Electronic configuration quantized states

Ail the above choices present some problems. The definition of the diabatic states is complicated, and the associated solvent coordinate is only valid if the solute wave function may be written as a linear combination of the two diabatic states. If more complex wave functions are used (Cl, for instance), a larger set of solvent coordinates must be introduced. In this case it is necessary to consider as many solvent coordinates as electronic configurations. Anyway, we cannot forget to recall that just this diabatic states description has more recently permitted a very interesting development of the continuum solvent methods with the introduction of a full quantization of the solvent electronic polarization in the work of Kim and Hynes, ... 

The symmetry properties of the quantities used in the theory of complex atomic spectra made it possible to establish new important relationships and, in a number of cases, to simplify markedly the mathematical procedures and expressions, or, at least, to check the numerical results obtained. For one shell of equivalent electrons the best known property of this kind is the symmetry between the states belonging to partially and almost filled shells (complementary shells). Using the second-quantization and quasispin methods we can generalize these relationships and represent them as recurrence relations between respective quantities (CFP, matrix elements of irreducible tensors or operators of physical quantities) describing the configurations with different numbers of electrons but with the same sets of other quantum numbers. Another property of this kind is the symmetry of the quantities under transpositions of the quantum numbers of spin and quasispin. 

The operator of the energy of electrostatic interaction of electrons in (14.65) is represented as a sum of second-quantization operators, and the appropriate submatrix element of each term is proportional to the energy of electrostatic interaction of a pair of equivalent electrons with orbital Lu and spin S12 angular momenta. The values of these submatrix elements are different for different pairing states, since, as follows from (14.66), the two-electron submatrix elements concerned are explicitly dependent on L12, and, hence, implicitly - on S12 (sum L12 + S12 is even). It is in this way that, in the second-quantization representation for the lN configuration, the dependence of the energy of electrostatic interaction on the angles between the particles shows up. This dependence violates the central field approximation. 

The second-quantization counterpart of this approach is the replacement (for the lN configuration) of operator (14.65) by some effective operator, whose two-particle submatrix elements are independent of characteristics L12, S12 of the pairing state of electrons. To this end, we introduce the submatrix element averaged over the number of various antisymmetric pairing states in shell, equal to (4/ + 2)(4/ + l)/2 ... 

A. Potential surfaces for Hg Ar2 Hg in its ground electronic state is spherical. The interactions are only function of the distance between atoms, independently of the quantization axis considered. Hence the equilibrium configuration is T-shaped, with the individual atom-atom distances given by the minimum of the corresponding two body-potentials, the well depth being the sum of the atom-atom well depths = 373.045 cm , = 3.76 A and... 

Chapters 1-3 introduce second quantization, emphasizing those aspects of the theory that are useful for molecular electronic-structure theory. In Chapter 1, second quantization is introduced in the spin-orbital basis, and we show how first-quantization operators and states are represented in the language of second quantization. Next, in Chapter 2, we make spin adaptations of such operators and states, introducing spin tensor operators and configuration state functions. Finally, in Chapter 3, we discuss unitary transformations and, in particular, their nonredundant formulation in terms of exponentials of matrices and operators. Of particular importance is the exponential parametrization of unitary orbital transformations, used in the subsequent chapters of the book. 

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