Equilibrium isomeric mixtures: potential energy hypersurfaces as the origin of the overall thermodynamics and kinetics

Theoretical investigation of the structures, stabilities, and vibrational and rotational spectroscopic parameters of linear HOMgNC and HMgNCO molecules by density functional theory and coupled-cluster method

Linear HOMgNC and HMgNCO molecules: two appropriate candidates for interstellar observation and experimental preparation.

Significant Roles of a Particularly Stable Two-Center Two-Electron Lu-Lu σ Bond in Lu2@C86: Electronic Structure of Lu and Radius of Lu2

There is still dispute over the stability of endohedral metallofullerenes (EMFs) M₂C_2n, and recently, multiform lutetium-based dimetallofullerenes have been dropped in experiments. The thermodynamic stabilities of Lu₂C₈₆ EMFs are revealed by density functional theory (DFT) in conjunction with statistical thermodynamic analyses. Inevitably, besides the experimentally reported Lu₂@C_2v(63751)-C₈₆, Lu₂@C_s(63750)-C₈₆, and Lu₂@C_s(63757)-C₈₆, other three metal carbide clusterfullerenes, Lu₂C₂@D_2d(51591)-C₈₄, Lu₂C₂@C₁(51383)-C₈₄, and Lu₂C₂@C_s(id207430)-C₈₄, rather than Lu₂@C₈₆ are first characterized as thermodynamically stable isomers of Lu₂C₈₆. Specially, the C_s(id207430)-C₈₄ is a newly non-classical fullerene containing one heptagon, which is stabilized via encaging Lu₂C₂. Another interesting phenomenon is that the outer fullerene cages of thermodynamically stable Lu₂C_82-88 molecules are geometrically connected through C₂ addition/loss and Stone-Wales (SW) transformation, suggesting a special relationship between thermodynamic stabilities and geometries of Lu₂C_82-88 EMFs. Furthermore, the electronic configurations of (Lu₂)⁴⁺@C₈₆^4- and (Lu₂C₂)⁴⁺@C₈₄^4- were confirmed. A significantly stable two-center two-electron (2c-2e) Lu-Lu σ single bond is formed in Lu₂@C₈₆. By comparing M-M bonds in M₂@C_2v(63751)-C₈₆ (M = Sc, Y, La, and Lu), two significant factors, the valence atomic orbital (ns) of metal atoms and radius of M²⁺, are found to determine the stability of the M-M bond in the C_2v(63751)-C₈₆. Additionally, the simulated UV-vis-NIR spectra of thermodynamically stable Lu₂C₈₆ isomers were simulated, which further disclose their electronic features.

Covalent interactions depend on the distances between metals and fullerenes for thermodynamically stable M@C78 (M = La, Ce, and Sm)

Thermodynamic selectivity occurs between fullerenes and metals in M@C₇₈ (M = La, Ce, Sm), including non-IPR C₁(22 595)-C₇₈; the different number of electrons transferred from metals to C₇₈ leads to the first EMF with diradical features.

La–La bonded dimetallofullerenes [La2@C2n]−: species for stabilizing C2n (2n = 92–96) besides La2C2@C2n

Theoretical investigations suggest that carbon cages C_2n could be captured as both electron reduced [La₂@C_2n]⁻ with La–La bonding and pristine La₂C₂@C_2n forms.

Eu@C72: Computed Comparable Populations of Two Non-IPR Isomers

Relative concentrations of six isomeric Eu@C 72 -one based on the IPR C 72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon-pentagon junction (symmetries C 2 and C 2 v ), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon-pentagon fusions-are DFT computed using the Gibbs energy in a broad temperature interval. It is shown that the two non-IPR isomers with one pentagon-pentagon junction prevail at any relevant temperature and exhibit comparable populations. The IPR-satisfying structure is disfavored by both energy and entropy.

Dimetallofullerene M2@C100 or carbide cluster fullerene M2C2@C98 (M = La, Y, and Sc): which ones are more stable?

The geometric and thermodynamic stability of the M₂C₁₀₀ (M = La, Y, and Sc) series was systematically investigated using density functional theory calculations on the level of B3LYP/6-31G(d) ∼ Lanl2dz.

Preferential stabilization of HeI2 van der Waals isomers: the effect of energetics and temperature

Energetics and temperature dependence on the preferential stabilization of the linear/T-shaped HeI₂ isomers.

