Serguei Patchkovskii

Interaction energies and NMR chemical shifts of noble gases in C60

Abstract He, Ne, Ar, Kr and Xe are computed to be bound inside C 60 by −0.3, −1.9, −2.5, −7.5 and −5.4 kcal/mol respectively, at the counterpoise-corrected MP2/6-31G ∗∗ level (using a DZP basis for Kr and Xe). Even though the basis-set superposition error is still quite large at this level, it seems remarkable that there is no destabilization even for Xe@C 60 . Unlike 3 He, which is shielded by −6 ppm in He@C 60 , 129 Xe is predicted to be deshielded in Xe@C 60 (by ca. + 60 to +70 ppm) and also in the higher fullerence compounds Xe@C 70 and Xe@C 84 (by smaller amounts).

Equilibrium yield for helium incorporation into buckminsterfullerene: Quantum-chemical evaluation

The binding energy and equilibrium constant for the endohedral He@C60 compound have been determined from ab initio and density functional (DFT) calculations. Very large grids for the numerical integration are necessary to converge the DFT results to within 0.1 kcal/mol. Gradient-corrected DFT methods incorrectly predict He@C60 to be less stable than He+C60. At the highest ab initio level employed, i.e., second-order Mo/ller–Plesset perturbation theory (MP2) with extended basis sets and counterpoise corrections, He@C60 is bound by 2.0 kcal/mol. The equilibrium constant for He incorporation into C60 has been evaluated from Hartree–Fock and DFT interaction potentials adjusted to reproduce the MP2 binding energy. Computed equilibrium yields at 3000 atm and 900 K exceed 10%, compared with 0.1% observed in the experiment, which indicates that suitable catalysts could increase the observed yield significantly.

Electronic structures, geometries, and energetics of highly charged cations of the C60 fullerene

Abstract Electronic structure calculations carried out at the HF/6–311G∗ level of theory predict the C602+ and C604+ species to possess D5d and C3 symmetries, respectively. On the other hand, the pentagonally distorted C608+ species undergoes further lowering of symmetry that is readily rationalized by its small HOMO-LUMO gap. Although the C6010+, C6018+, and C6028+ closed-shell icosahedral cages are found stable with respect to a totally symmetrical Coulomb explosion by both ab inito and semiempirical calculations, the MNDO, AM1, and PM3 vibrational frequencies indicate that only the decacation is a minimum on the potential energy hypersurface whereas the other two cations have many imaginary frequencies for non-totally symmetrical modes.

Analytical second derivatives of the energy in MNDO methods

Analytical second derivatives of the energy are derived and efficiently implemented for semiempirical MNDO‐type methods including AM1, PM3, and MNDO/d. A new algorithm for the simultaneous solution of several CPHF equations is proposed in which the amount of memory required is independent of the number of iterations. The analytical approach is faster than the numerical approach typically by a factor of 5 and exhibits a reliable convergence over a wide range of molecules. The asymptotic memory and secondary storage requirements of the reported procedure can be as low as O(N2) without significant degradation of the performance.

Analytical first derivatives of the energy in the MNDO half-electron open-shell treatment

SummaryUsing the Z-vector formalism the analytical gradient of the energy in the half-electron open-shell treatment is derived and implemented for semiempirical MNDO-type methods. The computation time is shown to scale asO(N3) with the size of the system, with the memory requirements growing asO(N2). The evaluation of the analytical gradient is significantly faster than the half-electron SCF calculation, so that routine full geometry optimizations become possible for large open-shell systems. The approach can easily be extended to the treatment of the small CI expansions typically encountered in semiempirical computations.