Ab initio calculations of nonlinear optical rotation by several small chiral molecules and by uridine stereoisomers

Expressions for nonlinear optical rotation are presented based on the quantum theory of optical birefringence of Atkins and Barron [Proc. R. Soc. London, Ser. A 304, 303 (1968); 306, 119 (1968)]. As concrete examples, the ordinary and nonlinear optical rotations are calculated with density functional theory (DFT) methodology for some simple single-ring molecules, namely, oxaziridine, diaziridine, and their derivatives, and for two, somewhat more complicated, conformations of uridine. For the single-ring molecules, (1) the angles of the ordinary optical rotation are mostly positive and (2) the contributions of the nonlinear effect to the total optical rotation depend both on the nature of the substituted species and of the host atom located on the ring. For the two conformations of uridine, (1) the signs of nonlinear optical rotation differ even though their ordinary optical rotations have the same sign and (2) whether the molecular structures are geometrically optimized with Hartree-Fock or DFT methodologies has no significant effect on the calculated nonlinear optical rotation when gauge-including atomic orbitals were used, even though the basis sets are small. These studies are expected to be helpful for interpretation of experimental results on nonlinear optical rotation by molecules underway in our research group.     

Disymmetry indices based on optical rotational polarizability of chiral molecules

New molecular disymmetry indices are suggested based on an analysis of the moments of rotational polarizability defining optical activity. It is shown that the fourth moment of rotational polarizability coincides with the electron-kinematic index of chirality, introduced previously by one of the authors. The norm of imaginary frequency rotational polarizability is suggested for use as an additional disymmetry index. Illustrative Hartree-Fock calculations of these chirality indices with the 6-31G basis set are performed for hydrogen peroxide, water trimer, and some amino acids. Kharkov State University. Rostov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 319–327, March–April, 1998.     

Determination of the absolute configuration of chiral molecules via density functional theory calculations of vibrational circular dichroism and optical rotation: The chiral alkane D3-anti-trans-anti-trans-anti-trans-perhydrotriphenylene

The Absolute configuration (AC) of the chiral alkane D₃-anti-trans-anti-trans-anti-trans-perhydrotriphenylene (PHTP), 1, is determined by comparison of density functional theory (DFT) calculations of its vibrational circular dichroism (VCD) and optical rotation (OR) to the experimental VCD and OR of (+)−1, obtained in high enantiomeric excess using chiral gas chromatography. Conformational analysis of 1 demonstrates that the all-chair (CCCC) conformation is the lowest in energy and that other conformations are too high in energy to be significantly populated at room temperature. The B3PW91/TZ2P calculated IR spectrum of the CCCC conformation of 1 is in excellent agreement with the experimental IR spectrum, confirming the conformational analysis and demonstrating the excellent accuracy of the B3PW91 functional and the TZ2P basis set. The B3PW91/TZ2P calculated VCD spectrum of the CCCC conformation of S-1 is in excellent agreement with the experimental VCD spectrum of (+)−1, unambiguously defining the AC of 1 to be S(+)/R(−). The B3LYP/aug-cc-pVDZ calculated OR of S-1 over the range 589–365 nm has the same sign and dispersion as the experimental OR of (+)−1, further supporting the AC S(+)/R(−). Our results confirm the AC proposed earlier by Farina and Audisio. This study provides a further demonstration of the excellent accuracy of VCD spectra predicted using Stephens’ equation for vibrational rotational strengths together with the ab initio DFT methodology, and further documents the utility of VCD spectroscopy in determining the ACs of chiral molecules.     

Matrix model to predict specific optical rotations of acyclic chiral molecules

This paper constructs a new matrix model to analyze the relationship of the stereogenic center and its substituents to the specific optical rotation. The variables used as matrix elements include (1) the substituents' comprehensive masses (m), (2) radii (r), (3) symmetries (s), and (4) the electronegativities (χ) of the atoms or groups which are bound to the stereogenic center. Solution of the matrix determinants was postulated to give scalar numbers proportional to the magnitudes of the specific rotations of the molecules being considered. A total of 94 example calculations were performed to predict the relative magnitude and direction of rotation at the sodium D line. Only two calculations failed to predict the correct direction of rotation and this occurred only when their optical rotation values were less than 0.01°. The B3LYP functional at the aug-cc-pVDZ basis set level was also used to compute the optical rotations of the 66 example chiral molecules whose geometries were previously obtained at the B3LYP/6-31G(d) level. The expected successful predictions for these acyclic molecules' optical rotation values did not appear. Overall, the matrix model is one approach to understand the optical rotation.     

