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Old 04-10-2017, 10:09 PM
 
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Quote:
Originally Posted by Countess Capital View Post
In the VB method, the wave equations as well as in the
theory of resonance are written for each of the possible electronic structures of the molecule [3] (each of
them is called the canonical structure)

Not arguing...just noting...I never wrote that the Wave function was the same equation as the Electromagnetic or Electronic field equation that I presented...I wrote that you need to account for the field equation if assuming the premises that you have proposed; I adhere to the theory that electricity (or electromagnetism) is prevalent in every chemical reaction due to what I term "Atomic Friction" at the electron level or "Molecular Friction" at the molecular level...That is why for example the little crustaceans that glow on the beach and in the ocean through, what is popularly termed "Bioluminescence" " chemiluminescence" or "phosphorescence" is actually an atomic "electro-magnetic" reaction happening between luciferin, luciferase, calcium and magnesium ions at an atomic level which is expressed at the molecular level and which is then witnessed with the unaided eye at the structural level...or for example the fact that static electricity happens over both organic and inorganic structures or photovoltaic reaction that can occur outside of a vacuum...
Essentially, my proposal is that the field creates the environment for the wave to exist as thus we have two very similar equations; "" ( copied from Wikipedia by the way ) and Φ = ∫E cos θdA <---although this has slightly more relaxed assumptions and assumes a degree less of conditionality (and yes is traditionally used between two plates and their dipole moments)
and please visit---> https://en.wikipedia.org/wiki/Electrochemistry ; if you feel so inclined[CENTER]GuardarGuardar[/CENTER]
Okay, I get what you are saying now.

 
Old 04-10-2017, 10:17 PM
 
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Quote:
Originally Posted by chemist777 View Post
To understand the contradiction between the VB theory and the superposition principle, look at this reference (note that the resonance theory is a special case of the VB theory):
http://vixra.org/pdf/1702.0333v2.pdf

What is important to understand in chemistry is that the molecule of benzene, the molecule of methane, and any other molecule are single and real. That is, the substance corresponds to a single molecule and a point (there is tautomerism, etc. phenomena in chemistry, but this does not apply to the case). And if in any theory we come to the result that for the description of a substance (that is, a single molecule) there is a selection of discrete structures, this is fundamentally wrong. That's all.

The reality of the molecules (that they exist and we will find out someday their structure) chemists do not doubt for more than 100 years. Previously, chemists have "shared" into two camps: some believe that we will ever know the true structure of molecules (arrangement of atoms, the structure itself), while others categorically rejected and thought that we will never know the true structure of the molecules, notice is never (does not resemble today's quantum mechanics?), and our designations are only conventions that have nothing to do with the "true" structure. And in all two camps there were the greatest minds of mankind who literally created that chemistry that we know and study.
Most logically and systematically outlined the theory of the chemical structure in 1858 (in fact, the structure of organic compounds) Alexander Mikhaylovich Butlerov (Russian chemist-organic). He was an ardent adherent of the fact that we can learn the true structure of molecules, he created a theory, synthesized isomers to confirm his theory, explained very much in organics. Think about those ancient times, acetic acid was represented by almost 20 formulas (one chemical property - one formula, another - another formula, etc., those formulas were not entirely true).

