Does Quantum Mechanics Explain Chemical Bonding?

This is a follow up of the recent post posing the question if quantum mechanics explains the Periodic Table connecting to the work by Eric Scerri as a world authority on the chemistry of the Periodic Table. In this article from 2023 A commentary on Robin Hendry’s views on molecular structure, emergence and chemical bonding Scerri starts out:

• There is a long-standing problem in the philosophy of chemistry arising from the fact that molecular structure cannot be strictly derived from quantum mechanics. 
• Two or more compounds which share a molecular formula, but which differ with respect to their structures, have identical Hamiltonian operators within the quantum mechanical formalism. 
• As a consequence, the properties of all such isomers yield precisely the same calculated quantities such as their energies, dipole moments etc. 
• The only means through which the difference between the isomers can be recovered is to build their structures into the quantum mechanical calculations, something that is carried out by the application of the Born-Oppenheimer approximation. 
•  I agree that chemists view bonding in a more realistic fashion and may consider bonds to be in some senses real, while physicists may consider bonding in more abstract energetic terms. 

We learn from Scerri that quantum mechanics does not distinguish between isomers like C2H5OH (ethanol)  CH3OCH3 (dimethyl ether) with vastly different chemistry from different bonding and so must be complemented by some form of expertise, which differs between chemists who seek explanation in some real terms and physicists satisfied with something purely abstract.

RealQM is a new form of quantum mechanics in terms of classical continuum mechanics as a system of non-overlapping charge densities with direct physical meaning in 3d space, which meets a chemist's demand of a reality. In RealQM the formation/bonding of a molecule can be simulated which can make a distinction between isomers without need of expertise. The window opened by RealQM is explored in posts on Real Quantum Chemistry. 

Non-Overlapping Wave Functions/Charge Densities

This is a follow up of the recent post on The Secret of Covalent Bonding with further computations comparing the non-overlapping wave functions/charge densities of RealQM meeting with (i) continuity and zero derivative, with a hypothetical case of instead (ii) zero density. 

To pin-point the essential aspect, we consider the following 1d model problem of an atom with N electrons: 

Find the function $\Psi (x)$ on the interval $[0,1]$ which minimises the energy $E=E_k + E_p$ with

• $E_p=\frac{1}{2}\int_0^1D\psi^2dx$             (kinetic energy)
• $E_k =-\int_0^1P(x)\psi (x)$           (potential energy)

over wave functions $\psi (x)$ with $D\psi =\frac{d\psi}{dx}$ the derivative, with total charge 

• $\int_0^1\psi^2dx = N$,

where $-P(x)$ is a given potential.

The Ansatz of RealQM is to seek $\Psi (x)$ on the form 

•  $\Psi (x) = \Psi_1(x) + \Psi_2(x) + .... + \Psi_N(x)$,

where the $\Psi_i(x)$ are one-electron wave functions with disjoint supports which meet on a Bernoulli free boundary with continuity and zero derivative. Running this code in a case with $N=4$ and $P(x)$ the potential from two kernels, we get the following result for case (i): 

We see in red 4 non-overlapping wave functions meeting at a free boundary marked by green with continuity and zero derivative. The total energy is -247 with kinetic energy 30. 

We run the same code but require wave-functions to vanish at meeting points and get for case (ii):

We see total energy larger total energy -231 with much larger kinetic energy 308. 

We understand that requiring wave functions to vanish as in (ii) when meeting, gives much larger kinetic energy than asking only for continuity and zero derivate as in (i), and that the net effect is larger total energy.

The purpose of this exercise is to exhibit the possibility opened by RealQM of electron concentration between kernels decreasing potential energy without balancing increase of kinetic energy, which appears as the holy grail of covalent bonding. 

In StdQM wave functions have global support, which may be overlapping, and so like the functions in (ii) above have to pay a price of added kinetic energy from charge concentration which is less favourable for binding than RealQM.

The finding of this post agrees with the real case considered in previous posts.

 

Does Quantum Mechanics Explain the Periodic Table?

Eric Scerri is a leading expert on the Periodic Table as the foundation of chemistry. This is what chatGPT says when asking the simple question to what extent the Periodic Table, formed before the emergence of quantum mechanics in the 1920s, has been explained by quantum mechanics during the now 100 years since then:

Eric Scerri, a philosopher and historian of chemistry, is known for his critical stance on the idea that quantum mechanics fully explains the periodic table. While he acknowledges the importance of quantum mechanics in understanding atomic structure and trends in the periodic table (such as electron configurations, periodicity, and chemical behavior), Scerri argues that the explanation is incomplete or limited if we rely solely on quantum mechanics.

Here are the key points of Scerri's position:

1. Quantum mechanics is useful but not fully explanatory: Scerri believes that while quantum mechanics (especially the Schrödinger equation and quantum numbers) helps rationalize some features of the periodic table, it does not provide a complete or entirely satisfactory explanation, especially for the actual order of elements.

2. Electron configurations are not derived solely from quantum mechanics: He points out that the Aufbau principle, which is used to predict electron configurations, is not a strict consequence of quantum theory but rather a semi-empirical rule. Some observed configurations (especially for heavier elements) deviate from the predicted ones.

3. Many-body problem: Scerri highlights the complexity of solving the many-body Schrödinger equation for atoms with more than one electron. Since exact solutions don't exist for such systems, approximations are required, which limits the explanatory power of quantum mechanics.

4. Philosophical perspective: He often argues from a philosophy of science perspective, suggesting that science often progresses through approximations, models, and partial explanations, rather than final, complete theories. Thus, he sees the periodic table as something emergent, not entirely reducible to quantum mechanics.

5. Chemistry's autonomy: Scerri also defends a degree of autonomy for chemistry, pushing back against the idea that chemistry is just applied physics. He sees the periodic system as a chemical construct that has its own foundations and logic, not fully subsumed under physics.

In summary, Scerri does not reject quantum mechanics, but he questions the common claim that it fully explains the periodic system. He calls for a more nuanced understanding of how different scientific disciplines interrelate, especially in the case of chemistry and physics.

We learn that Scerri as an expert in the field does not see that the Periodic Table can satisfactorily be explained by quantum mechanics and so calls for something more. But there is nothing more to grab. Quantum mechanics is supposed to be the best scientific model/explanation of the physics of atoms forming molecules forming chemistry. Quantum mechanics has fully replaced older atomic theories. If quantum mechanics cannot explain the Periodic Table, nothing can it would seem. 

