Beáta Hroncová, Daniel Franta, Jan Dvořák, and David Pavliňák, "Dispersion models exhibiting natural optical activity: application to tartaric acid solutions," J. Opt. Soc. Am. B 40, 3209-3220 (2023)
A physically consistent dispersion model, incorporating the optical activity of an isotropic medium and dependent on the size and direction of the wave vector, is presented and used in the optical characterization of a solution of tartaric acid in dimethyl sulfoxide. It is shown that the optical activity can be described simply by three optically active harmonic oscillators. Two of these oscillators effectively describe the excitation of valence electrons, while the third describes the excitation of vibrational states in tartaric acid molecules. Higher-energy valence electron excitations are identified as the bond energies of C-C bonds, and lower-energy excitations correspond to the remaining bonds. The results presented in this work are compared with the results that can be obtained using the phenomenological models commonly used in practice. As part of the optical characterization, the non-locality radius of the dielectric response was found to be surprisingly large, namely, 56 nm.
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Dispersion Parameters of TA Solutions in DMSO Describing Fraction of DMSO and OAHOsa
Regularization Function
LWA
Gaussian
Concentration (g/100 ml)
38.9
21.9
38.9
21.9
DMSO fraction
0.7537(7)
0.8610(4)
0.7533(7)
0.8609(4)
Transition strength ()
85(6)
48(4)
70(5)
40(3)
Relative strength
Strength splitting ()
Excitation energy ()
5.027(7)
5.029(11)
Energy splitting ()
Relative strength
67(3)
69(3)
Strength splitting ()
Excitation energy ()
13.7(5)
12.4(5)
Energy splitting ()
Relative strength
Strength splitting ()
Excitation energy ()
0.39(3)
0.40(3)
Energy splitting ()
Characteristic length (nm)
0
56(24)
(LTA, )
3.577
3.310
3.574
3.309
(DTA, )
–
2.811
–
2.811
Concentration ratio
Transition strength ratio
1.748
1.749
Values are taken from the fits using the dispersion model IR+2UV with an uncoupled IR oscillator under long-wave approximation (LWA) and using Gaussian regularization functions. The signs of the splitting parameters depend on used isomer. The signs shown in the table correspond to LTA solutions; DTA solutions would have opposite signs. The symbol $^\dagger$ denotes a fixed parameter, and the symbol $^{{\ddagger}}$ denotes a dependent parameter calculated by Eq. (21). Below the dispersion parameters, the achieved $\chi$ values for the experimental ellipsometric data from the 5.02 mm thick cuvette are listed. The last two rows show a comparison of the ratio of the solution concentrations and the corresponding ratio of the transition strengths. Values in parentheses are statistical errors.
Table 4.
Dispersion Parameters of TA Solutions in DMSO Describing Overtonesa
Concentration (g/100 ml)
38.9
21.9
Transition str. ()
Relative strength
Peak position ()
5487(10)
FWHM ()
911(30)
891(28)
Lorentz fraction
0.00(2)
Relative strength
0.08(3)
0.10(3)
Peak position ()
6240(3)
FWHM ()
363(31)
375(28)
Lorentz fraction
0.0(3)
Relative strength
0.14(2)
0.14(2)
Peak position ()
6618(29)
FWHM ()
606(25)
623(26)
Lorentz fraction
0.00(13)
Relative strength
0.035(7)
0.031(6)
Peak position ()
7653(75)
FWHM ()
1467(95)
1411(89)
Lorentz fraction
0.0(2)
Relative strength
0.038(13)
0.027(10)
Peak position ()
6835.9(8)
FWHM ()
224(16)
224(17)
Lorentz fraction
0.0(3)
Relative strength
0.0067(12)
0.0060(11)
Peak position ()
7228(3)
FWHM ()
214(8)
188(10)
Lorentz fraction
0.4(2)
Relative strength
0.003(2)
0.0019(12)
Peak position ()
9469(18)
FWHM ()
652(88)
595(79)
Lorentz fraction
0.0(9)
Relative strength
0.0017(4)
0.0014(3)
Peak position ()
8188(2)
FWHM ()
256(11)
227(9)
Lorentz fraction
0.0(3)
Relative strength
0.0037(5)
0.0027(4)
Peak position ()
9962(9)
FWHM ()
488(13)
476(13)
Lorentz fraction
0.12(14)
Transition strength ratio
1.736
Values are taken from the best fit. The symbol $^\dagger$ denotes a fixed parameter. Values in parentheses are statistical errors.