In the MO theory, it is simpler, with the linear combination of AO receiving MO, but the principle of quantum superposition directly prohibits this, that's all.
I will quote:
"It should also be noted that since L. Pauling's resonance theory is a particular case of the VB theory, the
conclusion made about the insuperable conflict of resonance theory with the quantum superposition
principle [4] can be transferred to the VB theory. In the VB method, the wave equations as well as in the
theory of resonance are written for each of the possible electronic structures of the molecule [3] (each of
them is called the canonical structure) and the total function ψ is obtained by summing all conceivable
functions with the corresponding weight coefficients:
ψ = С1ψ1 + С2ψ2 + С3ψ3 + …
where ψ1, ψ2, ψ3 — are wave functions of canonical structures.
In calculations using the MO method, the wave function is represented by a linear combination of
overlapping atomic orbitals [3] (called linear combination of atomic orbitals):
ψ = С1ψ1 + С2ψ2
where ψ1, ψ2 — wave functions of atomic orbitals, and С1, С2 — represent their weight coefficients.
But then it is obvious that both the MO method and the VB method contradict the principle of quantum
superposition. Since the real molecule in the VB method will be described by a discrete set of canonical
structures, which does not correspond to the existence of a single real molecule.
Similarly, in the MO method, the molecular orbital will be described by a discrete set of AO, which also
does not correspond to the provisions of the MO theory. Next, we will carry out a more detailed analysis
of the theory of the VB and the theory of MO." p. 2 http://vixra.org/pdf/1704.0068v1.pdf

Now about the multiplication of wave functions: they multiply in the VB theory (here it is essential), but then there will be a description not of molecules of ensembles of atoms for the reasons described in the work.

And yes, the wave function has nothing to do with the electromagnetic field, it's a bit different.

In quantum mechanics, there are no trajectories of particle, there is a principle of uncertainty, and many things are still saving, only a probabilistic picture of the world (in fact, a wave function), all other interpretations were less successful.
Okay, let me boil this down really to the fundamentals. Why does ψ = С1ψ1 + С2ψ2 + С3ψ3 + …, and ψ = С1ψ1 + С2ψ2 contradict quantum superposition? They seem to be identical to the general superposition equation.

Let's assume you flip a coin that behaves quantum mechanically. The "wave function" would be ψ = 0.5|heads>+0.5|tails>. Before you make an observation of the coin, the coin is in a quantum superposition of heads and tails. When you make the observation, the wave function collapses, either to the state |heads> or the state |tails>. I don't see how this is different for orbitals. Before you make a measurement/observation of the molecule, the molecule exists in a superposition of states.
 
Old 04-11-2017, 11:16 AM
 
19 posts, read 15,473 times
Reputation: 20
The idea of the VB method is that the real molecule is described by a selection of canonical structures. And if this is so, then according to the equation VB (linear combination) and PQS we will have a discrete description of the molecule. But chemists know for sure that this is not so. If the discrete description were correct, many characteristics of the molecule (experimentally determined and not only) would have a discrete spectrum of values. But this is not so.

This requires a "chemical" understanding of the problem. The Pauling theory of resonance (a special case of the VB method) for the description of benzene is very indicative in this case. So, we have the resonance of the horse and donkey (canonical structures, Kekule structures) and as a result of their resonance we will have a hybrid, that is, a mule (the real molecule of benzene). Note, not a discrete selection of horse and donkey, but mule (the animal has a genetic hybrid of a horse and a donkey). This comparison is known in organic chemistry for a very long time (the Welland, University of Chicago) and is used in textbooks to understand the essence of resonance.
In the MO method, in essence, the same happens, only with AO and MO orbitals.
 
Old 04-11-2017, 11:42 AM
 
Location: Groznia
205 posts, read 149,165 times
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Quote:
Originally Posted by Iaskwhy View Post
Okay, I get what you are saying now.
My biggest conceptual dilemma, Iaskwhy, is one that I have continual dreams over---in fact, I had a dream about it last night, and the direction to which our OP moderator has steered the discussion; is which is a prequisite condition for the other a wave or a field? If we examine the very rudimentary analysis of a wave (or wavelength) for example, a practitioner must present the problem and the basic properties of a wave or wavelength initially, on the Cartesian plane (an interpretation of a two-dimensional field) or if they are exceptional prolific on the three-dimensional plane...within Einstein's theory of relativity "spacetime," in its natural state is essentially an undisturbed field; particle interactions (that later constitute the existence of gravity) which make up "waves" thus disturb the field (perturbation theory) to create waves within the field...and for example, If light is a photon (particle) that exhibits a behavioral pattern that is characteristic of a wavelength then it must be operating in a larger field...but at the same time it is difficult to describe a field or its properties without referring to the basic waves that constitute its dimensions (for example an electromagnetic field is comprised of electronic wavelengths; I've called this a "WAVE-FIELD" or "Field of Waves" to keep myself sane)... I realize that this concept is restricted when all constituents are subject to gravity and atmosphere with the exception of light but, even light becomes subject to the Earth's atmosphere under photovoltaic conditions (e.g. at Earth's surface) but, if we proceed with the rationale of this argument we can begin to visualize an infinite amount of fields and waves that are all interacting with one another...
 
