tailieunhanh - Ideas of Quantum Chemistry P68

Ideas of Quantum Chemistry P68 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. | 636 12. The Molecule in an Electric or Magnetic Field The next term already takes into account that the induced moment also interacts with the electric field eq. 0 i n - E n l 0 E 1 X-------E 0 _ E 0 --- -Maw W 12 39 where the component qq of the polarizability is equal to o 0 rq n n Aq 0 ziojnA qq 2X -----Tn------ where A E - E 0 . The polarizability has the dimension of Similarly we may obtain the perturbational expressions for the dipole quadrupole octupole hyperpolarizabilities etc. For example the ground-state dipole hyperpolarizability ft0 has the form the qq q component where the prime means that the ground state is omitted - we skip the derivation 0 Aq n n rq m l tn Eq 0l 0 Aq n n Eq 0 A q q- g A problem with the SOS method is its slow convergence and the fact that whenever the expansion functions do not cover the energy continuum the result is incomplete. Example 1. The hydrogen atom in an electric field - perturbational approach An atom or molecule when located in electric field undergoes a deformation. We will show this in detail taking the example of the hydrogen atom. First let us introduce a Cartesian coordinate system within which the whole event will be described. Let the electric field be directed towards your right . has the form E E 0 0 with a constant E 0. The positive value of E means according to the definition of electric field intensity that a positive unit charge would move along E . from left to right. Thus the anode is on your left and the cathode on your right. We will consider a weak electric field therefore the perturbation theory is applicable this means just small corrections to the unperturbed situation. In our case the first-order correction to the wave function see eq. will be expanded in the series of hydrogen atoms orbitals they form the complete set 23 cf. Chapter 5 1 WH 1 0 0 1 E 0 k k 0 2 Ek 22Because E2 has the dimension of charge2 x length2 and AK has the dimension of energy as .

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