Structure of protonated tryptophan dimer in the gas phase investigated by IRPD spectroscopy and theoretical calculations

RATIONAL

In addition to proton affinity (PA), side chains may also have an effect on the structures of amino acid complex ions in the gas phase. A previous study showed that the most stable isomer of Pro2 H(+) favored a salt-bridged structure. Tryptophan has a PA close to that of proline, but a quite different side chain. Thus, it will be interesting to discover whether the salt-bridged or charge-solvated conformation is energetically more favorable for Trp2 H(+) in the gas phase.

METHODS

The infrared photodissociation (IRPD) spectrum of Trp2 H(+) was obtained using a Fourier transform ion cyclotron resonance mass spectrometer equipped with a tunable OPO laser. The non-covalent cluster ions were generated by electrospray ionization. Structural optimization and frequency calculation of the selected isomers were performed at the M062X/6-311++G(d,p) level.

RESULTS

The experimental IRPD spectrum of Trp2 H(+) was reported in the region of 2700-3750 cm(-1) . Theoretical calculations show that the most stable isomer has a charge-solvated structure. Its energy was found to be 9 kcal/mol lower than that of the most stable salt-bridged isomer. The experimental spectrum is consistent with the predicted spectra of the most stable charge-solvated structures. Temperature effect on the stability of isomers was also evaluated and it was revealed that the contribution from salt-bridged isomers can be neglected at a temperature of 300 K.

CONCLUSIONS

Combining the method of IRPD spectroscopy with theoretical calculations, the structures of Trp2 H(+) were investigated. It is shown that the structures of Trp2 H(+) are dominated by charge-solvated forms. The results also indicate that the side chain may considerably affect the stability of the zwitterionic forms. Copyright © 2016 John Wiley & Sons, Ltd.

Sc3N@Cs(39715)–C82: a missing isomer linked to Sc3N@C2v(39718)–C82 by a single step Stone–Wales transformation

Density functional theory combined with statistical mechanics calculations indicate that Sc₃N@C_2v(39718)–C₈₂ and Sc₃N@C_s(39715)–C₈₂ linked by a single Stone–Wales transformation can be obtained at the fullerene formation temperature region.

Structure of Protonated Threonine Dimers in the Gas Phase: Salt-Bridged or Charge-Solvated?

For homodimers of amino acids, their salt-bridged structures are gradually stabilized as the proton affinity of the component amino acid increases. Threonine has a proton affinity value located in the middle of the list of 20 natural amino acids. Thus, identifying whether the most stable isomer of protonated threonine dimer (Thr(2)H(+)) has a charge-solvated or salt-bridged structure is important and helpful for understanding the structures of other homodimers. By combining infrared photodissociation (IRPD) spectroscopy and theoretical calculations, the structures of Thr(2)H(+) were investigated. Based on calculations at the M062X/6-311++G(d,p)//M062X/6-311++G(d,p) level, the most stable isomer of Thr(2)H(+) was computed to be a charge-solvated structure, with an energy 3.87 kcal/mol lower than the most stable salt-bridged isomer. The predicted infrared spectrum is in good agreement with the experimental spectrum. To evaluate the temperature effect on the distribution of different isomers, the relative concentrations of the six isomers of Thr(2)H(+) were calculated at different temperatures, according to their partition functions and enthalpies. The results show that the isomers are dominated by charge-solvated structures at a temperature of 300 K.

Molecular structures of Pr@C72 and Pr@C72(C6H3Cl2): a combined experimental–theoretical investigation

The carbon-cage structure of the lowest-lying Pr@C₇₂ and its dichlorophenyl-functionalized derivative is C₂(10612)-C₇₂.

