Dispersion models exhibiting natural optical activity: application to tartaric acid solutions

Beáta Hroncová; Daniel Franta; Jan Dvořák; David Pavliňák

doi:10.1364/JOSAB.498720

Journal of the Optical Society of America B
Vol. 40,
Issue 12,
pp. 3209-3220
(2023)
•https://doi.org/10.1364/JOSAB.498720

Dispersion models exhibiting natural optical activity: application to tartaric acid solutions

Beáta Hroncová, Daniel Franta, Jan Dvořák, and David Pavliňák

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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)

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Abstract

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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Supplementary Material (2)

Name	Description
Dataset 1	Output file from newAD2 software.
Supplement 1	Supplemental document.

Data availability

Data underlying the results presented in this paper are available in Dataset 1, Ref. [36].

36. D. Franta and B. Hroncová, “Output file of newAD2 software,” figshare (2023), https://doi.org/10.6084/m9.figshare.23576478.

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Equations (23)

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Solute	Solvent	Concentration (g/100 ml)
LTA	$H_{2} O$	22.0
DTA	$H_{2} O$	22.0
LTA	DMSO	38.9
LTA	DMSO	21.9
DTA	DMSO	21.9

Solution	Fitted Quantity	$C_{1}$ ( $µ m^{2}$ )	$λ_{1}$ (nm)	$C_{2}$ ( $µ m^{2}$ )	$λ_{2}$ (nm)	Figure
LTA: $H_{2} O$ ( $c = 22.0$ )	$[α_{L}]$	14.4(3)	135(3)	−8.6(4)	208.5(6)	4
DTA: $H_{2} O$ ( $c = 22.0$ )	$[α_{D}]$	−18.2(12)	162(3)	13.5(12)	203.4(10)	4
LTA: DMSO ( $c = 21.9$ )	$[α_{L}]$	15.4(7)	116(14)	−11.0(9)	212.2(12)	4
DTA: DMSO ( $c = 21.9$ )	$[α_{D}]$	−314(49380)	197.5(1338)	315(49380)	199.0(957)	4
LTA: $H_{2} O$ and DTA: $H_{2} O$ ( $c = 22.0$ )	$([α_{L}] - [α_{D}]) / 2$	15.5(5)	149(3)	−10.2(5)	206.4(6)	5
LTA: DMSO and DTA: DMSO ( $c = 21.9$ )	$([α_{L}] - [α_{D}]) / 2$	53(87)	188(12)	−52(87)	200(8)	5

Regularization Function	LWA		Gaussian
Concentration $c$ (g/100 ml)	38.9	21.9	38.9	21.9
DMSO fraction $f$	0.7537(7)	0.8610(4)	0.7533(7)	0.8609(4)
Transition strength $N_{e v}$ ( ${e V}^{2}$ )	85(6)	48(4)	70(5)	40(3)
Relative strength $A_{e v, 1}$	$1^{†}$		$1^{†}$
Strength splitting $η_{e v, 1}^{(1)}$ ( ${e V}^{- 1}$ )	$- 9.777 \cdot 10^{- 6}^{‡}$		$- 12.9 \cdot 10^{- 6}^{‡}$
Excitation energy $E_{e v, 1}$ ( $e V$ )	5.027(7)		5.029(11)
Energy splitting $υ_{e v, 1}^{(1)}$ ( ${e V}^{- 1}$ )	$0.44 (3) \cdot 10^{- 6}$		$0.58 (8) \cdot 10^{- 6}$
Relative strength $A_{e v, 2}$	67(3)		69(3)
Strength splitting $η_{e v, 2}^{(1)}$ ( ${e V}^{- 1}$ )	$0.146 (13) \cdot 10^{- 6}$		$0.19 (2) \cdot 10^{- 6}$
Excitation energy $E_{e v, 2}$ ( $e V$ )	13.7(5)		12.4(5)
Energy splitting $υ_{e v, 2}^{(1)}$ ( ${e V}^{- 1}$ )	$1.101 (14) \cdot 10^{- 6}$		$1.11 (3) \cdot 10^{- 6}$
Relative strength $A_{e v, 3}$	$84 (8) \cdot 10^{- 4}$		$97 (11) \cdot 10^{- 4}$
Strength splitting $η_{e v, 3}^{(1)}$ ( ${e V}^{- 1}$ )	$0^{†}$		$0^{†}$
Excitation energy $E_{e v, 3}$ ( $e V$ )	0.39(3)		0.40(3)
Energy splitting $υ_{e v, 3}^{(1)}$ ( ${e V}^{- 1}$ )	$95 (19) \cdot 10^{- 6}$		$90 (19) \cdot 10^{- 6}$
Characteristic length $Λ$ (nm)	0 $^{†}$		56(24)
$χ$ (LTA, $l = 5.02 m m$ )	3.577	3.310	3.574	3.309
$χ$ (DTA, $l = 5.02 m m$ )	–	2.811	–	2.811
Concentration ratio	$38.9 / 21.9 = 1.776$
Transition strength ratio $N_{e v} (c = 38.9) / N_{e v} (c = 21.9)$	1.748		1.749

