Chemical Bond: He2 vs 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.

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 Li+ participates in bonding and the StdQM idea that it cannot because its two electrons form a "filled shell", does not seem to represent physics.

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.
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;

  }

}