The basic feature of the Periodic Table are the periods 2, 8, 18 and 32 of the form $2n^2$ with $n=1,2,3,4$, which appear as the number of atoms/elements in the rows of the table as 2, 8, 8, 18, 18, 32 and 32 thus with repetitions, as the number of electrons of the noble gases at the end of the row. What is the quantum mechanical explanation of these periods? 

The story is that this is because the eigenfunctions of the Schrödinger equation for the Hydrogen atom with one electron appear with a multiplicity of $n^2$ for $n=1,2,3,4$, which is doubled to fit with $2n^2$ by counting each electron twice. 

But the logic appears to be missing: Why expect the multiplicity of eigenfunctions of the Hydrogen atom with one electron to give the periodicity of atoms with many electrons? Why double the count of the number of electrons? Why is the periodicity repeated?

As concerns the sequence $2n^2$, there are many ways to this result. In RealQM it comes out as the solution to an electron packing problem partitioned into shells $n=1,2,3,...$ of increasing radius divided into half-shells filled with up to $n^2$ electrons allowing repetition of periods. This explanation carries the physical logic of packing of electrons of occupying different volumes depending on distance to the kernel.   

Stupid Swedish Foreign Policy

All political parties in Sweden from left to right have come to a historic consensus on foreign policy:

1. Trump is bad even if what he now does is to continue the politics of Biden: Genocide in Gaza, proxy war against Russia in Ukraine and bombing of the Houtis. 
2. Putin is bad and the only way to stop him from invading Sweden is to participate in the US/NATO proxy war against Russia in Ukraine with maximal military support.  

1. means that Trump will not come to help Sweden in case of Russian retaliation because of 2. Worst possible combination.

This is leading into catastrophe for the Swedish people, but opposition to this stupid policy is suppressed by very effective propaganda.

A better alternative is to come to a peaceful agreement with Putin by stoping sending Swedish weapons to Ukraine. This would open to rightful criticism of Trump without ruining Swedish society.

Form Classical to Modern to Post-Modern Physics

Classical physics in the form Newtonian mechanics emerged during the scientific revolution of the 18th and 19th centuries from an Enlightenment of rational logic/mathematics combined with observation of reality in a fundamental shift away from religion scholastics. The basic idea was rational mechanics as physics, which was (more or less) understandable and not only magical.  

In the late 19th century classical physics incorporated electro-magnetics made understandable through Maxwell's equations.  

But the modern physics of relativity theory and quantum mechanics emerging in the beginning of the 20th century signified a return to magical thinking. 

All the great physicists of the 20th century Einstein, Bohr, Schrödinger, Dirac, Feynman, Gell Mann, Weinberg admitted that quantum mechanics cannot be understood, while suggesting that this only adds to its beauty as the prime achievement of human intellect. 

To teachers of quantum mechanics this created a problem: How to teach a subject that is not understood by even the sharpest minds? The only way out for the average teacher was to pretend to understand and refer to the admissions of the top physicists of non understanding, as only a sort of teasing: Of course quantum mechanics is well understood and so can be presented in text books to students expected to come to understanding by diligent study. 

The computer is often presented as an off-spring of quantum mechanics thus showing its power, but the first realisations of the idea of a computer was made in rational mechanical terms as the Analytical Engine by Babbage with all its wheels and gears. A realisation in terms of quantum mechanics would be a quantum computer but the question is if there will ever be such a thing. 

Is it possible to imaging a form of post-modern physics with a return to the rationality of classical physics. My answer in all modesty is RealQM.  

Ab Initio Chemistry: StdQM vs RealQM

Discovering the World from a desk.

The ideal mathematical model of some physics is according to Einstein a model without parameters. Newton's Law of Gravitation is the prime example within classical physics/mechanics taking the from

• $\Delta\phi (x)  = \rho (x)$

where $\phi (x)$ is gravitational potential, $\rho$ mass density and $\Delta$ the Laplacian differential operator with respect to a Euclidean coordinate $x$. 

The prime example within modern physics/quantum mechanics is Schrödinger's equation for the hydrogen atom taking the form of an eigenvalue problem with eigenvalue $E$ 

• $-\frac{1}{2}\Delta\psi (x) -\frac{\psi (x)}{\vert x\vert} = E\psi (x)$  

where $\psi (x)$ is a wave-function and $-\frac{1}{\vert x\vert}$ is a kernel potential. No parameter appears if units are properly chosen.

The amazing property of a parameter-free model is to give information about physics without other physics input than a mathematical model without parameters. This allows the theoretical physicist at his desk to make predictions about the world without any input from the world. Such a prediction is said to be ab initio. Amazing! A priori knowledge in the sense of Kant.

In general, however, mathematical models of some physics contain parameters which have to be known from experiment or other models, in order to get anything out of the model. The Standard Model of particle physics contains 19 parameters which cannot be normalised by choice of units. It is very difficult to determine these parameters by experiment. 

Let us now compare StdQM with RealQM as concerns ab initio simulation of chemical bonding. 

For StdQM we turn to chatGPT and get this response stating that this is impossible because the Schrödinger equation of StdQM, which is parameter free, is uncomputable and thus has to be modified or prepared to deliver any result and the preparation builds on massive input of know-how and parameters/experiments.

In contrast the new Schrödinger equation of RealQM is parameter-free and readily computable and thus delivers ab initio simulation capability of e g chemical bonding.  See posts on Real Quantum Chemistry with links to everything about RealQM.

PS Here is what Eric Scerri says about ab initio StdQM in Selected Papers on the Periodic Table:

• Whereas most chemists and educators seem to believe that all is well, I think that there is some benefit in pursuing the question of how much is strictly explained from the theory. 
• It is indeed something of a miracle that quantum mechanics explains the periodic table to the extent that it does at present. 
• But we should not let this fact seduce us into believing that it is a completely ab initio explanation. We have not yet arrived at the super - ab initio phase of quantum chemistry and nor are we even close. 
• If anything, the compromises that have been struck with the acceptance of parametrization as well as the mixing of wavefunction and DFT approaches begin to question the earlier promise of ab initio quantum chemistry.

