Electrical moments quantum-mechanical wave function

In his pioneering work Baetzold used the Hartree-Fock (HF) method for quantum mechanical calculations for the cluster structure (the details are summarized in Reference 33). The value of the HF procedure is that it yields the best possible single-determinant wave function, which in turn should give correct values for expectation values of single-particle operators such as electric moments and... 

Although the relation between the vibrational g factor and the derivative of electric dipolar moment, equation (10), is formally equivalent to the relation between the rotational g factor and this dipolar moment, equation (9), there arises an important distinction. The derivative of the electrical dipolar moment involves the linear response of the ground-state wave function and thus a non-adiabatic expression for a sum over excited states similar to electronic contributions to the g factors. The vibrational g factor can hence not be partitioned in the same as was the rotational g factor into a contribution that depends only on the ground-state wave function and irreducible non-adiabatic contribution. Nevertheless g "(R) is treated as such. A detailed expression for ( ) in terms of quantum-mechanical operators and a sum over excited states, similar to equations (11) and (12), is not yet reported. 

One of the more profound manifestations of quantum mechanics is that this curve does not accurately describe reality. Instead, because the motions of electrons are correlated (more properly, the electronic wave functions are correlated), the two atoms simultaneously develop electrical moments that are oriented so as to be mutually attractive. The force associated with tills interaction is referred to variously as dispersion , the London force, or the attractive van der Waals force. In the absence of a permanent charge, the strongest such interaction is a dipole-dipole interaction, usually referred to as an induced dipole-induced dipole interaction, since the moments in question are not permanent. Such an interaction has an inverse sixtli power dependence on the distance between the two atoms. Thus, the potential energy becomes increasingly negative as the two noble gas atoms approach one another from infinity. 

Not only must the difference E2 - E1 be correct for absorption but also there must always be a change in the dipole moment of the molecule in going from one energy level to another. Only when this is true can the electric field of the light wave interact with the molecule. A further limitation comes from the symmetry properties of the wave functions associated with each energy level. Quantum mechanical considerations... 

Optical absorption in a medium can take place because of the existence of electric or magnetic dipole moments associated with atomic, molecular or crystal entities. Unless otherwise specified, only electric dipoles are considered here. In quantum mechanics, the condition related to the dipole moment for discrete optical absorption appears in terms of transition probability between the initial and final states. It can be formally expressed as the modulus squared of a matrix element involving the wave functions and final states and the electric dipole operator, which reduces, within a proportionality factor to the general displacement coordinate ra ... 

Guided by the result in classical mechanics, that the amount of energy radiated by an oscillating charge is related to the dipole moment, the new quantum theory attempts to construct in terms of wave functions the quantity which will represent a fluctuating electric dipole moment. The function... 

---