Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis

Abstract

The static and dynamic second hyperpolarizability gamma has been investigated by time-dependent density functional cubic response theory. The third-order coupled perturbed Kohn-Sham equations were solved to obtain the third-order perturbed charge density. Calculations on a number of small molecules (N(2), CO(2), C(2)H(4), CO, HF, H(2)O, and CH(4)), paradisubstituted oligoacetylene chains, benzene, and eight paradisubstituted benzenes were performed to verify the implementation and to assess the accuracy of the nonhybrid and hybrid time-dependent density functional theory computations. Nitroaniline and a derivative were taken as examples to investigate the distribution of the "gamma density" and to demonstrate the feasibility of analyzing cubic response functions in terms of contributions from natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The results highlight the contributions from atoms and bonds on different functional groups to the total value of gamma based on the NBO/NLMO analysis, which might be helpful for new nonlinear optical materials design.

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

“…[39,[86][87][88][89] For the first hyperpolarizability of D/A systems of the type studied in this work, the basis set demands are less stringent. [39,[86][87][88][89] For the first hyperpolarizability of D/A systems of the type studied in this work, the basis set demands are less stringent.…”

Analyzing Pt chemical shifts calculated from relativistic density functional theory using localized orbitals: The role of Pt 5d lone pairs

“…However, we have previously pointed out that, for the cases studied so far, a visual inspection of the NLMOs yields the expected number of bonds-in some cases with a low-occupancy 'lone pair' as the parent NBO. [30,31,43,44] The NBO/NLMO-based relativistic shielding used here [31] yields contributions to the shielding from each occupied localized orbital (here: from each NLMO). It should be pointed out that the analysis is performed in terms of the occupied orbitals of the unperturbed system; i.e.…”

Calculating the Raman and HyperRaman Spectra of Large Molecules and Molecules Interacting with Nanoparticles

“…35 With a hybrid functional the kernel contains some nonlocal Hartree-Fock exchange. An implementation based on ADF's Slater-type basis and density-fitting approach has been reported by Ye et al 23 The last two terms in the expression for the change in effective potential are dependent on the change in the density. Calculation of the density change must therefore be done in a self-consistent manner.…”

“…With the change in density converged, the polarizability components are calculated. Similar procedures are adopted for calculating electric hyperpolarizabilities; see articles by van Gisbergen et al 16,22 and Ye et al 23,24 for further details regarding implementations in the ADF package and benchmark data.…”