The Secret of Covalent Chemical Bonding

Recent posts have exhibited the fact that the physics of chemical bonding still is debated as a fundamentally unresolved problem. Consensus appears to be that covalent bonding results from some form of "sharing of electrons", which decreases kernel potential energy by electron charge concentration between kernels without full compensation of increase of kinetic energy.

It is further agreed that this picture can be given support by quantum mechanics with the caveat that full solution of Schrödinger's equation for systems with several electrons is impossible. The idea is that somehow "delocalisation" of electrons over an entire molecule as a purely quantum mechanical effect, will make electron charge concentration possible without full compensation of increase of kinetic energy. But the quantitative details appear evasive.

RealQM offers a different account of the physics of covalent bonding which we here illustrate in a generic 1d molecule with two atomic kernels and two electrons. The crucial feature of RealQM is decomposition of the total electron wave function U(x) = U1(x) + U2(x) into one-electron wave functions with non-overlapping supports  meeting at a free boundary X with continuity and zero (normal) derivative. (Bernoulli condition). Running this code we get this result with kernel potential in blue and electron wave functions in red and green: 

We see a concentration of electron charge densities between the kernels meeting with non-zero joint value and zero (normal) derivates at the free boundary X. The total energy is -65.258 with kinetic energy 26.771.

We compare with a model with overlapping electron densities as in StdQM using this code:

We find a higher total energy -63.144 with substantially higher kinetic energy 35.111. 

We understand that the reason the non-overlapping wave functions above has smaller kinetic energy than the overlapping below, is that the non-overlapping meet at a free boundary with non-zero value and zero derivative allowing dU1/dx*dU1/dx and dU2/dx*dU2/dx to be smaller,  since overlapping wave functions have to meet zero end point values. The overlap region of StdQM is thus in RealQM replaced by a free boundary effectively decreasing the kinetic energy while keeping the potential energy and thus decreasing the total energy into bonding. 

Conclusion: 

RealQM offers an explanation in clear physical terms of covalent chemical bonding emerging from concentration of charge density between kernels without compensating increase of kinetic energy thus with lower total energy than separated atoms. The above experience in the basic model problem is reflected in the full molecule models reported in these posts. If this analysis is correct, it asks for major revision of the standard physics of covalent bonding.

Why Philosophy of Chemistry?

The recent post on the talk The Nature of Chemical Bonding by Eric Scerri, connects to an emerging field of Philosophy of Chemistry promoted by him. Asking chatGPT about the role of philoposphy in science we get the message that 

• Philosophy of Quantum Mechanics is a very active field since 100 years. 
• Philosophy of Newtonian Mechanics has played out its role since "science is settled".
• Philosophy of Chemistry is a new field formed during the last 20 years. 

We are led to an idea that if a philosophy of a certain scientific discipline is currently an active topic, like philosophy of quantum mechanics and chemistry, it expresses that "science is not yet settled".  It signals that there are foundational questions which cannot be resolved within the discipline itself using the tools of the discipline, and a resort to some form of metaphysics or philosophy is brought in to help.  

Beginning in the later 19th century and culminating in the 1930s, a search for the foundations of mathematics engaged many famous mathematicians like Cantor, Russell, Hilbert and Brouwer without ever coming to any agreement and the interest then slowly faded away when computer science gave its resolution, leaving pure mathematicians to explore new ideas without worrying about the true nature of in particular the infinite set of real numbers and the set of all square integrable functions of real numbers. Giving them names was decided to be enough. Today philosophy of mathematics is largely viewed as "settled science".

2nd Trump Talk to Putin

Who has the upper hand?

On March 18 Trump called Putin for the 2nd time since he won the November election on a promise to end the US/NATO proxy war against Russia in Ukraine in 24 hours. See also previous post.

To get a into a position of strength before the 2nd talk, T resumed military support to the proxy war, after a short stop to show good will to peace. In the talk P repeated his condition for progress towards peace as a return to a halt of military support from the US. 

P agreed to a proposal from T to have a 30-day cease-fire limited to energy infrastructure, and directly ordered Russian implementation, as a sign of good will. T did not say he was willing to stop military support, which could have been a sign of good will.

T suggested that the war possibly could be settled in ice-hockey matches between US and Russia, which was met positively by P.  But T did not say he was willing to stop military support, which would  have been welcomed by P as a sign of good will. 

T prides himself to be a man of quick action, but the talks with P follow a very slow schedule. It is still unclear if T really wants  peace or just seeks a way to prolong the war indefinitely giving in to neo-cons.

Swedish Defense Minister Pål Jonsson declares that Sweden will continue to send weapons to Ukraine independent of any peace talks between US and Russia, and that peace will only create even bigger problems for Sweden and Europe. The stocks of Saab sky-rocket. Anything which is good for Russia like peace, is bad for Sweden. Russia won over Sweden in Ice-hockey WC in 1967, 1969, 1970, 1973, 1981 and 1986.

Former Swedish Prime Minister Magdalena Andersson says that it absurd that T and P talk peace over the head of Sweden/Ukraine.

Sweden stands strong in its war against Russia. Finland lost to the Russian Empire in 1809 must be brought back under the Swedish Kingdom.

The Still Unknown Nature of Chemical Bonding

Eric Scerri named the 2nd most influential chemist for the decade 2010-2020 gave a plenary talk at 26th Conference of the ISPhil of Chemistry in 2022 on The Nature of Chemical Bonding starting out presenting two views according to Robin Hendry:

• Structural as actual "bonds".
• Energetic as "bonding". 

Scerri continues recalling Coulson's words (1955):

• A bond does not exist: no-one has ever seen it, no-one ever can. It is a figment of our own imagination.

Scerri adds a statement by his colleague Seifert from an email conversation:

• Neither the structural nor the energetic provide "suitable characterization of chemical bonding". 

This is not a good start in 2022 in view of Gilbert Lewis clarification in 1916: 

• In the mind of the organic chemist the chemical bond is no mere abstraction; it is a definite physical reality. a something that binds atom to atom.  

Scerri then proceeds to scrutinise of how chemical bonding is described in text books of chemistry concluding that there is no satisfactory explanation of in particular the covalent bond somehow emerging from "sharing of electrons" as the dominating theme (together with the ionic bond as simply Coulomb attraction between ions). 

