Guys thank you both immensely. Alxm - Cramer goes on to ensembles for molecular dynamics and thermostat and barostat algorithms. Although I have an eternal thirst for knowledge, I'm primarily focused on passing my oral general examination for my PhD at the moment. So I am preparing for...
Yahtzee. Agreed the second term MUST come from the fact that we have a set of interacting particles versus non-interacting. But where do we get the second term from? Is this some empirical lennard-jones treatment? Or can it be derived a priori, as they say. You know what I mean?
I mean the following seriously, not sarcastic or anything: Is your question really a question or a statement. The "net" force within a confined system has to be 0, I suppose, or a jar filled with an "ideal gas" would fall over due to a net force in one direction. However, that would be due to...
The following is a direct quote from Cramer's Essentials of Computational Chemistry:
Assuming ideal gas statistical mechanics and pairwise additive forces, pressure P can be computed as
P(t)=\frac{1}{V(t)}N(kb)(T(t))+(1/3)\sum\sumFF f(ij)r(ij)
My question is: I've always been taught P=NkT/V...
Admittedly I may have been a little irritated with your initial response and I apologize. I'm sure you understand, quantum chemistry can sometimes make one's head spin.
I still seek an answer to my question. I don't care about types of parametrization (e.g. PM3 or AM1) nor method development...
Excuse me for mis-typing then. The Roothan-Hall equations are merely a representation of the HF method, which is an approximation for the determination of the ground-state energy. I didn't realize you needed me to state all that information before asking my actual question. For the record...
In the explicitly-unsolvable Hamiltonian for a chemical system, approximations are made to solve the energy of the system. In particular we see CNDO (ZDO), INDO and MNDO theories.
CNDO - complete neglect of differential overlap; two-center electron integrals are zero.
INDO - intermediate...
From a textbook - The reason why the polarization plays a key role in the description of nonlinear optical phenomena is that a time-varying polarization can act as the source of new components of the electromagnetic field... the wave equation in nonlinear optical media often has the form...
OKAY! okay. But my question is, what is the SIGNIFICANCE of \gamma_{xxxx}
So by my earlier (and likely incorrect) attempt to explain it, this would be the constant of proportionality between the incident electric field and the polarizability of the molecule for the third-order interaction...
I think you are correct about me being wrong. For example, the third-order term is a fourth-rank tensor. So... in that case its \gammaijkl. If my picture were right then the ith direction induced electric field would be the result of the incident field in jth, kth and lth directions but now...
Linear Polarisability \alpha_{ij} is the amplitude of the electric field induced in the molecule in the i direction given a unit amplitude field in the j direction, hence
E_i^{induced} = \alpha_{ij} E_j^{incident}
(observing summation convention)
Extending this physical...