Non-additivity of polarizabilities and van der Waals C6 coefficients of fullerenes

Abstract

We present frequency-dependent polarizabilities and C6 dipole-dipole dispersion coefficients for a wide range of fullerene molecules including C60, C70, C78, C80, C82, and C84. The static and dynamic polarizabilities at imaginary frequencies are computed using time-dependent Hartree-Fock, B3LYP, and CAM-B3LYP ab initio methods by employing the complex linear polarization propagator and are subsequently utilized to determine the C6 coefficients using the Casimir-Polder relation. Overall, the C60 and C70 average static polarizabilities α(0) agree to better than 2% with linear-response coupled-cluster single double and experimental benchmark results, and the C6 coefficient of C60 agrees to better than 1% with the best accepted value. B3LYP provides the best agreement with benchmark results with deviations less than 0.1% in α(0) and C6. We find that the static polarizabilities and the C6 coefficients are non-additive, and scale, respectively, as N(1.2) and N(2.2) with the number of carbon atoms in the fullerene molecule. The exponent for C6 power-dependence on N is much smaller than the value predicted recently based on a classical-metallic spherical-shell approximation of the fullerenes.

Accurate van der Waals coefficients between fullerenes and fullerene-alkali atoms and clusters: Modified single-frequency approximation

“…A similar trend was observed for identical sodium cluster pairs 49,52 , but the decreasing rate between fullerene and sodium clusters is slower than that between identical sodium clusters. In both cases, the trends revealed our model agrees well with that displayed by TDHF 61,64 .…”

“…This suggests that the error of simple atom pairwise-based models grows with system size for molecular pairs involving fullerenes. The nonadditivity of C 6 between fullerene pairs including identical as well as nonidentical pairs is quite different from that of C 6 between identical pairs only, the latter of which was found to be monotonically increasing 48,49,61 . Interestingly, we find that C 6 per sodium atom decreases with the increase of the number of sodium atoms between a fullerene and sodium clusters, as shown in Fig.…”

“…MARE = mean absolute relative error. 39,48,49,61,[66][67][68] . This is particularly important for molecules with full valence electron delocalization, such as metallic systems (e.g.…”

“…56. The input static dipole polarizabilities of fullerenes are taken from the TDHF calculations 61 , while the static higher-order multipole polarizabilities are estimated from the conventional formula…”

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

“…The C 6 dispersion coefficients are conveniently expressed by the Casimir-Polder formula [2,3] involving imaginary-frequency dynamic dipole polarizabilities, and can be efficiently calculated from linear-response time-dependent density-functional theory (TDDFT) [4]. In such TDDFT calculations of C 6 coefficients, a number of approximations have been used for the Kohn-Sham exchange-correlation potential v xc and the corresponding response kernel f xc , including the local-density approximation (LDA) [4][5][6][7], generalized-gradient approximations (GGA) [8,9], hybrid approximations [10][11][12][13][14] and optimized effective potential (OEP) approaches [15][16][17][18][19][20]. Using the generalized Casimir-Polder formula [3], non-expanded dispersion energies can also be calculated from TDDFT [21,22].…”