Dimetallic sulfide endohedral metallofullerene Sc2S@C76: density functional theory characterization

In terms of density functional theory combined with statistic mechanics computations, we investigated a dimetallic sulfide endohedral fullerene Sc2S@C76 which has been synthesized without any characterization in experiments. Our theoretical study reveals that Sc2S@Td(19151)-C76 which satisfies the isolated-pentagon rule (IPR) possesses the lowest energy, followed by three non-IPR structures (Sc2S@C2v(19138)-C76, Sc2S@Cs(17490)-C76, and Sc2S@C1(17459)-C76). To clarify the relative stabilities of those isomers at high temperatures, enthalpy-entropy interplay has been taken into consideration. Calculation results indicate that three species Sc2S@Td(19151)-C76, Sc2S@C2v(19138)-C76, and Sc2S@C1(17459)-C76 have noticeable molar fractions at the fullerene-formation temperature region (500-3000K), and the Sc2S@C1(17459)-C76 with one pentagon pair becomes the most predominant isomer above 1800 K, suggesting that the unexpected non-IPR structure is thermodynamically favorable at elevated temperatures. In addition, the structural characteristics, electron features, UV-vis-NIR adsorptions, and (13)C NMR spectra of those three stable structures are introduced to assist experimental identification and characterization in future.

Stability computations for isomers of La@C(n) (n = 72, 74, 76)

Density-functional theory calculations are presented for low-energy La@C₇₂, La@C₇₄ and La@C₇₆ isomers with IPR (isolated pentagon rule) and non-IPR cages. The relative isomeric production yields at high temperatures are evaluated using the calculated terms, and the relationships to observations are discussed.

C₇₄ endohedral metallofullerenes violating the isolated pentagon rule: a density functional theory study

Precise studies on M(2)@C(74) (M = Sc, La) series by means of DFT methods have disclosed that certain non-IPR isomers are more stable than the IPR structure. M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74), both of which have two pentagon adjacencies (PA), present excellent thermodynamic stability with very small energy differences. Statistical mechanics calculations on the M(2)@C(74) series reveal that M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74) are quite favoured by entropy effects below 3000 K. Sc(2)@C(74) and La(2)@C(74) series are found to have similar electronic transfer but different electronic structures due to the distinct properties of scandium and lanthanum elements according to Natural Bond Orbital (NBO) analysis in conjunction with orbital interaction diagrams. Investigations of bonding energies reflect quite different influences of the two types of metal atoms to C(74) metallo-fullerenes. Further examinations on C(74) metallo-fullerenes uncover significant stabilization effects of metal atoms acting on PA fragments. Geometrical structures of certain non-IPR cages (from C(72) to C(76)), which exhibit splendid stabilities when encapsulating metallo-clusters, are found to be related by Stone-Wales transformation and C(2) addition. Furthermore, IR spectra and (13)C NMR spectra of M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74) have been simulated to assist further experimental characterization.

The shape of the Sc2(μ2-S) unit trapped in C82: crystallographic, computational, and electrochemical studies of the isomers, Sc2(μ2-S)@C(s)(6)-C82 and Sc2(μ2-S)@C(3v)(8)-C82

Single-crystal X-ray diffraction studies of Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82)·Ni(II)(OEP)·2C(6)H(6) reveal that both contain fully ordered fullerene cages. The crystallographic data for Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) show two remarkable features: the presence of two slightly different cage sites and a fully ordered molecule Sc(2)(μ(2)-S)@C(s)(6)-C(82) in one of these sites. The Sc-S-Sc angles in Sc(2)(μ(2)-S)@C(s)(6)-C(82) (113.84(3)°) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82) differ (97.34(13)°). This is the first case where the nature and structure of the fullerene cage isomer exerts a demonstrable effect on the geometry of the cluster contained within. Computational studies have shown that, among the nine isomers that follow the isolated pentagon rule for C(82), the cage stability changes markedly between 0 and 250 K, but the C(s)(6)-C(82) cage is preferred at temperatures ≥250 °C when using the energies obtained with the free encapsulated model (FEM). However, the C(3v)(8)-C(82) cage is preferred at temperatures ≥250 °C using the energies obtained by rigid rotor-harmonic oscillator (RRHO) approximation. These results corroborate the fact that both cages are observed and likely to trap the Sc(2)(μ(2)-S) cluster, whereas earlier FEM and RRHO calculations predicted only the C(s)(6)-C(82) cage is likely to trap the Sc(2)(μ(2)-O) cluster. We also compare the recently published electrochemistry of the sulfide-containing Sc(2)(μ(2)-S)@C(s)(6)-C(82) to that of corresponding oxide-containing Sc(2)(μ(2)-O)@C(s)(6)-C(82).