Old 04-11-2017, 01:11 PM
 
1,770 posts, read 1,290,462 times
Reputation: 1694
Quote:
Originally Posted by Countess Capital View Post
My biggest conceptual dilemma, Iaskwhy, is one that I have continual dreams over---in fact, I had a dream about it last night, and the direction to which our OP moderator has steered the discussion; is which is a prequisite condition for the other a wave or a field? If we examine the very rudimentary analysis of a wave (or wavelength) for example, a practitioner must present the problem and the basic properties of a wave or wavelength initially, on the Cartesian plane (an interpretation of a two-dimensional field) or if they are exceptional prolific on the three-dimensional plane...within Einstein's theory of relativity "spacetime," in its natural state is essentially an undisturbed field; particle interactions (that later constitute the existence of gravity) which make up "waves" thus disturb the field (perturbation theory) to create waves within the field...and for example, If light is a photon (particle) that exhibits a behavioral pattern that is characteristic of a wavelength then it must be operating in a larger field...but at the same time it is difficult to describe a field or its properties without referring to the basic waves that constitute its dimensions (for example an electromagnetic field is comprised of electronic wavelengths; I've called this a "WAVE-FIELD" or "Field of Waves" to keep myself sane)... I realize that this concept is restricted when all constituents are subject to gravity and atmosphere with the exception of light but, even light becomes subject to the Earth's atmosphere under photovoltaic conditions (e.g. at Earth's surface) but, if we proceed with the rationale of this argument we can begin to visualize an infinite amount of fields and waves that are all interacting with one another...
Hahaha, I remember during my undergraduate studies, I asked a professor of mine a similar question. He responded that was a question that cannot be answered and is therefore a question for philosophers. I wasn't content with that answer.
 
Old 04-11-2017, 01:22 PM
 
1,770 posts, read 1,290,462 times
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Quote:
Originally Posted by chemist777 View Post
The idea of the VB method is that the real molecule is described by a selection of canonical structures. And if this is so, then according to the equation VB (linear combination) and PQS we will have a discrete description of the molecule. But chemists know for sure that this is not so. If the discrete description were correct, many characteristics of the molecule (experimentally determined and not only) would have a discrete spectrum of values. But this is not so.

This requires a "chemical" understanding of the problem. The Pauling theory of resonance (a special case of the VB method) for the description of benzene is very indicative in this case. So, we have the resonance of the horse and donkey (canonical structures, Kekule structures) and as a result of their resonance we will have a hybrid, that is, a mule (the real molecule of benzene). Note, not a discrete selection of horse and donkey, but mule (the animal has a genetic hybrid of a horse and a donkey). This comparison is known in organic chemistry for a very long time (the Welland, University of Chicago) and is used in textbooks to understand the essence of resonance.
In the MO method, in essence, the same happens, only with AO and MO orbitals.
You can't even get a discrete value of both the momenta and position of a particle in free-space. What makes you think that quantum supersposition will give you a discrete discription of the molecule?
 
