Abstract
Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only ∼3.3% (one-photon off-resonance regions) and ∼10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine-tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than ∼5% when using the reduced expression as compared to the full form of the isotropic cubic response function.
Highlights
II A, we provide the connection between the observable Two-photon absorption (TPA) cross section and the microscopic γ-tensor associated with the intensity-dependent refractive index (IDRI) nonlinear optical process and introduce the isotropic average of the latter that is relevant in gas and liquid phases
II B, which is the main section of this work, we present novel algorithms for reaching TPA spectrum calculations based on complex cubic response functions that are optimized with respect to Fock matrix constructions
We have demonstrated a highly efficient algorithm for obtaining TPA cross sections for randomly oriented systems where the isotropic γ-tensor is put in computational focus without explicit reference to individual tensor components
Summary
Two-photon absorption (TPA) is a nonlinear optical process with a quadratic dependence on the intensity of the incoming electric field. It has been of high interest in the fields of chemistry and physics where it is used in fundamental studies of electronic structures and in applications such as 3D-microfabrication, multi-photon imaging, photodynamic therapy, optical power limiting, and optical data storage. During the past decade, the development of photo-removable protecting groups, or “caging compounds,” has been pursued with the aim to achieve targeted drug delivery by means of selective irradiation of damaged tissue and triggered by the TPA process. As another very recent application in medicine, we note the promising development of. The key reasons as to why the calculation of TPA spectra from the damped cubic response function is computationally expensive are not associated with the fact that response equations become complex per se as efficient and stable complex linear response equation solvers have been formulated and implemented, not least recently in the VeloxChem program.56 Instead, they are concerned with the facts that (i) response vectors that depend both linearly and quadratically on the external electric field amplitudes must be determined and (ii) there are a large number of components of the second-order hyperpolarizability tensor (or γ-tensor) that needs to be evaluated and each component involves multiple contractions of generalized Hessian matrices. We examine both the one-photon off-resonance and resonance regions in these calculations
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