Sc2C2@C80 rather than Sc2@C82: templated formation of unexpected C2v(5)-C80 and temperature-dependent dynamic motion of internal Sc2C2 cluster

Unambiguous X-ray crystallographic results of the carbene adduct of Sc(2)C(82) reveal a new carbide cluster metallofullerene with the unexpected C(2v)(5)-C(80) cage, that is, Sc(2)C(2)@C(2v)(5)-C(80). More interestingly, DFT calculations and NMR results disclose that the dynamic motion of the internal Sc(2)C(2) cluster depends strongly on temperature. At 293 K, the cluster is fixed inside the cage with two nonequivalent Sc atoms on the mirror plane, thereby leading to C(s) symmetry of the whole molecule. However, when the temperature increases to 413 K, the (13)C and (45)Sc NMR spectra show that the cluster rotates rapidly inside the C(2v)(5)-C(80) cage, featuring two equivalent Sc atoms and weaker metal-cage interactions.

Sc2(mu2-O) trapped in a fullerene cage: the isolation and structural characterization of Sc2(mu2-O)@C(s)6-C82 and the relevance of the thermal and entropic effects in fullerene isomer selection

The new endohedral fullerene, Sc(2)(mu(2)-O)@C(s)(6)-C(82), has been isolated from the carbon soot obtained by electric arc generation of fullerenes utilizing graphite rods doped with 90% Sc(2)O(3) and 10% Cu (w/w). Sc(2)(mu(2)-O)@C(s)(6)-C(82) has been characterized by single crystal X-ray diffraction, mass spectrometry, and UV/vis spectroscopy. Computational studies have shown that, among the nine isomers that follow the isolated pentagon rule (IPR) for C(82), cage 6 with C(s) symmetry is the most favorable to encapsulate the cluster at T > 1200 K. Sc(2)(mu(2)-O)@C(s)(6)-C(82) is the first example in which the relevance of the thermal and entropic contributions to the stability of the fullerene isomer has been clearly confirmed through the characterization of the X-ray crystal structure.

A global search for the lowest energy isomer of C(26)

The complete set of 2333 isomers of C(26) fullerene composed of square, pentagonal, hexagonal, and heptagonal faces together with some noncage structures is investigated at the Hartree-Fock and density functional theory (DFT) levels. For the singlet states, a nonclassical isomer C(26)-10-01 with a square embedded is predicted by the DFT method as the lowest energy isomer, followed by the sole classical isomer C(26)-00-01. Further explorations reveal that the electronic ground state of C(26)-10-01 is triplet state in C(s) symmetry, while that of C(26)-00-01 corresponds to its quintet in D(3h) symmetry. Both the total energies and nucleus independent chemical shift values at DFT level favor the classical isomer. It is found that both C(26)-00-01 and C(26)-10-01 possess high vertical electron affinity. The addition of electron(s) to C(26)-10-01 increases its aromatic character and encapsulation of Li atom into this cage is highly exothermic, indicating that it may be captured in the form of derivatives. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account based on the Gibbs free energy at the B3LYP/6-311+G( *) level. C(26)-10-01 behaves thermodynamically more stable than the classical isomer over a wide range of temperatures related to fullerene formation. The IR spectra of these two lowest energy isomers are simulated to facilitate their experimental identification.

Search for the most stable Ca@C44 isomer: structural stability and electronic property investigations

Stimulated by the mass spectroscopic observation of the metallofullerene Ca@C(44), we have performed a systematic investigation to search for the most stable isomer using HF/3-21G approximately LanL2DZ, HF/6-31+G(d), B3LYP/6-31+G(d), and MP2/6-31+G(d)//B3LYP/6-31+G(d) methods. The Ca@C(44) (D(2):53) isomer with eight adjacent pentagons in the fullerene framework is predicted to possess the lowest energy. The thermodynamics stability explorations of Ca@C(44) isomers at different temperatures show that Ca@C(44) (D(2):53) is the most thermodynamically stable in the temperature range of absolute zero to 4000 K. The encapsulation of Ca atom in C(44) fullerene is exothermic, and the electronic structure of Ca@C(44) (D(2):53) can be described formally as Ca(2+)@C(44) (2-). Further analysis on the frontier molecular orbitals and density of states of Ca@C(44) (D(2):53) suggests that both highest occupied molecular orbital and lowest unoccupied molecular orbital are carbonlike with low Ca character, and the carbon cage possesses high chemical activity. In addition, the vibrational spectrum of Ca@C(44) (D(2):53) has been simulated and analyzed to gain an insight into the metal-cage vibrations.

