Electronic and vibrational contributions to first hyperpolarizability of donor–acceptor-substituted azobenzene

Abstract

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptorsubstituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.

Ro-vibrational averaging of the isotropic hyperfine coupling constant for the methyl radical

“…(7)-(9) requires the eigenvalues E (i) rv and eigenvectors Φ (i) rv which are obtained variationally with TROVE. The degeneracy factor is computed as (2J + 1)g ns , where g ns is the nuclear spin statistical weight taking values in D 3h symmetry group in the order (A ′ 1 , A ′ 2 , E ′ , A ′′ 1 , A ′′ 2 , E ′′ ) as (8, 0, 4, 8, 0, 4) for 13 CH 3 and (2, 20, 16, 2, 20, 16) for 13 CD 3 . (Note that the symmetry of the electronic wave function is A ′′ 2 .)…”

“…The importance of the nuclear motion contributions to various electromagnetic molecular properties is by now well understood. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The zero-point vibrational corrections (ZPVCs) are proved to be non-negligible for the electron paramagnetic resonance (EPR), 18,20 nuclear magnetic resonance (NMR), 8,15,21 and non-linear optical (NLO) properties. 9,22 The so-called pure vibrational contributions to NLO properties 23 are often comparable or even larger in magnitude than that due to electronic motions.…”

Can Gap Tuning Schemes of Long-Range Corrected Hybrid Functionals Improve the Description of Hyperpolarizabilities?

“…Numerous studies have found that LC-DFT methods provide better estimates for hyperpolarizabilities and related properties in chargetransfer compounds as compared to hybrid and GGA functionals. 18,[32][33][34][35][36][37][38][39][40][41][42] However, some recent works have also concluded that LC-DFT does not consistently outperform hybrids and GGAs; for example, in Ref. 43, the range-separated CAM-B3LYP provides the best results in some solvents, but the standard hybrid B3LYP is better in others.…”

Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds?

“…This is the idea behind long-range corrected (LC)-DFT functionals, [29][30][31][32][33][34] which have been shown to provide an improved description of long-range properties (including CT excitations and hyperpolarizabilities) as compared to global hybrids and GGAs. [35][36][37][38][39][40][41][42][43][44][45][46][47][48] Furthermore, the range-separation parameter of LC-DFT can be optimized ab initio for the system of interest by demanding that the molecule, and its corresponding anion, obey the Coulomb operator is divided in three parts). However, these functionals are rarely used in hyperpolarizability calculations since it is believed that the incorrect asymptotic behavior of the exchange potential would lead to catastrophic overshooting of GGAs.…”