Scerri struggles to make sense of the textbook explanations following the very natural idea that somehow a bond can form if electrons can find a configuration close to kernels with decreasing potential energy which is not balanced by increase of kinetic energy supposedly emerging from two conflicting actions: 

• concentration of electron charge distribution decreasing potential energy
• delocalisation of electrons charge distribution avoiding increase of kinetic energy.   

But Scerri stops there: The Nature of Chemical Bonding is still a mystery, since it is the title of hus talk in 2022. But it must have a nature in physical terms, it cannot just be imagination. The World consists of molecules as atoms held together by chemical bonds.

It seems to me that Scerri is saying that only modest progress has been made over more than 100 years, despite the giant progress of modern physics in the form of quantum mechanics supposedly describing all of the physics of atoms and molecules including chemical bonding. How can this be? How is it possible that the nature of chemical bonding is still basically a mystery?

Here RealQM comes in offering a physical explanation how electrons can concentrate between atomic kernels to form a "glue" from decrease of potential energy without increase of kinetic energy. The secret is revealed in this plot as print-out of this code from a previous post from a collection of posts on H2:

We see two H kernels in black and a cross-cut along a line through the kernels of two electron wave functions with non-overlapping supports meeting at a plane orthogonal to the line midway between the kernels (as a free boundary) in yellow with plots of characteristic functions of the supports in black.

Computations are 3d on a fixed mesh with 1 million mesh points with mesh sise 0.1 in atomic units. The code is fully explicit consisting of 3 lines for update pf wave functions, potentials and free boundary. The computed energy  (-1.146) is in fair agreement with observation (-1.17) with further improvement under additional iterations. 

The essence is that in RealQM electron wave functions can meet with non-zero joint values at a free boundary which makes concentration of electron charge between the kernels possible without increase of kinetic energy. 

RealQM offers a new theoretical explanation of chemical bonding which agrees with previous intuition without theory.  Here are posts on Real Quantum Chemistry.

Geometry of the H2O Molecule by RealQM

This is a follow up of the previous post with now special attention to the non-symmetric geometry of the  H2O (or HOH) molecule with the two H atoms on one side the O atom, thus forming a dipole with positive charge on the side of the H atoms and negative on the other. 

An O atom has 8 electrons with 2 electrons in a first shell and the remaining 6 with the following thinkable electron distributions in 2nd + 3rd shell:

1.  6
2.  4 + 2
3.  3 + 3
4.  2 + 4   

We compute using RealQM in spherical symmetry using this code to find that 3 matches the observed ground state energy. We conclude that the O atom has an electron shell distribution as 2+3+3 and understand that 3 electrons in the outer shell invites to non-symmetry. 

We now turn to RealQM in 3d with 3 electrons in a third shell out of which 2 bind to the 2 electrons of the H atoms on one side leaving 1 electron free on the other side. We compute dissociation energy using this code with output: 

We see the 2 valence electrons of O (red and yellow) bonding with the 2 electrons of the H atoms (green) leaving 1 O electron on the other side (blue). We see that a somewhat bigger angle than 90 degrees of the HOH molecule is compatible with the 3 O electrons (red, yellow and blue), in qualitative agreement with observed 104.5 degrees.  

We see that RealQM offers an explanation of the non-symmetric geometry of the HOH molecule in direct physical terms of electron charge distribution.  This is different from that offered by StdQM in terms of 2 2 valence electrons and 2 lone-pair electrons in a shell with 6 electrons without direct physics. 

Towards Understanding of Chemical Bonding

RealQM based on a new form of Schrödinger's equation in terms of non-overlapping electron charge densities meeting at a Bernoulli free boundary, gives a new view on the physics of formation of molecules by groups of atoms coming together into states of lower energy than when apart by establishing chemical bonds.  

StdQM describes chemical bonds as either covalent by "sharing of electrons" or ionic with "transfer of electrons" creating Coulomb bonds between charged ions, but in general as some sort of mix.  

RealQM gives a different description as basically covalent where the "sharing of electrons" is realised through the Bernoulli free boundary, where electrons meet with continuity of charge density with corresponding wave functions having vanishing normal derivatives. "Sharing" is thus replaced by "meeting". This allows electrons to meet between atom kernels and so decrease potential energy, without increase of kinetic energy because the "meeting" does not require vanishing charge density only normal derivative of wave function. 

The basic case is the formation of a H2 molecule from two H atoms considered e g in this post .

Let us now consider molecules of the form HXH with X an atom with two valence electrons in two forms as the 2nd column of the periodic table: Be, Mg, Ca, Sr, Ba,Ra, and 5th column: O, S, Se, Te, Po, Lv. Here the 2nd column is linear molecule, while the 5th including HOH is a bent molecule. 

RealQM offers a reduced model of X in the form of two valence electrons outside an inner shell of certain radius R representing the net effect of the other electrons + kernel as a +2 kernel. Running this code we get for a molecule bent to 90 degrees we get for R=0.5 a dissociation energy of 0.3178 Hartree (compared with 0.354 for HOH) with this output (code 3d on regular mesh with mesh size 0.1 atomic unit thus about 20 mesh points between kernels):

For a linear molecule like HBeH, we get with this code 

We see in these pictures as sections of 3d output the following:

• X atom electrons in red connecting to two H atoms in green, in bent and linear configurations.
• H atom meeting X in a narrow overlap region from level set representation of free boundary.
• Line section through kernels show wave function in yellow with in particular continuity of non-zero charge density/wave function at the free boundary as expression of the binding effect of the meeting between kernels. 
• We see small dissociation energy for large radius R of inner shell. 

More precisely we may compare to the following list values of dissociation energies:

• HOH   0.35 Hartree
• HSH    0.247
• HSeH  0.221
• HTeH  0.193
• HPoH  0.176
• HBeH  0.17
• HMgH 0.10
• HCaH  0.079
• HSrH   0.070
• HBaH  0.064
• HRaH  0.059

to see that R = 0.5 corresponds to HOH and R = 1 to HMgH. 

It remains to explain why HOH is bent but HBeH not. We expect this to depend on the different electron configurations of O and Be, with two electrons in the outer shell for Be, but possibly up to 6 for O. Will return with details. This connects to the dipole quality of HOH with the outer part of O negative and those of H positive. 

