts below ca. 220 K, when rattling dynamics of a given TMP molecules due to the cage effect of neighbouring molecules becomes important.     

An empirical formula to estimate off-diagonal adiabatic corrections to rotation–vibrational energy levels

The empirical one-parameter formula proposed by Alijah and Hinze (Philos Trans R Soc Lond A 364:2877, 2006) to estimate the off-diagonal adiabatic energy corrections has been tested systematically on the diatomic molecules for which exact data are known. It was found that the simple formula reproduces at least 90% of the energy shift. The parameter of the model, called c, is dimensionless and approximately independent of the molecule. Thus, the method can be applied to arbitrary molecules, diatomic or polyatomic, using the recommended value c = 0.11 of the parameter.     

Blue shift in X-H stretching frequency of molecules due to confinement

The effect of spatial confinement on the properties of isoelectronic molecules HF, H2O, NH3, and CH4 has been studied by encapsulating them in a C60 fullerene cage. Second-order M?ller-Plesset perturbation theoretical (MP2) calculations suggest that all the guest species are stable inside the fullerene cage. This stabilization arises from the dispersion interaction between the guest and the host. It is shown that the excitation energy (Esigma*-Esigma) for the X-H bond increases and that there is a blue shift in the stretching frequencies due to confinement.     

Electronegativity based on the simple bond charge model

A single physical interpretation of the various electronegativity scales of Pauling, Mulliken and Gordy is suggested, based on the simple bond charge (SBC) model of Parr and Borkman for the covalent bond. With a charge partition determined from vibrational frequencies, the SBC model is shown to account for the covalent bond energy in single-bonded homonuclear diatomic molecules and diamond-type crystals. The binding energy to the atom of a bond-electron in the single-bonded homonuclear diatomic molecules agrees with Mulliken's electroaffinity, and provides a definition for electronegativity. Gordy's empirical relation between the bond-stretching force constant and electronegativity is explained. It is then suggested that the physical effect underlying Pauling's thermochemical formula for electronagativity is the location of the bond charge in the heteronuclear molecule. The deviation of Pauling's formula from experiment in the case of the alkali hydrides can then be explained.     

How many hydrogen molecules can be inserted into C60? Comments on the paper ‘AM1 treatment of endohedrally hydrogen doped fullerene, nH2@C60’ by L. Türker and Ş. Erkoç [J. Mol. Struct. (Theochem) 638 (2003) 37–40]

The possibility of the formation of endohedral complexes between H₂ molecules and C₆₀ fullerene is discussed on the basis of general geometric considerations as well as the results of molecular mechanics calculations. The obtained results revealed that only one hydrogen molecule being incorporated inside the C₆₀ cage can form the stable complex in agreement with geometric considerations and recent experimental data. The reliability of semiempirical methods to study the problem of H₂ insertion into C₆₀ is also discussed.     

A density functional study of Ce@C82: explanation of the Ce preferential bonding site

Ce has been found experimentally to be preferentially incorporated into the C82 isomer of C2v symmetry as have other lanthanoids in M@C82 (M = La, Pr, Nd, etc.). We have investigated the underlying reason for this preference by calculating structural and electronic properties of Ce@C82 using density functional theory. The ground-state structure of Ce@C82 is found to have the cerium atom attached to the six-membered ring on the C2 axis of the C82-C2v cage, and the encapsulated atom is found to perturb the carbon cage due to chemical bonding. We have found Ce to favor this C2v chemisorption site in C82 by 0.62 eV compared to other positions on the inside wall of the cage. The specific preference of the metal atom to this six-membered ring is explained through electronic structure analysis, which reveals strong hybridization between the d orbitals of cerium and the pi orbitals of the cage that is particularly favorable for this chemisorption site. We propose that this symmetry dictated interaction between the cage and the lanthanide d orbital plays a crucial role when C82 forms in the presence of Ce to produce Ce@C82 and is also more generally applicable for the formation of other lanthanoid M@C82 molecules. Our theoretical computations are the first to explain this well-established fact. Last, the vibrational spectrum of Ce@C82 has been simulated and analyzed to gain insight into the metal-cage vibrations.     

Theoretical studies of CH4 inside an open-cage fullerene: translation-rotation coupling and thermodynamic effects

Molecules trapped inside fullerenes exhibit interesting quantum behavior, including quantization of their translational degrees of freedom. In this study, a theoretical framework for predicting quantum properties of nonlinear small molecules in nonsymmetric open-cage fullerenes (OCFs) has been described along the lines of similar theories which treat small molecules inside C(60) and clathrate cages. As an example, the coupled translational-rotational energy structure has been calculated for the case of CH(4) inside a known OCF. The calculated energy levels have been used to calculate the equilibrium fraction of incorporated CH(4) as well as the translational heat capacity for the encapsulated molecule. The heat capacity shows an anomalous maximum at 239 K for CH(4) and 215 K for CD(4) which are not present in free methane.     

外电场对N@C60, P@C60, As@C60分子结构和性质的影响

用量子力学方法研究了N@C60, P@C60, As@C60分子的几何和电子特征. 计算结果表明, 形成富勒烯包合物后, 碳笼只有微小的变形, 3种内包原子在笼中处于不同的位置, 碳笼与内包原子之间有明显的电荷转移和自旋轨道相互作用, 生成能分别为6.32, 70.88, -53.05 kJ/mol. 内包原子的3个单占据分子轨道(SOMO)能量变化很大, 并由于和碳笼作用而发生劈裂. 在外电场作用下, 分子的电子密度沿电场方向发生转移.分子的能量随外加电场的增强而降低. 分子轨道能级、能隙及SOMO轨道的能量和能级劈裂也发生了变化.     