Old 04-11-2017, 01:31 PM
 
19 posts, read 15,473 times
Reputation: 20
"For example, consider two quantum states (actually existing) are described by wave
functions ψ1 and ψ2. From the principle of superposition [1, p. 21] it should be clearly, that their
linear combination (ψ3 = C1ψ1 + C2ψ2) will be the third quantum state (as actually existing), which
will be described by a wave function ψ3. What does it mean? The fact that the measurement of a
certain physical value d in the state |ψ1> will result d1, and for measure a value for of d in the state
|ψ2> will result d2. When the third quantum state |ψ3> is realized, then when measuring a physical
quantity, the quantum system will take the values d1 and d2 with probabilities, respectively, |C1|^2
and |C2|^2. That is, in a quantum state |ψ3> when we will have many dimensions sometimes d1
value and sometimes d2 (with certain known frequency). But this is in resonance theory can not be."

"We describe for simplicity resonance of two Kekule structures (resonance structures)
excluding structures Dewar. Then, the resonance theory it is assumed that |ψ1> is a quantum state 1,
which is describes a resonance structure 1 and |ψ2> is a quantum state 2, which is describes a
resonance structure 2.
Wave functions ψ1 and ψ2 for the resonance structures 1 and 2 (Kekule structures):
The linear combination of the (ψ3 = C1ψ1 + C2ψ2) is normally the third quantum state |ψ3>,
which is described by a wave function ψ3 and will describes the actual benzene molecule
(resonance hybrid). The coefficients C1 and C2 will specify the contributions of resonance structures
(Kekule structures, for our case C1/C2 = 1, |С1|^2 = |С2|^2 = 0.5) in a real molecule of benzene
(resonance hybrid), which can not be described by separate resonance structures. And now it is
important to note that the real molecule of benzene it really real and unique, and can not have a
discrete description, ie the measurements we will never "see" the one Kekule molecule (resonance
structure 1), then another (resonance structure 2), and this is directly contrary to the principle of
quantum superposition. Moreover, adopted in theory of resonance Kekule structure, ie resonance
structures are ideal structures that do not exist in reality, because they have all the bonds are equal,
and this is despite the alternation of single and double C-C bonds, which in reality are different
length. Therefore, the principle of quantum superposition (for resonance theory) is not executed,
even for quantum states |ψ1> and |ψ2>, because as resonance structures is not reality, and any
physical quantity (real) we can not measure.
If, however, as the resonance structures we take the real "curved" Kekule structures with ties
that have different lengths, then the resonance theory does not make sense, since the transition from
one structure to the other will vary internuclear distance. But then the principle of quantum
superposition is applicable to all three quantum states (for |ψ1> and |ψ2> it is obvious, and for |ψ3>
will be the one "twisted" Kekule structure, then the other, at 50 : 50). In fact, no change bond
lengths have therefore chemistry is not applicable."

http://vixra.org/pdf/1702.0333v2.pdf
 
Old 04-11-2017, 05:13 PM
 
Location: Groznia
205 posts, read 149,165 times
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Quote:
Originally Posted by Iaskwhy View Post
Hahaha, I remember during my undergraduate studies, I asked a professor of mine a similar question. He responded that was a question that cannot be answered and is therefore a question for philosophers. I wasn't content with that answer.
I have a new friend...
 
Old 04-14-2017, 11:56 AM
 
Location: God's Country
5,188 posts, read 3,788,020 times
Reputation: 8689
This explains why male seahorses bear the young, bumblebees fly, and eohippuses are not extinct but running around in the southern steppes.
 
Old 04-15-2017, 03:40 AM
 
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Quote:
Originally Posted by Iaskwhy View Post

...Another thing, you say "This means that the wave function ψ12 (q1, q2) of the system can be represented as the multiplication of the wave functions ψ1 (q1) and ψ2 (q2) of its parts:". You cannot combine wavefunctions like that unless the particles are distinguishable.

In the case of identical fermions, the wavefunction is

https://wikimedia.org/api/rest_v1/me...2b538e3b283694

In the case of identical bosons, the wavefunction is

https://wikimedia.org/api/rest_v1/me...ed33505b17accb

The wavefunction for identical bosons looks exactly like the one for the MO and VB theories...