Bottom line so far:

• In RealQM electrons meet at a free boundary between kernels which decreases potential energy without increase of kinetic energy, as something easy to understand.  
• In StdQM electrons are "shared" which is a complex subject. 

We may view electrons as rivals competing to come close to kernels while repelling each other. An idea of meeting of rivals as a form of coexistence keeping integrity, may seem to be more natural than an idea of "sharing" between rivals with loss of integrity.  

Why Trump Does Not Dare to Speak to Putin

This is a follow up of the post from Nov 28 2024 asking When Will Trump Call Putin?  

Since then Trump has had one telephone conversation with Putin (on Febr 12 2025). 

On March 12 Trump proposed to Russia an unconditional 30-day cease-fire of the war in Ukraine. Putin was given the ball.

On March 13 Putin responded that a cease-fire would be fine, but not unconditional allowing US/NATO to rearm for continued war after 30 days. Trump was given the ball.

On March 14 Trump responded that he hopes Putin will show good will. The ball went over the fence.

Trump does not lift the telephone to speak directly to Putin. Trump sends his buddy real estate mogul Witkoff to Moscow to do the talking. Witkoff left Moscow after a Thursday late night meeting with Putin. 

P nows the facts, T does not and so does not dare to talk directly to P again. The time for mutual congratulation to excellency of political leadership is over. Now it is time to talk, and T has nothing to say.

On March 15 T send P a message asking for mercy for the Ukrainian troops including mercenaries from the West encircled in Kursk. What dos that say about the weight of T vs P?

RealQM 1st Ionization Energy of Alkaline Earth Metals

We let RealQM compute the 1st ionization energy of atoms with 2 valence electrons outside an inner shell of radius R (atomic unit) with a net charge of +2 and get the following result with this code + this code:

• R = 0        E = 0.903  Hartree
• R = 0.4     E = 0.711
• R = 0.6     E = 0.509
• R = 0.8     E = 0.373
• R = 1.0     E = 0.270
• R = 1.2     E = 0.192

We compare with the following list values:

• Be            E = 0.4125
• Mg           E = 0.3381
• Ca            E = 0.2707
• Sr             E = 0.2514
• Ba            E = 0.2308
• Ra            E = 0.2336

We see that Be to Ra roughly corresponds to R = 0.7 to 1.1, which can be made more precise by finding the exact R corresponding to a list value such as R =1.0 closely corresponding to Ca. It is also possible to directly let RealQM compute R in spherical symmetry with this code (with spatial scale change of $0.4301$).

The value of this exercise is to show a particular feature of the non-overlapping electron charge densities of RealQM, which makes it possible to model an atom with kernel charge Z only in terms of its V valence electron wave functions/charge densities with support outside a sphere of radius R around the kernel, subject to a kernel charge of Z - V as the net effect outside the sphere of all electrons inside the sphere and the kernel. 

The outside wave functions meet the inner sphere with zero normal derivative as part of the Bernoulli free boundary condition of RealQM.

This opens to very efficient modeling of molecules in terms of only valence electrons as will be demonstrated in upcoming posts.

In StdQM electron wave functions have global support and a reduction to only valence electrons is difficult in terms of   ”electron shielding of the kernel”. 

Physics of RealQM in Nutshell

Real Quantum Mechanics RealQM offers a generalisation (newS) of Schrödinger's equation (S) for the Hydrogen atom with one electron from 1926, to atoms and molecules with $N>$ electrons, in the form of a system of one-electron wave functions with non-overlapping supports representing non-overlapping charge densities in 3d, which has a clear physical meaning. The computational complexity of (newS) scales linearly with $N$, which makes solutions computable for large $N$.

This is different from the generalisation by formal mathematics coming to serve as the foundation of modern physics in the form of Standard Quantum Mechanics StdQM, obtained by adding a new 3d coordinate system for each new electron, thus forming a multi-dimensional Schrödinger equation (oldS) in $3N$ spatial dimensions for a system with $N$ electrons, without direct physical meaning. The computational complexity of (oldS) scales exponentially with $N$, which makes solutions to (oldS) uncomputable already for $N$ bigger than 5. 

We compare:

• (newS) has physical meaning and is computable for even for large number of electrons.
• (oldS) has no direct physical meaning and is uncomputable already for small number of electrons. 

I have reported on many cases in this book and on this blog showing fair/good agreement of computed solutions to (newS) with observations, typically atomic ground state energies, atomic ionization energies and molecular dissociation energies. The computations were performed on an iPad on a 3d mesh with 1 million mesh points as an iterative energy minimisation explicit update in a code with essentially three lines. 

In general the results using (newS) agree with those reported in the literature using (oldS) with both results in fair/good agreement with observations. RealQM based on (newS) offers quick computation with physical meaning, to be compared with StdQM based on (oldS) demanding heavy computation without direct physical meaning. 

Let us recall the essence of (newS) coming to expression in a 3-line computer code:

1. (newS) is a system of partial differential equations in terms of one-electron wave functions with non-overlapping supports representing non-overlapping charge densities.
2. Each wave functions seeks to minimise its energy subject to Coulomb potentials from the other electrons and the kernels  
3. Wave functions meet at a free boundary with continuity of wave functions and zero normal derivates as a Bernoulli free boundary.
4. The free boundary is updated using a level set method. 

The 3-line code consists of update of (i) wave functions, (ii) electron potentials and  (iii) free boundary.

Since charge densities of (newS) do not overlap, there is no need to involve electron spin, nor Pauli Exclusion Principle. 

RealQM offers a new view on chemical bonds as essentially all covalent with the Bernoulli free boundary serving a key role by allowing electrons to accumulate between kernels resulting in energy drop from kernel potentials without increase of kinetic energy. 

Major Shift in Sweden

The recent admission by the US government that the war against Russia in Ukraine is a proxy war initiated by US/NATO with objective to weaken Russia into regime change, has changed Sweden's foreign policy from brave opposition to Russian aggression, to instead Swedish aggression against Russia under safe shield of US/NATO as main aggressor. 

This changes the moral of the war completely, from protection of innocent victim of aggression to instead participating on the side of US/NATO as the perpetrator. 

