Do We Understand The Chemical Bond?

Following the *Alternative interpretations* theme, I shall write a series of posts about the chemical bond. As to why, and I hope to suggest that there is somewhat more to the chemical bond than we now consider. I suspect the chemical bond is something almost all chemists "know" what it is, but most would have trouble articulating it. We can calculate its properties, or at least we believe we can, but do we understand what it is? I think part of the problem here is that not very many people actually think about what quantum mechanics implies.

In the August*Chemistry World* it was stated that to understand molecules, all you have to do is to solve the Schrödinger equation for all the particles that are present. However, supposing this were possible, would you actually understand what is going on? How many chemists can claim to understand quantum mechanics, at least to some degree? We know there is something called "wave particle duality" but what does that mean? There are a number of interpretations of quantum mechanics, but to my mind the first question is, is there actually a wave? There are only two answers to such a discrete question: yes or no. De Broglie and Bohm said yes, and developed what they call the pilot wave theory. I agree with them, but I have made a couple of alterations, so I call my modification the guidance wave. The standard theory would answer no. There is no wave, and everything is calculated on the basis of a mathematical formalism.

Each of these answers raises its own problems. The problem with there being a wave piloting or guiding the particle is that there is no physical evidence for the wave. There is absolutely no evidence so far that can be attributed solely to the wave because all we ever detect is the particle. The "empty wave" cannot be detected, and there have been efforts to find it. Of course just because you cannot find something does not mean it is not there; it merely means it is not detectable with whatever tool you are using, or it is not where you are looking. For my guidance wave, the problem is somewhat worse in some ways, although better in others. My guidance wave transmits energy, which is what waves do. This arises because the phase velocity of a wave equals E/p, where E is the energy and p the momentum. The problem is, while the momentum is unambiguous (the momentum of the particle) what is the energy? Bohm had a quantum potential, but the problem with this is it is not assignable because his relationship for it did not lead to a definable value. I have argued that to make the two slit experiment work, the phase velocity should equal the particle velocity, so that both arrive at the slits at the same time, and that is one of the two differences between my guidance wave and the pilot wave. The problem with that is, it puts the energy of the system at twice the particle kinetic energy. The question then is, why cannot we detect the energy in the wave? My answer probably requires another dimension. The wave function is known to be complex; if you try to make it real,*e.g.* represent it as a sine wave, quantum mechanics does not work.

However, the "non-real" wave has its problems. If there is actually nothing there, how does the wave make the two-slit experiment work? The answer that the "particle" goes through*both* slits is demonstrably wrong, although there has been a lot of arm-waving to preserve this option. For example, if you shine light on electrons in the two slit experiment, it is clear the electron only goes through one slit. What we then see is claims that this procedure "collapsed the wave function", and herein lies a problem with such physics: if it is mysterious enough, there is always an escape clause. However, weak measurements have shown that photons go though only one slit, and the diffraction pattern still arises, exactly according to Bohm's calculations (Kocsis, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer *Science 332*: 1170 – 1173.) There is another issue. If the wave has zero energy, the energy of the particle is known, and following Heisenberg, the phase velocity of the wave is half that of the particle. That implies everything happens, then the wave catches up and sorts things out. That seems to me to be bizarre in the extreme.

So, you may ask, what has all this to do with the chemical bond? Well, my guidance wave approach actually leads to a dramatic simplification because if the waves transmit energy that equals the particle energy, then the stationary state can now be reduced to a wave problem. As an example of what I mean, think of the sound coming from a church organ pipe. In principle you could calculate it from the turbulent motion of all the air particles, and you could derive equations to statistically account for all the motion. Alternatively, you could argue that there will be sound, and it must form a standing wave in the pipe, so the sound frequency is defined by the dimensions of the pipe. That is somewhat easier, and also, in my opinion, it conveys more information.

All of which is all very well, but where does it take us? I hope to offer some food for thought in the posts that will follow.

In the August

Each of these answers raises its own problems. The problem with there being a wave piloting or guiding the particle is that there is no physical evidence for the wave. There is absolutely no evidence so far that can be attributed solely to the wave because all we ever detect is the particle. The "empty wave" cannot be detected, and there have been efforts to find it. Of course just because you cannot find something does not mean it is not there; it merely means it is not detectable with whatever tool you are using, or it is not where you are looking. For my guidance wave, the problem is somewhat worse in some ways, although better in others. My guidance wave transmits energy, which is what waves do. This arises because the phase velocity of a wave equals E/p, where E is the energy and p the momentum. The problem is, while the momentum is unambiguous (the momentum of the particle) what is the energy? Bohm had a quantum potential, but the problem with this is it is not assignable because his relationship for it did not lead to a definable value. I have argued that to make the two slit experiment work, the phase velocity should equal the particle velocity, so that both arrive at the slits at the same time, and that is one of the two differences between my guidance wave and the pilot wave. The problem with that is, it puts the energy of the system at twice the particle kinetic energy. The question then is, why cannot we detect the energy in the wave? My answer probably requires another dimension. The wave function is known to be complex; if you try to make it real,

However, the "non-real" wave has its problems. If there is actually nothing there, how does the wave make the two-slit experiment work? The answer that the "particle" goes through

So, you may ask, what has all this to do with the chemical bond? Well, my guidance wave approach actually leads to a dramatic simplification because if the waves transmit energy that equals the particle energy, then the stationary state can now be reduced to a wave problem. As an example of what I mean, think of the sound coming from a church organ pipe. In principle you could calculate it from the turbulent motion of all the air particles, and you could derive equations to statistically account for all the motion. Alternatively, you could argue that there will be sound, and it must form a standing wave in the pipe, so the sound frequency is defined by the dimensions of the pipe. That is somewhat easier, and also, in my opinion, it conveys more information.

All of which is all very well, but where does it take us? I hope to offer some food for thought in the posts that will follow.

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