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Ideas of Quantum Chemistry P69

Ideas of Quantum Chemistry P69 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 646 12. The Molecule in an Electric or Magnetic Field q x y z we obtain q i 0 q 2 aqq Eq q cos wt 2 EPqq q q q cos wt x q cos wt 6 E Tqq q q 0 q CoS wt 0 q Cos wt q q q x q cos w t . 12.49 Second SHG and Third THG Harmonic Generation After multiplication and simple trigonometry we have q t I1w 0 q I1u q cos W t M2 w q cos 2 Wt 3.3 ffl q cos 3 Mf 12.50 where the amplitudes v corresponding to the coordinate q e x y z and to the particular resulting frequencies 0 w 2 w 3 w have the following form46 v w 0 q v0 q 12 aqq 0 0 0 1 E qq q 0 0 0 o 0 1 6 E yqq q q 0 0 0 0 q q q q q q 1 4 IL Pq q q 0 - w w 1 4 E yqq q q 0 0 - w w q q q q q q V w q E aqq - w w q 2 Pqq q - w w 0 q q q q q 1 2 E yqq q q - w w 0 0 q q qm q q q 46According to convention a given hyper polarizability e.g. yqqiqiiqm -3 w w w w is accompanied in parenthesis by the frequencies w corresponding to the three directions x y z of the incident light polarization here q q and q preceded by minus the Fourier frequency of the term -3 w which symbolizes the photon energy conservation law . Some of the symbols e.g. Yqq q q - w w - w w after a semicolon have negative values which means a partial as in Yqq q q - w w - w w or complete as in fiq qi qii 0 - w w cancellation of the intensity of the oscillating electric field. 12.5 A molecule in an oscillating electric field 647 8 E E y - - - -.- . q q q 2 q 4 q q q -2 4 yqq q q -2 0 q q q q q 24 Yqq q q -3 . q q q 12.51 12.52 We see that An oscillating electric field may result in a non-oscillating dipole moment related to the hyperpolarizabilities fiq q q 0 - w w and Yqq qq- 0 0 - w w which manifests as an electric potential difference on two opposite crystal faces. The dipole moment oscillates with the basic frequency w of the incident light and in addition with two other frequencies the second 2 w and third 3 w harmonics SHG and THG respectively . This is supported by experiment mentioned in the example at the beginning of the chapter applying incident light of .