For Sweden formed under social-democratic education for 80 years describing itself as humanitarian superpower way into the open door policies of up to 2015, this drastic shift from rescuer of victim to perpetrator will pose serious challenges. All political parties and main media have embraced strong Swedish participation in the US/NATO proxy war against Russia. With the roles now drastically changed all the political leaders and media asking Swedish people to go to war, have lost moral credibility and so will have to step down and the people will have to be re-educated. It will require a major shift.

   

The Fundamental Belief of a Modern Physicist

Profession of Faith

According to the conversation with chatGPT linked below, a modern physicist will have to confess to the following fundamental faith (F): 

• True solution of Schrödinger's equation of quantum mechanics (S) always match experimental observation.   

The confession includes the following qualifications:

1. There is no experiment contradicting (F).
2. (F) is to be viewed true until proven wrong. 
3. True solutions to (S) are uncomputable. 

In the conversation I bring up the following questions:

• What is the meaning of 1 if true solutions cannot be computed and compared to experiments?
• What is the scientific meaning of 2?
• How can one computed approximate solution to (S) be viewed to be closer to the true solution than another, when convergence to a true solution is not computable?

I get no convincing arguments. In view of Ockham's razor it seems to me that (F) serves no role in evaluating an approximate solution to (S) for some specific experiment. 

In fact, in practice an approximate solution with better match to experiment is viewed to be better, but it cannot be determined if it is also gives better match with the true solution, since this is uncomputable. It could well be that some approximate solution gives better match with experiment than the true solution.

(F) thus emerges as a self full-filling prophecy without scientific substance. What do you think? Do you confess to (F), and if so why? If not, RealQM may be of interest to you.

The above considerations in particular apply to quantum chemistry postulated to reduce to (S) while relying on a veritable zoo of approximate solutions and the true solution safely hidden.  

Is there any possible negative aspect of adopting (F) as a fundamental belief, or is it a luxury/safety guard that we can safely enjoy? Yes, there is. If (F) is viewed as the ultimate truth of e g quantum chemistry, then a search for some alternative to (S) can be dismissed without even trying and that has been the case all along since 1926. RealQM presents (S) in new computable form.  

The reason that (S) is uncomputable is that it involves 3N spatial dimensions for a system with N electrons, which makes it an unphysical model. The generalisation of (S) for N=1 to N>1 was made by formally adding new spatial dimension for each additional electron as a purely formal mathematical generalisation without physics. RealQM offers a different generalisation staying within physical 3 spatial dimensions with physical meaning. 

The idea that formal mathematics can reveal deep insights into physics is a working hypothesis of a physicist. It was fruitful in Newtonian mechanics but seems to have led astray in modern physics with (S) a too easy catch. 

 

chatGPT conversation.

Chemical Bond: He2 vs Li+H- vs LiH

1. Li+H-

Let us now let RealQM explain why two Helium He atoms do not bond to a He2 molecule, while a lithium cation Li+ forms a molecule with the anion H- with strong bond. The set up is thus

• Each He has a +2 kernel surrounded by 2 electrons.
• Li+ has a +3 kernel surrounded by 2 electrons and H- has +1 kernel surrounded by 2 electrons.  

The essential difference is thus the two +2 kernels of He2 to be compared with the +3 and +1 kernels of Li+H- with 4 electrons in both cases. We shall below compare Li+H- (solid phase) with LiH (gas phase).

As concerns He2 we refer to this post explaining the lack bond of He2 as a consequence of an outward  shift of the electron charge distribution counteracting the bonding effect from accumulation of charge between the kernels.

We now compare the He2 computation with corresponding computation for Li+H- with thus a change from +2 and +2 kernel charge to +3 and +1 and get the following result running this code:

• 

We obtain a ground state energy of Li+H- = -8.08 Hartree to be compared with the energy of Li+ = -7.28 and H- = -0.527 altogether = -7.807, which indicates a dissociation energy of Li+H- = 0.27. According to chatGPT this matches the value 0.26 by FCI and CCSD(T) as best value using Standard Quantum Mechanics StdQM. 

RealQM and StdQM thus give the same dissociation energy for Li+H- but from different mathematical models: RealQM is based on non-overlapping one-electron charge densities as problem in 3 space dimensions, while StdQM requires 12 space dimensions for the 4 electrons involved. RealQM has a direct deterministic physical meaning, while the physical meaning of StdQM is still an open problem.  

The advantage of RealQM is that an explanation of the binding of Li+H- can be read from the above 2d section through the kernels of Li+ and H-, and the 1d section of the one-electron wave functions in yellow:

1. We see to the left 2 half-spherical electron/wave function distributions around the +3 kernel meeting at a free boundary represented in the meeting of yellow curves.
2. Similarly we see to the right 2 half-spherical electron distributions around the +1 kernel meeting at a free boundary.
3. We see an accumulation of charge between the kernels with wave functions meeting at a free boundary, which creates a bond because the accumulation does not require increase of kinetic energy since the wave functions meet with non-zero common value.
4. We see that the free boundary for H- is shifted to the right which decreases the presence of the left half-spherical electron between the kernels and so decreases the bond.
5. The effect of 3 shows to dominate over 4 and so forms a strong bond. 

We now compare with the finding of this post that the Helium atom He does not form a molecule He2 since there is no binding, because in this case the effect of 3 is cancelled by 4 to no bond. 

RealQM offers a concrete physical explanation of both the strong bond of Li+H- and the no bond of He2.

RealQM agrees with StdQM as concerns dissociation energies in both cases. 

StdQM does not offer any physical explanation because it is based on a non-physical model. 

We see also that even if the Li+H- is viewed to have an ionic bond, because an electron has been transferred for Li to H, the actual bond between Li+ and H- is formed as a covalent bond from electron accumulation between the kernels, or "sharing electrons" in StdQM terminology. It suggest that ultimately all chemical bonds are covalent. In particular, both H- and Li+ participate in covalent bonding and the StdQM idea that they cannot because their two electrons form a "filled shell", does not seem to represent physics.

2. LiH

We compare with the smaller dissociation energy 0.0906 of LiH with a covalent bond between Li and H according to the following list of atoms of the form XH with X an alkaline metal with one valence electron.

