Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory

Abstract

A comparison of two theoretical methods based on time-dependent density functional theory for the calculation of the linear dispersive and absorptive properties of chiral molecules has been made. For this purpose, a recently proposed computational method for the calculation of circular dichroism (CD) spectra from the imaginary part of the optical rotation parameter has been applied to six rigid organic molecules. The results have been compared to the CD spectra obtained from the rotatory strengths and from the Kramers-Kronig transformation of optical rotatory dispersion (ORD) curves. We have also investigated a criterion based on the Kramers-Kronig integration formula to determine a number of excitations in truncated CD spectra which may yield a reasonable low frequency resonant ORD. It has been tested by calculating the ORD from the sum-over-states formula both in the nonresonant and resonant regions. Finally, we have applied these methods to model the resonant optical activity of proline at low pH.

Damped response theory description of two-photon absorption

“…Damped linear response properties that have been addressed using damped response theory include one-photon absorption (OPA) spectra and dispersion coefficients, [8][9][10][11][12][13][14][15][16] optical rotation and electronic circular dichroism spectra, [17][18][19][20][21] x-ray absorption and natural circular dichroism spectra, [22][23][24][25][26][27] the dynamic dipole magnetizability, 28 and relativistic linear response functions. 29,30 Damped non-linear molecular properties described by quadratic response theory have been addressed, including Raman scattering, [31][32][33][34][35][36][37][38][39][40][41] the electro-optical Kerr effect and second-harmonic generation, 6 and magnetic circular dichroism.…”

Spectral curve fitting of dielectric constants

“…The idea is to extrapolate the imaginary part linearly until its value is zero, zero-fill both above and below the available range, and then form a new data set that is antisymmetric about the origin. The negative axis values can be set toε (−v) = −ε (v) to allow the new data set to be fitted to Equation (8). The p k values returned can then be inserted into Equation (9) to calculate the real part.…”

“…As an intrinsic property of the material, 1 optical constants contain information on the composition of material, 2-4 its anisotropy, [5][6][7] and its optical activity. 8 The optical properties of a material can be inferred from experimental spectra from X-ray frequencies through to the Far-Infrared/Terahertz regions, in either transmittance or absorbance or reflectance mode. 2,[9][10][11][12][13] From the measured spectra, it is possible to extract both the real and imaginary components of the complex optical constants by employing the Kramer-Kronig (K-K) relation, a mathematical expression that connects the real and imaginary parts.…”

Fast generation of nonresonant and resonant optical rotatory dispersion curves with the help of circular dichroism calculations and Kramers‐Kronig transformations

“…[37][38][39] Our group has recently studied the conversion of ORD into CD and vice versa in detail from a theoretical point of view, using LR calculations with empirical damping to obtain u and y from the complex response along with direct computations of rotatory strengths R 0j and excitation frequencies x 0j to obtain the same quantities. 40 One of the disadvantages of calculating a wellresolved ORD over a large frequency range (with or without use of damping) is that the LR computations have to be repeated at each frequency point. Depending on the level of theory and the intended resolution of the ORD this may require significant computational time.…”

“…Depending on the level of theory and the intended resolution of the ORD this may require significant computational time. 21,23,40,41 The purpose of this study is to investigate several protocols involving KK transformations which combine LR computations of ORD at a relatively small number of frequencies with computations of rotatory strengths R 0j and excitation frequencies x 0j (from which CD spectra are usually simulated). The goal is to obtain well resolved ORD curves that do not contain large truncation errors from finite frequency range KK transformations of the CD.…”