Concentration $c$ (g/100 ml)	38.9	21.9
Transition str. $N_{o t}$ ( ${e V}^{2}$ )	$2.28 (4) \cdot 10^{- 5}$	$1.31 (3) \cdot 10^{- 5}$
Relative strength $A_{o t, 1}$	$1^{†}$	$1^{†}$
Peak position $ν_{o t, 1}$ ( ${c m}^{- 1}$ )	5487(10)
FWHM $β_{o t, 1}$ ( ${c m}^{- 1}$ )	911(30)	891(28)
Lorentz fraction $L_{o t, 1}$	0.00(2)
Relative strength $A_{o t, 2}$	0.08(3)	0.10(3)
Peak position $ν_{o t, 2}$ ( ${c m}^{- 1}$ )	6240(3)
FWHM $β_{o t, 2}$ ( ${c m}^{- 1}$ )	363(31)	375(28)
Lorentz fraction $L_{o t, 2}$	0.0(3)
Relative strength $A_{o t, 3}$	0.14(2)	0.14(2)
Peak position $ν_{o t, 3}$ ( ${c m}^{- 1}$ )	6618(29)
FWHM $β_{o t, 3}$ ( ${c m}^{- 1}$ )	606(25)	623(26)
Lorentz fraction $L_{o t, 3}$	0.00(13)
Relative strength $A_{o t, 4}$	0.035(7)	0.031(6)
Peak position $ν_{o t, 4}$ ( ${c m}^{- 1}$ )	7653(75)
FWHM $β_{o t, 4}$ ( ${c m}^{- 1}$ )	1467(95)	1411(89)
Lorentz fraction $L_{o t, 4}$	0.0(2)
Relative strength $A_{o t, 5}$	0.038(13)	0.027(10)
Peak position $ν_{o t, 5}$ ( ${c m}^{- 1}$ )	6835.9(8)
FWHM $β_{o t, 5}$ ( ${c m}^{- 1}$ )	224(16)	224(17)
Lorentz fraction $L_{o t, 5}$	0.0(3)
Relative strength $A_{o t, 6}$	0.0067(12)	0.0060(11)
Peak position $ν_{o t, 6}$ ( ${c m}^{- 1}$ )	7228(3)
FWHM $β_{o t, 6}$ ( ${c m}^{- 1}$ )	214(8)	188(10)
Lorentz fraction $L_{o t, 6}$	0.4(2)
Relative strength $A_{o t, 7}$	0.003(2)	0.0019(12)
Peak position $ν_{o t, 7}$ ( ${c m}^{- 1}$ )	9469(18)
FWHM $β_{o t, 7}$ ( ${c m}^{- 1}$ )	652(88)	595(79)
Lorentz fraction $L_{o t, 7}$	0.0(9)
Relative strength $A_{o t, 8}$	0.0017(4)	0.0014(3)
Peak position $ν_{o t, 8}$ ( ${c m}^{- 1}$ )	8188(2)
FWHM $β_{o t, 8}$ ( ${c m}^{- 1}$ )	256(11)	227(9)
Lorentz fraction $L_{o t, 8}$	0.0(3)
Relative strength $A_{o t, 9}$	0.0037(5)	0.0027(4)
Peak position $ν_{o t, 9}$ ( ${c m}^{- 1}$ )	9962(9)
FWHM $β_{o t, 9}$ ( ${c m}^{- 1}$ )	488(13)	476(13)
Lorentz fraction $L_{o t, 9}$	0.12(14)
Transition strength ratio	1.736

Solute	Solvent	Concentration (g/100 ml)
LTA	$H_{2} O$	22.0
DTA	$H_{2} O$	22.0
LTA	DMSO	38.9
LTA	DMSO	21.9
DTA	DMSO	21.9

Abstract

Supplementary Material (2)

Data availability

Cited By

Figures (12)

Tables (4)

Equations (23)

Journal of the Optical Society of America B