Dipole molecule

because the charges are equal and opposite ... actually, that is only the case for dipoles in electrically neutral systems ... there is no restriction that dipoles cannot be defined for electrically charged systems. To create a dipole, you just need a non-isotropic charge distribution.

Hmmm ... not sure what you are asking here. However, in general, the wavefunctions describing the characteristic states (eigenstates in QM parlance) of any quantum system is related to the energy is a very fundamental way, according to the time-independent Schrodinger equation, which says:

[tex]\hat{H}\psi=E\psi[/tex],

where "H" is the Hamiltonian operator. It's correct definition is indeed technical, but if you can stand a little math, for a simple 1-D system, the expanded version of this equation is:

[tex]\frac{\partial^{2}\psi\left(x\right)}{\partial x^{2}} + \frac{2m}{\hbar^2}\left[E-V\left(x\right)\right]\psi\left(x\right)=0[/tex]

So it is just a simple 2nd-order differential equation, where m is that mass of the particle, E is the total energy, and V(x) is the potential energy, which can be a variable function of position. For a bound system (e.g. and electron orbiting an atom), there are only certain values of E that will satisfy this equation ... these are the characteristic energies (or energy eigenvalues). For each characteristic energy, there is also a characteristic wave-function [tex]\psi(x)[/tex] (called an eigenfunction or eigenstate).

Does that help?

Dipole moment is a vector because both its direction and its magnitude are significant. Just imagine a simple diatomic molecule AB, which has a dipole moment, which we can understand in terms of partial charges on each of the atoms, one positive and an equally large negative partial charge. Now, the physical and chemical properties of that molecule will be different depending on whether the partial positive charge is on atom A, or on atom B.

More generally, if you consider a discrete collection of charges in space, the dipole moment is given by:

[tex]\vec{\mu}=\sum_{i}q_{i}\vec{r_{i}}[/tex]

where q_i is the value of each point charge (positive or negative), and the vector quantity r_i defines the position of each charge relative to some common origin.

Clear?

 

Nobody said that it was ... a dipole certainly has an electric field .. that is how you know it is a dipole. It's just that it has no net charge.

I agree with you in the case of an atom ... electron screening in an atom has the general effect of *decreasing* the attractive coulomb interaction between the nucleus and the other electrons, therefore it results in a higher energy (i.e. less stable) system. However, one could also imagine a case where there is analogous screening of a repulsive interaction, in which case the energy would be decreased, although I cannot think of an example right now.

 

Electrical neutrality only means that a "system" (I'll define that in a minute) has no *net* charge, that is, that all of the positive and negative charges in the systems are exactly balanced.

To define the system, just draw a closed surface in space. There is a theorem of electrostatics called Gauss's theorem, which says that the total charge enclosed in that surface is linearly proportional to electric flux passing through that surface, which is given by the normal component of the electric field, integrated over the enclosing surface. There is also a differential form of the theorem, which just says that the divergence of the electric field surrounding the closed surface is proportional to the charge density inside of it.

So, electrical neutrality does not mean that the electric field surrounding the closed surface defining the system is identically zero everywhere, it just means that it satisfies the conditions of Gauss's theorem (also known as Gauss's Law). Thus it is perfectly consistent for a test charge moving near a neutral system to experience a non-zero electrostatic interaction. In fact, that is how we typically characterize the electrostatic potential of a neutral molecule in chemical physics.