We thus let RealQM compute dissociation energies E of molecules of the form XH with X=Li, Na, K, Rb, Cs an Fr the Alkaline Metals, and H Hydrogen, with the computation in 3d reduced to the covalent bond from the valence electron of X meeting inner shell electrons a certain distance R to the kernel, and the valence electron of H.  We obtain the following results using this code:

• R = 0.5     E = 0.13
• R = 0.55   E = 0.087
• R = 0.6     E = 0.08
• R = 0.7     E = 0.06
• R = 0.8     E = 0.047
• R = 0.9     E = 0.034 
• R = 1.0.    E = 0.02

with R in atomic units and E in Hartree.

We compare with the following list values:

• LiH   E = 0.0906
• NaH   E = 0.0769
• KH     E = 0.0701
• RbH   E = 0.0655
• CsH   E = 0.0609
• FrH   E = 0.0571

We see a match over the column LiH - FrH with R in the range 0.55 - 0.8.

.

3. Transition LiH to Li+H-

Since Li+H- has lower energy than LiH, there is an energy minimisation path from LiH to Li+H- which we seek to capture in this code. We see here the valence electron of Li concentrating charge to the region between the kernels thus forming a form of covalent bond of Li+H- as a new view on the physics. 

RealQM for XH with X Alkaline (Earth) Metal

We now let RealQM compute dissociation energies E of molecules of the form XH with X=Li, Na, K, Rb, Cs an Fr the Alkaline Metals, and H Hydrogen, with the computation in 3d reduced to the covalent bond from the valence electron of X meeting inner shell electrons a certain distance R to the kernel, and the valence electron of H.  We obtain the following results using this code:

• R = 0.5     E = 0.13
• R = 0.55   E = 0.087
• R = 0.6     E = 0.08
• R = 0.7     E = 0.06
• R = 0.8     E = 0.047
• R = 0.9     E = 0.034 
• R = 1.0    E = 0.02

with R in atomic units and E in Hartree.

We compare with the following list values:

• LiH   E = 0.0906
• NaH   E = 0.0769
• KH     E = 0.0701
• RbH   E = 0.0655
• CsH   E = 0.0609
• FrH   E = 0.0571

We see a match over the column LiH - FrH with R in the range 0.55 - 0.8.

Let us complement with Alkaline Earth Metal with X = Be, Mg, Ca, Sr, Ba, Ra. RealQM in the same form as above with now two valence electrons outside an inner shell of radius R, gives the following dissociation energy E of XH with this code:

• R = 0.8       E = 0.10
• R = 1          E = 0.08
• R = 1.2       E = 0.07

again in fair agreement with the following list values:

• BeH     E = 0.0812
• MgH    E = 0.0493
• CaH     E = 0.0687
• SrH     E = 0.0647
• BaH    E = 0.0585
• RaH    E = 0.0566
• 
  

How Much Will Sweden Have to Pay?

US has with Trump taken a radically new position vs Ukraine by acknowledging that it was NATO expansion that provoked the Special Military Operation in Febr 2022, which developed into a US/NATO proxy war against Russia with heavy destruction of life and land. 

The view from Russia is presented here: Russia will not forget. More on forever war.

Trump now seeks to end the war (because he has no money) by coming to an agreement with Putin, while putting all blame on Zelenskyy and asking for compensation for all US weapons in the form of Ukrainian minerals. The moral is lacking since US/NATO started the war and for three years has pushed Zelenskyy to let Ukraine serve as battle ground. Not so nice.

In March 2024 Sweden joined the US/NATO proxy war against Russia with the stated goal of forcing Russia back to at least 2014, when the provocation erupted in the Kiew coup forming an anti-Russia regime later led by Z.  

Sweden has participated in the proxy war against Ukraine with weapons and training, about 70 Billion SKr, which will not be forgotten by Russia. Sweden drastically reduced military spending following the collapse of Soviet Union in 1991, from 3.7% 1960-1970  during the Cold War gradually down to 1% 2000-2010 and 1.5% 2010-2023 apparently because there was no perceived threat from Russia, with a rapid return to Cold War levels in 2024-.

The war will soon end on terms set by Russia, since without the US the Ukraine military will have to give up, and continued war efforts by Sweden/Europe will serve to nothing. 

Russia will thus emerge as the winner, and in war it is the loser who will pay. This mean that Sweden will have to compensate Russia for all lives lost. How much? Russia will not forget, nor the Ukrainian people.    

And what will the Swedish people say when they understand that they have misled into a catastrophe by the all the political parties from left to right?

Let us use elementary computational mathematics to set the bill:

• Swedish weapons: 10 Billion Euro
• Russian soldiers killed by Swedish weapons: 10.000 
• Value of lost soldier: 1 million Euro
• Swedish repay to Russia: 10 Billion Euro.
• Swedish State Budget: 60 Billion Euro

So Sweden has to pay another 10 Billion Euro to break even at a total cost of 20 Billion Euro for nothing.

What Is the Shape of an Atom?

Standard Quantum Mechanics StdQM presents a picture of an atom as being built from electron configurations/orbitals represented by the eigenfunctions for the Hydrogen atom H as the excited states of its one and only electron according to the following partial list:

There is no real rationale for this choice of representation for the electron configuration of an atom with many electrons, other than the completeness of the set of Hydrogen eigenfunctions like any other set. 

The idea is thus to build many-electron configurations as combinations of the above list. Is it a good idea? Does it appear to be complicated? Is it likely that real physics is built this way from some storage of Hydrogen eigenfunctions? It has the same ad hoc character as the Linne's Sexual System classifying  plants into groups based on the arrangement of stamens and pistils, today completed in the Standard Model of particle physics.

We see in the above collection a presence of a shell structure which connects to a different representation of a many-electron configuration as organized in an expanding sequence of shells with at most $2*n^2$ electrons in shell $n=1,2,,$. Here is this shell structure for Iron complemented by electron orbitals below

RealQM is based on a new form of Schrödinger equation for a collection of one-electron wave functions with non-overlapping supports meeting at a Bernoulli free boundary, which for an atom has a shell structure carrying the supports and where the actual electron distribution comes out as a packing problem under energy minimisation. You can inspect the representation of a Gold atom in this code by pressing start.   

The basic shape of an atom in RealQM in spherical symmetry thus consists of a sequence of non-overlapping spherical shells with a certain number of equally distributed electrons in each shell, like a spherical onion built from spherical shells:

In this model there is no need of complicated Hydrogen electron orbitals from the above lists. Using Ockham's razor we can thus leave these out and make life much simpler as concerns mathematical modeling of atoms. This model meets the requirement of Anschaulichkeit demanded by Schrödinger, but not met by StdQM.