Magneto-optical rotation in molecules

A quantum-mechanical theory for the magneto-optica rotation in diamagnetic polyatomic molecules is formulated using the timedependent second-order perturbation theory. The treatment is not restricted to molecules having non-degenerate excited wave functions. The contributions of the induced magnetic moment and the perturbed Boltzmann factor are included. The results are compared with some of the former theories.

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Zusammenfassung Es wird eine quantenmechanische Theorie für die magneto-optische Drehung in diamagnetischen mehratomigen Molekülen unter Anwendung der zeitabhängigen Störungstheorie zweiter Ordnung formuliert. Die Behandlung ist nicht auf Moleküle mit nicht-entarteten angeregten Zuständen beschränkt. Die Beiträge des induzierten magnetischen Moments und des gestörten Boltzmann-Faktors sind eingeschlossen. Die Ergebnisse werden mit denen einiger früherer Theorien verglichen.

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Résumé La théorie des perturbations dépendantes du temps, limitée au second ordre, est utilisée pour formuler une théorie quantique de la polarisation rotatoire magnétique dans les molécules polyatomiques diamagnétiques. L'étude est étendue aux molécules ayant des fonctions d'onde excitées dégénérées. On tient compte de l'effet du moment magnétique induit et du facteur de Boltzmann perturbé. Les résultats sont comparés à ceux de certaines théories antérieures.

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The work reported in this paper has been supported in part by the King Gustaf VI Adolf's 70-Years Fund for Swedish Culture, the Knut and Alice Wallenberg's Foundation, and in part by the U.S. Public Health Service Research Grant under Contract CA 06850-01 with Uppsala University.

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On leave from: Department of Materials Science, The University of Electro-Communications, Chofu-shi, Tokyo, Japan.

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I should like to thank Professor P. O. Löwdin for valuable discussions. This paper is dedicated to Professor Masao Kotani on his sexagenary birthday.     

Three-coupled-oscillator model for nonlinear optical response of chiral molecules with tripod-like structure

In this paper, we further study on the relation between the first hyperpolarizability and molecular configuration based on the three-coupled-oscillator model proposed by us. The model is suitable for chiral molecules with the tripod-like structure. We numerically simulate the spectra of first hyperpolarizabilities, and investigate the effects of molecular chiral parameters and coupling coefficients on the hyperpolarizabilities. As an example, we show a calculation of the first-hyperpolarizability spectra for NPAN molecules, which accord well with the experimental result obtained by Barzoukas et al. [M. Barzoukas, D. Josse, P. Fremaux, J. Zyss, J. Opt. Soc. Am. B 4 (1987) 977–986].     

Temperature dependence of specific optical rotation of an aqueous levoglucosan solution

Russian Chemical Bulletin -     

Determination of absolute configuration using density functional theory calculation of optical rotation: chiral alkanes

The recently developed Gauge-Invariant (Including) Atomic Orbital (GIAO) based Time-Dependent Density Functional Theory (TDDFT) methodology for the calculation of transparent spectral region optical rotations of chiral molecules provides a new approach to the determination of absolute configurations. Here, we discuss the application of the TDDFT/GIAO methodology to chiral alkanes. We report B3LYP/aug-cc-pVDZ calculations of the specific rotations of the 22 chiral alkanes, 2-23, of well-established Absolute Configuration. The average absolute deviation of calculated and experimental [alpha](D) values for molecules 2-22 is 24.8. In two of the molecules 2-23, trans-pinane, 10, and endo-isocamphane, 13, the sign of [alpha](D) is incorrectly predicted. Our results demonstrate that absolute configurations of alkanes can be reliably assigned by using B3LYP/aug-cc-pVDZ TDDFT/GIAO calculations if, but only if, [alpha](D) is significantly greater than 25. In the case of (-)-anti-trans-anti-trans-anti-trans-perhydrotriphenylene, 1, [alpha](D) is -93 and TDDFT/GIAO calculations reliably lead to the absolute configuration R(-).     