Tables (4)
Table 1.
Set of Samples
Solute
Solvent
Concentration (g/100 ml)
LTA
22.0
DTA
22.0
LTA
DMSO
38.9
LTA
DMSO
21.9
DTA
DMSO
21.9
Table 2.
Dispersion Parameters Describing Specific Rotation (SR) by Eq. (9)a
Dispersion Parameters of TA Solutions in DMSO Describing Fraction of DMSO and OAHOsa
Regularization Function
LWA
Gaussian
Concentration (g/100 ml)
38.9
21.9
38.9
21.9
DMSO fraction
0.7537(7)
0.8610(4)
0.7533(7)
0.8609(4)
Transition strength ()
85(6)
48(4)
70(5)
40(3)
Relative strength
Strength splitting ()
Excitation energy ()
5.027(7)
5.029(11)
Energy splitting ()
Relative strength
67(3)
69(3)
Strength splitting ()
Excitation energy ()
13.7(5)
12.4(5)
Energy splitting ()
Relative strength
Strength splitting ()
Excitation energy ()
0.39(3)
0.40(3)
Energy splitting ()
Characteristic length (nm)
0
56(24)
(LTA, )
3.577
3.310
3.574
3.309
(DTA, )
–
2.811
–
2.811
Concentration ratio
Transition strength ratio
1.748
1.749
Values are taken from the fits using the dispersion model IR+2UV with an uncoupled IR oscillator under long-wave approximation (LWA) and using Gaussian regularization functions. The signs of the splitting parameters depend on used isomer. The signs shown in the table correspond to LTA solutions; DTA solutions would have opposite signs. The symbol $^\dagger$ denotes a fixed parameter, and the symbol $^{{\ddagger}}$ denotes a dependent parameter calculated by Eq. (21). Below the dispersion parameters, the achieved $\chi$ values for the experimental ellipsometric data from the 5.02 mm thick cuvette are listed. The last two rows show a comparison of the ratio of the solution concentrations and the corresponding ratio of the transition strengths. Values in parentheses are statistical errors.
Table 4.
Dispersion Parameters of TA Solutions in DMSO Describing Overtonesa
Concentration (g/100 ml)
38.9
21.9
Transition str. ()
Relative strength
Peak position ()
5487(10)
FWHM ()
911(30)
891(28)
Lorentz fraction
0.00(2)
Relative strength
0.08(3)
0.10(3)
Peak position ()
6240(3)
FWHM ()
363(31)
375(28)
Lorentz fraction
0.0(3)
Relative strength
0.14(2)
0.14(2)
Peak position ()
6618(29)
FWHM ()
606(25)
623(26)
Lorentz fraction
0.00(13)
Relative strength
0.035(7)
0.031(6)
Peak position ()
7653(75)
FWHM ()
1467(95)
1411(89)
Lorentz fraction
0.0(2)
Relative strength
0.038(13)
0.027(10)
Peak position ()
6835.9(8)
FWHM ()
224(16)
224(17)
Lorentz fraction
0.0(3)
Relative strength
0.0067(12)
0.0060(11)
Peak position ()
7228(3)
FWHM ()
214(8)
188(10)
Lorentz fraction
0.4(2)
Relative strength
0.003(2)
0.0019(12)
Peak position ()
9469(18)
FWHM ()
652(88)
595(79)
Lorentz fraction
0.0(9)
Relative strength
0.0017(4)
0.0014(3)
Peak position ()
8188(2)
FWHM ()
256(11)
227(9)
Lorentz fraction
0.0(3)
Relative strength
0.0037(5)
0.0027(4)
Peak position ()
9962(9)
FWHM ()
488(13)
476(13)
Lorentz fraction
0.12(14)
Transition strength ratio
1.736
Values are taken from the best fit. The symbol $^\dagger$ denotes a fixed parameter. Values in parentheses are statistical errors.