You misunderstood what was written in the paper about multiplication of functions. It means system consisting of two parts, and then the wave functions that describe these parts that allow us to obtain wave information that describes the system as a whole.

ψ12 (q1, q2, t) = ψ1 (q1, t) * ψ2 (q2, t)

All this is known and elaborated in quantum mechanics for probably about 100 years. And then parts can be (and will be) different. About the identity of particles is not here. Moreover, electrons are fermions and they are indistinguishable, that is, identical.

Your statement "The wave function for identical bosons looks the same as for MO and VB theories" is not quite correct (I note once again, electrons are fermions and they are identical, that is, indistinguishable). Here everything is more complicated. The point is that the Schrödinger equation does not take into account the spin of the particles. But the electrical interaction does not depend on the spin, and so when the spin is not important, everything is OK (Hamiltonian of a system of electrically interacting particles (In the absence of a magnetic field) does not contain spin operators, and therefore, when applied to the wave function, it does not affect the spin variables in any way).

But if the spin should be taken into account (as in the formation of a chemical bond), then one must understand that the Schrödinger equation Satisfy both the coordinate component (the wave function that depends on the coordinates) of the wave function and the spin component (the wave function depends only on the spin of the particles). That is, the Schrödinger equation can be written in the form:

ψ12 (ξ1, ξ2, ξ3, ξ4...) = ψ1 (r1, r2, r3, r4...) * ψ2 (σ1, σ2, σ3, σ4, …)

where ψ1 is the wave function of the system depending only on the coordinates of the particles,

and ψ2 is the wave function of the system which depends only on the spin of the particles,

Ψ12 (ξ1, ξ2) is, naturally, the wave function of the system, but here it must be noted,
That ξ1, ξ2, ξ3, ξ4 conditionally designate the sets of three coordinates and the projection of the spin of each of the particles.

Now it is necessary to recall that for fermions the principle of indistinguishability of particles leads to the fact that the wave function must be antisymmetric (When the permutation changes sign). For bosons it is symmetric (it does not change sign when it is permuted). This is easy to understand if we write the wave function of the system ψ12 (ξ1, ξ2) as follows:

ψ12 (ξ1, ξ2) = e^(i * α) * ψ12 (ξ1, ξ2)

Where α — is a real constant.

e^(2*i * α) = 1,
e^(i * α) = +, - 1

ψ12 (ξ1, ξ2, ξ3, ξ4) = +, - ψ12 (ξ1, ξ2, ξ3, ξ4)

(In the permutation of indistinguishable particles the wave function of the system can only change to an unimportant phase factor; this follows from the fact that when the particles are rearrangedIdentical states are obtained, that is, the particle systems physically must be completely equivalent).

And after this we return to the equation:

ψ12 (ξ1, ξ2, ξ3, ξ4) = ψ1 (r1, r2, r3, r4...) * ψ2 (σ1, σ2, σ3, σ4, …)

And it is natural that for fermions (the principle of indistinguishability) the total function of the system must be antisymmetric (it changes sign on a permutation), but this function is the product of the coordinate wave function of the system (ψ1 (r1, r2, r3, r4 ...)) and the spin wave function of system (ψ2 (σ1, σ2, σ3, σ4, ...)). Therefore, for a symmetric coordinate function, the spin function must be antisymmetric, and vice versa.

But in quantum mechanics it is shown that a symmetric spinor of the second rank describes a system with a total spin equal to unity (for two particles), and an antisymmetric spinor reduces to a scalar, which corresponds to zero spin.
Therefore, when the chemical bond is formed (two electrons, the spins are opposite, the resultant spin is zero), the spinor ψ2 (σ1, σ2) is antisymmetric, and hence from the equation (see above) we get that ψ1 (r1, r2) is symmetric.
I note that ψ1 (r1, r2) is symmetric, and this is for fermions.
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