Quantum-mechanical calculation of the fourth-order tensor X(4)D (wa; w1, w1, w1, -w2) for a nonracemic solution of chiral molecules

N. I. Konovalov; Tamara M. Il'inova; A. V. Karzanov; Nikolai I. Koroteev

doi:10.1117/12.197458

2 January 1995 Quantum-mechanical calculation of the fourth-order tensor X^(4)D (w_a; w₁, w₁, w₁, -w₂) for a nonracemic solution of chiral molecules

N. I. Konovalov, Tamara M. Il'inova, A. V. Karzanov, Nikolai I. Koroteev

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Proceedings Volume 2370, 5th International Conference on Laser Applications in Life Sciences; (1995) https://doi.org/10.1117/12.197458
Event: Laser Applications in Life Sciences: 5th International Conference, 1994, Minsk, Belarus

Abstract

New spectroscopic schemes studying noncentrosymmetrical media (nonracemic solutions of chiral molecules) are based on investigation of frequency dispersion of the fourth-order dipole susceptibility tensor (chi) _ijklm⁽⁴D)((omega) _a;(omega) ₁,(omega) ₁,(omega) ₁,-(omega) ₂). This paper contains the accurate quantum-mechanical calculations of the resonance part of hyper-polarizability tensor (gamma) '⁽⁴D) and its connection with Raman ((alpha) '⁽²) and hyper-Raman ((beta) '⁽³)) scattering tensors. In the case it was suggested pump frequencies' combination (omega) ₁ - (omega) ₂ scanning one of the vibrational resonance of the molecule: (omega) ₁ - (omega) ₂ approximately equals (Omega) . Tensor (gamma) '⁽⁴D) was averaged over arbitrary orientations of noncentrosymmetrical molecules in the solution by applying irreducible tensors operators' technique giving dipole susceptibility tensor (chi) '⁽⁴D) equals NL⁴<(gamma) '⁽⁴D)>. Symmetry of this tensor coincides with the model calculations. As it was expected, tensor (chi) _ijklm⁽⁴D)((omega) _a;(omega) ₁,(omega) ₁,(omega) ₁,-(omega) ₂) includes only 6 non zero components equal by their absolute values. For centrosymmetrical molecules in isotropic medium tensor (chi) '⁽⁴D) is equal to zero. Similar computations were made in the hyper-Raman resonance case 2(omega) ₁ - (omega) ₂ approximately equals (Omega) .

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N. I. Konovalov, Tamara M. Il'inova, A. V. Karzanov, and Nikolai I. Koroteev "Quantum-mechanical calculation of the fourth-order tensor X^(4)D (w_a; w₁, w₁, w₁, -w₂) for a nonracemic solution of chiral molecules", Proc. SPIE 2370, 5th International Conference on Laser Applications in Life Sciences, (2 January 1995); https://doi.org/10.1117/12.197458

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KEYWORDS

Molecules

Chemical elements

Polarization

Laser applications

Life sciences

Fourier transforms

Magnetism

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