Structures, Stabilities, and Electronic and Optical Properties of C62 Fullerene Isomers

The 2385 classical isomers and four nonclassical isomers of fullerene C62 have been studied by PM3, HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-31G(d)//B3LYP/6-31G(d). The Cs:7mbr isomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbr which is 3.15 kcal/mol higher in energy. C2:0032 with three pairs of adjacent pentagons is the most stable isomer in the classical framework. To clarify the relative stabilities of C62 isomers at high temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. Analyses reveal that Cs:7mbr prevails in a wide temperature range. The vibrational frequencies of the five most stable C62 fullerene isomers are also predicted at the B3LYP/6-31G(d) level, and the simulated IR spectra show important differences in positions and intensities of the vibrational modes for different isomers. The nucleus-independent chemical shift and the density of states of the three most stable isomers show that the square in C2v:4mbr and the adjacent pentagons in Cs:7mbr and C2:0032 possess high chemical reactivity. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and the sum-over-states mode. The intensity-dependent refractive index gamma(-omega; omega, omega, -omega) at omega = 2.3305 eV of Cs:7mbr is very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62 are predicted to be larger than those of C60.

Structures, Stabilities, and Electronic and Optical Properties of C58 Fullerene Isomers, Ions, and Metallofullerenes

The 1205 classical isomers of fullerene C58, as well as one quasi-fullerene C58 isomer with a heptagonal ring (labeled as Cs:hept) have been investigated by the quantum chemical methods PM3, HCTH/3-21G, and B3LYP/6-31G(d). Isomer C3v:0001, which has the lowest number of adjacent pentagons, is predicted to be the most stable isomer, but the quasi-fullerene isomer Cs:hept is only 2.50 kcal mol-1 higher in energy. Systematic investigations of the electronic properties of C3v:0001 and Cs:hept find that the C3v:0001 isomer has high vertical electron affinity (3.19 eV). The nucleus-independent chemical shifts (NICS) value at the center of Cs:hept (-5.1 ppm) is more negative than that of C60 (-2.8 ppm). The NICS value at the center of the heptagonal ring in Cs:hept (-2.5 ppm) indicates weakly aromatic character. In contrast, the C58(6-) and C58(8-) ions of the C3v:0001 and Cs:hept geometries possess large aromatic character, with NICS values between -14.0 and -26.2 ppm. To clarify the thermodynamic stabilities of C58 isomers at different temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. The C3v:0001 isomer prevails in a wide range of temperatures, and the Cs:hept isomer is also an important component around 2800 K. The IR spectra of C58 isomers are simulated to facilitate experimental identification of different isomers. In addition, the electronic spectra and the second-order hyperpolarizabilities are predicted by ZINDO and the sum-over-states model. The static second-order hyperpolarizability of the C3v:0001 isomer is 96.5 % larger than that of C60, and its second-order hyperpolarizabilities at external field frequencies are at least nine times larger than those of C60.

Structures, stabilities, and electronic and optical properties of C52 fullerene, ions, and metallofullerenes

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP6-31G(d). C(2):029 with the least number of adjacent pentagons is predicted to be the most stable isomer. The investigations show that both the number of adjacent pentagons and the degree of aromaticity play important roles in the relative stabilities of fullerene isomers. To clarify the relative stabilities of the C52 isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP6-31G(d) level. C(2):029 prevails in a wide temperature range. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and sum-over-states model. The static second-order hyperpolarizability of C(2):029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index gamma (-omega;omega,omega,-omega) (omega=1.1653 eV) of C(2):029 is 13 times larger than that of C60. The encapsulation of Ca atom in C52 fullerene is exothermic and the metallofullerene Ca-C52 is described as Ca2+-C52(2-).

Computed Structures of Two Known Yb@C74 Isomers

Six isomers of Yb@C74 are considered, namely one cage with isolated pentagons, three isomers with a pentagon-pentagon junction, two structures with one pentagon-pentagon pair, and one heptagon. The computations based on the Gibbs energy point out the endohedral derived from the only C74 cage with the isolated pentagons and from a cage with one pentagon-pentagon junction as the major and minor observed isomer, respectively. Temperatures giving the best agreement with the experimental production ratio are evaluated.