Comparison of the polarizability of periodic systems computed by using the length and velocity operators

Polarizabilities of carbon nanotubes: Importance of the crystalline orbitals relaxation in presence of an electric field

“…This weak difference should be due to the non completeness of the atomic orbitals basis set. Note that the effect of the basis set on the quality of the SOS and CPKS results was studied in a previous work [38]. The comparison between the unscreened (SOS) and screened (CPKS) values shows that the local field effect affects only weakly the longitudinal component at the LDA level (less than 2% for the length operator).…”

“…ÀikÁr ¼r þ ir k ) can be used within both SOS and CPKS formalisms [38]. In our previous works [39][40][41][42], the velocity operator was preferred for SOS calculations: the transition moments between orthogonal crystalline orbitals are equal to hijr r jjik=ðe jk À e ik Þ, instead of, hijr þ ir k jjik as if the hypervirial theorem was checked.…”

First-principles study of the optical properties of BeO in its ambient and high-pressure phases

“…The dynamic optical properties were obtained using a ''sum over states'' (SOS) method [16]. This method has been applied successfully to determine accurately the index of refraction, real and imaginary parts of dielectric function and energy-loss spectra of wide-band-gap systems, such as Ga 2 O 3 [17], BN, GaN and MgO [18]. No attempt was made to calculate the equation of state for the ground and metastable phases of BeO since it was the focus of previous theoretical studies [3][4][5][6][7][8].…”

“…For calculations, the velocity operator rr þ ik used by Gajdos et al [26] was preferred, and the transition moments between orthogonal crystalline orbitals are equal to hijrrjji=ð jk À ik Þ instead of hijr þ ir k jji, as the hypervirial theorem was checked [18]. We note here that, in such a gauge, the values of transition moment are very sensitive to the transition energy values between occupied and unoccupied crystalline orbitals.…”

Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields

“…The substitution of Eq. (6) can, then, be viewed as replacing E · r by E ·Ω (k) = E · ıe ık·r ∇ k e −ık·r = E · (r + ı∇ k ) [52]. Thus, one might consider replacing the linear magnetic field term in the kineticenergy operator 1 2 p + 1 c A 2 operator by an expression that involves the angular momentum operator B ·L = 1 c B · (−ıΩ (k) × ∇).…”