For molecules, RealQM offers a richer set of shapes formed by shell interaction of outermost shells of several atoms. See label RealQM Quantum Chemistry.

Swedish Stupidity

Sad to say the following video all too well describes the Stupidity of Swedish Foreign Policy of today:

In March 7 2024 Sweden gave up its 200 years of neutrality by joining NATO in its proxy war against Russia to expand NATO into Ukraine. This happened without debate over night and since then the Swedish people has been led by massive propaganda to prepare for war with opposition to war efficiently suppressed. 

Bonhoeffer says that stupidity has no moral, which in Sweden today is expressed in the mantra that the death of 1 million Ukrainian soldiers is justified because it has saved Sweden from Russian invasion.  

Bonhoeffer’s Argument on Stupidity

1. Stupidity is more dangerous than evil – While evil can be confronted and exposed, stupidity is much harder to counter because a stupid person is often unaware of their own ignorance.
2. Stupidity is not an intellectual defect but a moral one – Bonhoeffer did not see stupidity as a lack of intelligence but rather as a failure to think critically or ethically. It arises when people allow themselves to be manipulated.
3. People become stupid in groups – He observed that individuals often lose their ability to think independently when they conform to mass movements, propaganda, or authoritarian regimes. Stupidity thrives in environments where people surrender their autonomy to power.
4. Stupid people are resistant to facts – Reasoning with a stupid person is almost impossible because they refuse to listen to reason. Instead, they cling to slogans and ideologies fed to them by those in power.
5. The only way to counter stupidity is through inner liberation – Bonhoeffer believed that true wisdom comes from a deep ethical and spiritual awakening, not just education. A society can only free itself from stupidity when people take responsibility for their thinking.

Weak Reactivity of Gold Explained by RealQM

This is a follow up on the two previous posts letting RealQM explain the weak reactivity of Gold Au as compared to the strong reactivity of Caesium Cs both in 6th row of the periodic table having one valence electron. The same argument applies to Silver Ag vs Rubidium Rb (5th row) and Copper Cu vs Potassium K (4th row). 

Recall the following electron configurations (number of electrons in expanding sequence of shells)

• Au: 2+8+18+32+18+1    79 electrons in  6 shells
• Cs: 2+8+18+18+8+1      55  electrons in 6 shells   
• Ag: 2+8+18+18+1          47  electrons in 5 shells
• Rb: 2+8+18+8+1            37   electrons in 5 shells
• Cu: 2+8+18+1                 29   electrons in 4 shells
• K: 2+8+8+1                     19   electrons in 4 shells

We observe that the electron sequences for Au, Ag and Cu end with 18+1, while Cs, Rb and K end with 8+1. 

We compute using RealQM in a spherical symmetric form to get the following radius R in atomic units of the outermost shell containing the valence electron 

• Au: R = 2.94  (run code by pressing start)
• Cs: R = 3.36   (code)
• Ag: R = 2.45  (code)
• Rb: R= 2.85    (code)           

We observe that the radius for Au is somewhat smaller than that of Cs although Au contains 22 more electrons than Ce. The same pattern for Ag vs Rb and Cu vs K. 

In the previous post we gave explanations using RealQM along the following lines of thought:

1. Weaker reactivity by more tightly bound valence electron for 18+1 than 8+1. For a further explanation see this later post giving reason why Au+H- does not form but Cs+H- can. 
2. Weaker reactivity down the column of Cu, Ag and Au because binding by electron sharing is increasingly counteracted.    

Here 1. expresses common insight, while 2. is new insight brought by RealQM, which can be illustrated as follows:

Small radius of inner shells (red): Binding (green)

  

Large radius of inner shells (red): Small binding (green).

Recall that StandardQM offers an explanation based on an idea that a Gold atom has inner electrons reaching half the speed of light with increased mass binding the valence electron. It is a mind-boggling explanation. More precisely, the value of relativity theory is that it can explain any observation outside mainstream science as a relativistic effect.  That the relativistic effect is very strong for Au(79) but very weak for Cs (55) is hard to accept, since they can differ by at most a factor $(55/79)^2\approx 0.5$. 

Here is an illuminating chat with GPT. In particular the seemingly contradictory fact that Francium Fr (87) has stronger relativistic effect and stronger reactivity is discussed.

Here are the basic (3) lines of the RealQM code: update of electrons, potential and free boundary:

//Update of shell-electron wave functions

for (var q=1;q<Q+1;q++){

  for (var i=M[q-1]+1;i<M[q]-1;i++){

  u[i]=u[i]+0.5*dt*(u[i+1]-2*u[i]+u[i-1])/pow(h,2)+0.5*dt*(u[i+1]-u[i-1])/(h*i*h) + dt*K[i]*u[i] -       dt*2*P[i]*u[i];

 if (q<Q}

  u[M[q]]=u[M[q]+1];

  u[M[q]-1]=u[M[q]-2];

}

}

//Normalisation of shell-electron charge

  normu[q]=0;

  for (var i=M[q-1];i<M[q];i++){ 

  normu[q]= normu[q] + pow(u[i]*(i*h),2)*h;

  }

  for (var i=M[q-1];i<M[q];i++){ 

  u[i]=sqrt(E[q])*u[i]/sqrt(normu[q]);

}

//Update of shell-electron potentials

for (var q=0;q<Q+1;q++){

  for (var i=M[q]+1;i<M[q+1]+1;i++){

  P[i]=0;

  for (var j=1;j<N+1;j++){

  P[i]=P[i]+0.5*pow(u[j],2)*pow(j*h,2)*h*min(1/(i*h),1/(j*h));

  if (j>M[q] && j<M[q+1]){

  P[i]=P[i]-0.25*pow(u[j],2)*pow(j*h,2)*h*min(1/(i*h),1/(j*h));

  }

  }

  }

}

//Update of free boundary

for (var q=1;q<Q;q++){

  if (u[M[q]]>u[M[q]-1]+diff){  

  M[q]=M[q]-2;

  }

  if (u[M[q]]<u[M[q]-1]-diff){

  M[q]=M[q]+1;

  }

}