Electronic and Vibrational Hyperpolarizabilities of Lithium Substituted (Aza)benzenes and (Aza)naphthalenes

Abstract

In this article we report results for the electronic and vibrational hyperpolarizabilities of ten molecules: Li@benzene, Li@pyridine, Li@pyrimidine, and Li@pyrazine; Li@naphthalene, Li@quinoline, Li@isoquinoline, Li@cinnolin, Li@quinazoline, and Li@quinoxaline. An electron correlation study shows that second-order many-body perturbation theory and density functional theory with CAM-B3LYP and M05-2X functionals give results for the electronic hyperpolarizabilities in good agreement with coupled cluster with single and doubles reference values. Static and dynamic vibrational corrections were computed through the perturbation theoretical method of Bishop and Kirtman and using a variational approach. In general, we obtained notable discrepancies between the results obtained by the two methods for the pure vibrational corrections because of the deficiency of the perturbation method to properly treat low-frequency normal modes present in the investigated systems. However, both methods give results similar to the zero-point vibrational average corrections.

Electronic and vibrational hyperpolarizabilities of alkali‐ and alkaline‐earth‐doped boron nitride nanotubes

“…frequencies higher than 300 cm −1 , indicating that the BKPT method is suitable for treating these effects. [55] An exception among the systems shown in Figure 3 is K@B-BNNT, whose mode giving the largest contribution has a frequency of 137 cm −1 . It is possible that its contribution is somewhat overestimated.…”

“…In this article, we did not calculate the zpva correction for two reasons: (a) the calculation of this property is computationally more expensive because it involves calculations of the first and second derivatives of the β components and (b) previous works show that in general the zpva correction is smaller than the electronic contribution and even the pv correction. [55][56][57][58] The calculation of the [μα] 0,0 harmonic term is more accessible because it requires only the computation of the first derivatives of the dipole moment and polarizability components. On the other hand, the [μ 3 ] 1,0 and [μ 3 ] 0,1 anharmonic terms were calculated by means of the field-induced coordinates methodology (FIC) of Luis et al [59] It was shown that, at the limits ω !…”

“…In this case, strong anharmonicities may be present, which is an indicative that the obtained result by using the BKPT method is overestimated. [55] Figure 3 helps to understand the role played by the vibrational corrections in the different systems studied. It shows the individual contributions of the normal modes to the first hyperpolarizabilities of four selected systems: Li@B-BNNT, Li@N-BNNT, K@B-BNNT, and Li@N-BNNT-B@Li.…”

“…It is possible that its contribution is somewhat overestimated. [55] F I G U R E 2 [Upper panels] Molecular orbitals relevant to the crucial transitions for Li@N-BNNT, Na@N-BNNT, and K@N-BNNT.…”

“…A possible way to overcome such a problem is to introduce a phenomenological damping factor. It is carried out by replacing ω a by ω a − iγ a , where γ a stands for the reciprocal lifetime of the excited vibrational state . For simplicity, the γ a value is the same for all excited states, and it is chosen to keep the structure of peaks without substantially modifying the calculated values of [ μα ] 0,0 away from the resonances.…”