Open-cage fullerene derivatives suitable for the encapsulation of a hydrogen molecule

The encapsulation of molecular hydrogen into an open-cage fullerene having a 16-membered ring orifice has been investigated. It is achieved by the pressurization of H2 at 0.6-13.5 MPa to afford endohedral hydrogen complexes of open-cage fullerenes in up to 83% yield. The efficiency of encapsulation is dominantly dependent on both H2 pressure and temperature. Hydrogen molecules inside the C60 cage are observed in the range of -7.3 to -7.5 ppm in 1H NMR spectra, and the formations of hydrogen complexes are further confirmed by mass spectrometry. The trapped hydrogen is released by heating. The activation energy barriers for this process are determined to be 22-24 kcal/mol. The DSC measurement of the endohedral H2 complex reveals that the escape of H2 from the C60 cage corresponds to an exothermic process, indicating that encapsulated H2 destabilizes the fullerene.     

Theoretical estimates of the IR spectrum of formamide intercalated into kaolinite

Calculations at PM3 and PBE/6‐31G levels of part of the IR spectrum of the formamide‐kaolinite intercalatation compound based on a 110‐atom cluster of kaolinite with one formamide molecule are reported. Frequencies and intensities for the formamide vibrations and stretchings of four cluster hydroxyls were calculated through partial hessian matrices and polar tensors obtained by numerical differentiation of energy gradients and dipole moment. The formamide molecule attaches to the kaolinite inner surfaces in multiple conformations with its CN bond vector parallel to the surfaces. Hydrogen bonds are formed between the formamide hydrogen atoms (both from NH₂ or CH groups) and the siloxane surface and between the formamide oxygen and nitrogen atoms and the aluminol hydroxyls. The general features of the experimental assignment of the spectrum are confirmed, but the observed splitting of formamide bands is attributed to vibrations from differently attached molecules. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Bromine-bromine energy transfer by binary collisions

The collisional energy transfer between a highly excited bromine molecule and a non-reactive monatomic (Ar or Br) or diatomic (Br₂) medium has been investigated by binary trajectory calculations over a wide range of medium temperatures and internal energies of the reactant molecule. The efficiency of the energy transfer is compared with expectations based on simple statistical approximations used in unimolecular reaction rate theory. Large deviations are found, particularly with respect to the contributions made by different types of degrees of freedom and to the dependence on the internal energy of the reactant molecule. Transfer to or from vibrational degrees of freedom appears to be very inefficient. Translational energy is most readily transferred. The rate coefficient for energy transfer appears to decrease with increasing internal energy in most cases.     

Characterizing and Manipulating Individual Molecules by Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) can provide us the special means to characterize the locally physical and chemical properties of individual molecules, and even help us to manipulate the individual molecules for constructing new molecule-scale devices. Here we have adopted two new types of STM techniques to characterize the encapsulated metal atom inside a fullerene cage, and to construct a molecule-device with strong Kondo effect, respectively. The spatially dI/dV mapping spectra were used to unveil the energy-resolved metal-cage hybrid states of individual Dy@C82 molecule, and the important information about the spatial position of Dy atom inside the cage and the Dy-cage interaction was revealed. The high-voltage pulse by STM tip is controlled to induce the dehydrogenation of Co phthalocyanine molecule and change its adsorption configuration on Au(111) surface, so as to recover Kondo effect that disappears in the case of intact adsorbed molecule.     

Electronic and magnetic properties of endohedrally doped fullerene Mn@C(60): a total energy study

We perform total energy calculations on a manganese atom encapsulated inside a C(60) cage using density functional theory with the generalized gradient approximation through three optimization schemes and along four paths inside the cage. We find that when Mn is located in the central region, its electronic and magnetic properties are not exactly the same as those of a free Mn atom due to weak coupling between Mn and the cage. As Mn is shifted toward to the edge, the total energy and spin start to change significantly when Mn is situated about one-third of the way between the cage center and edge, and the total energy reaches a local minimum. Finally the interaction between Mn and the cage turns repulsive as Mn approaches the edge. We also find that, along the lowest energy path, there exist three consecutive local energy minima and each of these has a different spin M. The ground state has the lowest M=3, Mn is located about 1.6 A away from the cage center, and the binding energy is 0.08 eV. We attribute the decrease in total energy and spin to Mn and C hybridization.     

Which do endohedral Ti2C80 metallofullerenes prefer energetically: Ti2@C80 or Ti2C2@C78? A theoretical study

Four possible isomers of the Ti2C80 metallofullerene are discussed in detail at the B3LYP DFT level of theory: two isomers in Ti2@C80 formula with two Ti atoms encapsulated inside a C80 cage and the other two in Ti2C2@C78 formula with a Ti2C2 cluster involved inside a C78 cage. In the encaged Ti2C2 cluster, there are end-on and side-on C2 bridging modes into the two Ti atoms. The optimized end-on cluster has a linear Ti-C-C-Ti array, whereas the side-on cluster has a butterfly-like structure where the two Ti atoms and the C2 unit do not lie in a plane. DFT calculations show that the Ti2C2@C78 molecule with the end-on Ti2C2 cluster is energetically most favorable in the four isomers. Stabilities of the Ti2C80 molecules are essentially dominated by Ti binding sites inside fullerene cages. The Ti atoms bind over the hexagon rings in preference to a junction between hexagon and pentagon rings. In the Ti2C2@C78 molecules, orbital interactions between the Ti2C2 cluster and the outer cage play a significant role in determining the C2 bridging modes into the dititanium center and their relative stabilities.