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3

Let me start by saying that this is a very difficult question to answer because it's not very hard to come up with pathological cases which I will address at the end. Also, as you point out, it is somewhat non-trivial to calculate $r_0$ from theory and also somewhat non-trivial to determine $r_e$ from experiment. That being said, I think I have a good first ...


2

The document the OP references has most of the information: The overall measured dipole moment, the way bond dipoles add up to the molecule dipole, and how to calculate the bond dipole. Also, it states that a proton and an electron at a distance of 100 pm have a dipole moment of 4.80 D. From that information, we should be able to figure everything out. Bond ...


2

Is there a difference in interpretation of dipole moment in Physics and Chemistry? Addressing the above part: The definition of dipole moment is the same in physics and chemistry. However, the chemist's dipole moment has opposite directions as compared to the physicist. Which one is right? Of course, the physicists draw it correctly, which is consistent ...


2

Radio waves $10^4$ to $10^{11}$ Hz are not that innocent as is commonly purported. Long time ago there was an demonstration that radio waves of certain frequency can decompose salt water into hydrogen and oxygen (and ignite). There was an article in Popular Mechanics. No other type of radiation can cause this effect. See the video of burning here Burning ...


3

This is a bit of a stretch, but the Zeeman and Stark effects are linked to radio frequencies, in that line splitting of a visible spectral frequency (~10^15 Hz) can give rise to a beat-frequency in the RF. Your answer of NMR, though, is more applicable. The most general term for precession in a magnetic field is Larmor precession.


1

Radio waves have a longer wavelength than infrared radiation and is classified between 3Hz and 300MHz frequencies. Due to its lower energy/longer wavelength, radio waves are able to penetrate deeper than higher energy radiation. For example, the skin depth is a function of frequency: $$\delta = \sqrt{\frac{2 \rho}{\omega \mu}}$$ where $\rho$ is the ...


2

What I think: A macroscopic chaotic system is a system whose "components" influence each other, and the macroscopic outcome depends on the status of the components. This happens for the two-arms pendulum, for air particles in cigarette smoke, and for particles in wind. Each microscopic variation can be propagated between particles, and the final status of ...


2

A homogeneous reaction mixture can hardly show macroscopical chaotic behaviour. Well known cyclic counterexamples exist, and practically any reaction which proceeds faster than diffusion or mechanical mixing can homogenise it again (e.g. any reaction that generates a lot of heat!) is liable to show some intermediate chaotic concentration gradients. Its ...


7

Well, this is a rather obvious development (in retrospect, that is). We had an $sp^3$ carbon with tetrahedral bonds, and it made diamond. We had an $sp^2$ carbon with trigonal bonds, and it made graphite. What if we just had a linear $sp$ carbon? Such thoughts have been around for more than quite a while. Theorists swarmed around that non-existent tree. No ...


10

It is perfectly fine, and actually quite common, to use big basis sets for the most important atoms (perhaps at the active site of the chemical reaction) and a smaller basis set for the surrounding hydrogen atoms (for example). The only problem you might face would be, that this complicates the basis set extrapolation to get closer to the complete basis set ...


3

As you have already stated in the question, (Ineq. 1) is the standard inequality used in Cauchy-Schwarz integral screening. (Ineq. 2) and (Ineq. 3) are not valid inequalities, which is clear if you select atomic orbitals such that a & b are spatially disjoint from c & d and the proposed upper bounds vanish. (Ineq. 4), (Ineq. 5), and (Ineq. 6) follow ...


7

I think it's useful to expand slightly on the comments because I think the language here should be as clear as possible. You're concerned about the convergence of the integral of a function when some piece of the function is unbounded, i.e., for $f(x)$ on domain $[a, b]$, $\exists c \in [a,b]$ such that $f(c) = \infty$. Frequently, integrals of this type do ...


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