Photo-orientation phenomena in photosensitive chiral nematic copolymers

Photo-orientational phenomena have been studied for two comb-shaped cholesteric copolyacrylates containing azobenzene side groups. Copolymer ^I contains nematogenic phenyl benzoate groups and photosensitive chiral menthyl-containing azobenzene side groups. Copolymer ^II is composed of nematogenic phenyl benzoate groups, photosensitive cyanoazobenzene groups and chiral photochromic benzylidene- ^p -methan-3-one fragments. Under the action of polarized Ar⁺ laser light (488 nm), orientation of the side groups of the copolymers takes place, and this orientation is perpendicular to the vector of the electric field of the incident light. This process shows a co-operative character; that is, it involves both photosensitive azobenzene and phenyl benzoate groups. The kinetics of growth of the photoinduced orientational order parameter were studied as a function of film thickness, incident light intensity, and preliminary UV irradiation. For the planar oriented films of the copolymers, irradiation with polarized light leads to the development of photoinduced birefringence δ ⁿ ; maximum values of δ ⁿ reach 0.01. The photo-optical properties of copolymers ^I and ^II are compared. Such materials may be used for ‘dual’ data recording by varying the helix pitch, selective light reflection maximum, and photoinduced birefringence or linear dichroism.     

Photo-orientation phenomena in photosensitive chiral nematic copolymers

Photo-orientational phenomena have been studied for two comb-shaped cholesteric copolyacrylates containing azobenzene side groups. Copolymer^I contains nematogenic phenyl benzoate groups and photosensitive chiral menthyl-containing azobenzene side groups. Copolymer^II is composed of nematogenic phenyl benzoate groups, photosensitive cyanoazobenzene groups and chiral photochromic benzylidene-^p-methan-3-one fragments. Under the action of polarized Ar⁺ laser light (488 nm), orientation of the side groups of the copolymers takes place, and this orientation is perpendicular to the vector of the electric field of the incident light. This process shows a co-operative character; that is, it involves both photosensitive azobenzene and phenyl benzoate groups. The kinetics of growth of the photoinduced orientational order parameter were studied as a function of film thickness, incident light intensity, and preliminary UV irradiation. For the planar oriented films of the copolymers, irradiation with polarized light leads to the development of photoinduced birefringence Δⁿ; maximum values of Δⁿ reach 0.01. The photo-optical properties of copolymers^I and ^II are compared. Such materials may be used for 'dual' data recording by varying the helix pitch, selective light reflection maximum, and photoinduced birefringence or linear dichroism.     

Semiclassical theory of optical rotation. Application of a closed form solution of the optical activity problem

A previously derived closed form solution to the problem of an atom interacting with an externally supplied classical circularly-polarized electromagnetic field is extended to the case of a freely rotating molecule. It is shown how the conventional Rosenfeld expression for the optical rotation parameter may be derived from the present formalism.     

Classification of topologically chiral molecules

Graphs are partitioned into six classes from the perspective of chirality, depending on whether they are topologically achiral, whether there is at least one topologically achiral embedding, whether there is at least one rigidly achiral embedding, and whether there is at least one rigidly achiral presentation. Three of these classes are well represented by a variety of chemical structures: topologically chiral molecular graphs with no topologically achiral embeddings, topologically chiral molecular graphs with at least one rigidly achiral embedding, and topologically achiral molecular graphs with at least one rigidly achiral presentation. Known representatives of these three classes are described. Various meanings associated with the concepts molecular graph and intrinsic chirality are critically discussed. Previous arrangements of molecular graphs and molecules in a hierarchical order, ranging from the most to the least chiral, are interpreted in terms of the graph's and molecule's chiral persistence.     

Temperature dependence of the optical rotation in six bicyclic organic molecules calculated by vibrational averaging.

The vibrational corrections and the temperature dependence of the specific rotation of six rigid organic molecules (alpha-pinene, beta-pinene, cis-pinane, camphene, camphor, and fenchone) were calculated at three wavelengths using hybrid time-dependent density functional theory (TDDFT). A technique for calculating the temperature dependence of the vibrational average of a molecular property has been applied to obtain the specific rotation of the molecules as a function of temperature. For cases in which accurate equilibrium optical rotations can be obtained as a "base value," and for which there is little effect from solvation, accurate predictions of the trends in the temperature-dependence of the specific rotations can be calculated. For other cases, the method can be used to extract purely vibrational contributions to the overall temperature dependence of optical rotation.     

The polarization phenomena of spherical molecules

The calculation of the polarizabilities of spherical molecules is discussed in the light of the average excitation energy approximation to perturbation theory. It is shown that whilst information about the energy in external fields can always be obtained from polarization phenomena, some information about the unperturbed wave function also can be obtained from magnetic susceptibility and Cotton–Mouton effect measurements. In the case of argon such information was found to agree with the results of self-consistent-field calculations. Predictions of the Cotton–Mouton constants of krypton and xenon are made.