Essence of Chemistry: H2 vs Au2

This post adds a concrete example to the discussion in the previous post about the form of QM in the physics of atoms and chemistry of molecules.  

Chemistry concerns molecules as combinations of atoms with lower energy than separate atoms. The first molecule to be studied after the Schrödinger Equation SE for the Hydrogen atom H with one electron around a proton kernel formulated in 1926 by Schrödinger, was the molecule H2 formed by two H atoms finding a total energy minimum of -1.17 at a kernel distance of 1.4 (atomic units) compared with -1 when separated in an analysis by Heitler and London 1927. 

The basic element of the analysis was accumulation of electron charge density between the kernels allowing decrease of potential energy by proximity of both electrons to both kernels. The analysis was complicated by the fact that the SE for the molecule of 2 H atoms has 6 spatial dimensions. Ingenious dimensional reduction was required to give the observe result.

An H atom has one shell with one valence electron taking part in the formation of H2 and the essence of molecule formation is accumulation of electron charge density between the kernels. 

We now compare with a Gold atom Au which has 79 electrons distributed over 6 shells according to the pattern 2+8+18+32+18+1 with again one valence electron in the outermost shell. We know that Au does not easily react to form molecules and so we are faced with the problem to explain in particular why Au2 is not formed? 

Standard non-relativistic Quantum Mechanics StdQM has no answer and so an explanation has been sought as a relativistic effect from very high speed electrons in the 1st shell with increase of mass contracting the valence electron, which does not make much sense.

RealQM is an alternative to StdQM which gives an answer without relativity, which is displayed in this post and this post with details in the book on RealQM.  The essential difference between H and Au is the geometry of the valence electron, which fills a sphere for H allowing electron accumulation between kernels in H2, which is prevented in the outermost shell for Au.  

In StdQM for molecules all electrons have presence (support) over the entire molecule which gives a very complex unphysical picture difficult to conceptualise.

In RealQM electrons have non-overlapping supports with direct physical meaning which can be visualised and conceptualised.  

  

   

Why H Forms Molecule H2, while He Does not form He2

Why does the Hydrogen atom H form a H2 molecule, while the Helium atom He does not form a He2 molecule?

Standard Quantum Mechanics StdQM offers a vague explanation of physics:

• The two electrons of H2 combine to form a bond.
• Out of the four electrons of He2, two electrons combine to form a bond and the other two electrons form an anti-bond, altogether a no-bond. 

StdQM computation (without explanation of physics) agrees with observation:  

• H2 exists as a molecule with minimal energy -1.17 Hartree at kernel distance 1.4 atomic units au, compared to the energy -1 of separated H atoms. The dissociation energy of H2 is thus 0.17 Hartree.
• He2 does not form a molecule since the energy of He2 for kernel distances smaller than 5 atomic units is not lower than that of separated He atoms.  

StdQM computations for He2 is viewed to be very difficult because of the 12 spatial dimensions involved for 4 electrons and so results are very scarce if any.  

Let us now show that RealQM as a new alternative to StdQM delivers (i) results in agreement with StdQM computation and (ii) explanation of physics more convincing than StdQM. 

RealQM computations with this code on a uniform 3d grid with mesh size 0.1 au gives the following energies E depending on kernel distance D normalised to zero for maximal distance D=4 au:

•  D = 4       E = 0.00
•  D = 3.2    E = -0.04
•  D = 2.4    E = 0.003
•  D = 1.6    E = 0.20

We see essentially no energy drop from 4 to 1.6 au giving the message that two He atoms do not form a chemical bond into He2. The total energy of two He atoms is -5.806 and so the drop of 0.04 for D=3.2 represents a relative drop less than 0.01 on a 0.1 au grid in accordance with second order convergence,

RealQM offers the following explanation of the physics of bond for H2 and no-bond for He2:

The secret of the bond for H2 is hidden in the electron configuration of RealQM as consisting of non-overlapping electron densities. As two H atoms approach the two electron densities meet at a free boundary which is a midway normal plane to the line between the kernels with equal non-zero density together with vanishing normal derivative on both sides of the plane. This means that electron density can accumulate between the kernels thus decreasing kernel potential energy by profiting from both kernels, without increase of kinetic energy, thus forming a bond. This explanation is different from that given by StdQM based on bonding orbitals, and is based on the new electron configuration of RealQM. 

You can follow the physics by running this code. Very educating.

With the explanation for H2 in mind we now turn to He and meet the question why apparently the same explanation does not work for He. We recall that the RealQM electron configuration of a He atom consists of two half-spherical distributions meeting at a plane through the kernel as free boundary. Let us now imagine two He atoms approaching with the free boundary planes normal to the line between the kernels, which thus two half-spherical electron distributions meeting at a free boundary between the kernels and the other two outside. Again there will be an accumulation of charge density between the kernels, which  will now create a jump in electron density between inner and our electrons, which will push the inter-atom free boundary outwards and so act to decrease the inter-kernel electron accumulation and disable bonding. Computation shows that this effect is real. 

In short: The new atom/molecule model of RealQM offers an explanation based on physics of both the bond of H2 and the no-bond of He2.

RealQM for He2 at kernel distance 2.4 au with energy 0.003 Hartree above two He atoms indicating no-bond. Notice shift of free boundary beyond kernel to reduce accumulation of charge between kernels allowing yellow curves to take on same value at inter-atom free boundary. 

   

The Mystery of the Covalent Bond of the H2 Molecule Resolved!?

The H2 molecule consisting of two Hydrogen H atoms joined by a covalent chemical bond is the simplest and most abundant molecule in the Universe, but the physical nature of the bond is still today after 100 years of quantum mechanics subject to (heated) discussion between physicists and chemists. A physicist would proclaim that the wave function of quantum mechanics describes everything there is to say, which is difficult for a chemist to embrace because the wave function lacks direct physicality. A chemist believes in the existence of molecules in space and so is not happy with only a mathematical formalism without direct physical meaning. 

In any case, both would agree that the bond is established by somehow the two electrons of the two H atoms finding minimal total energy E= -1.17 Hartree at a kernel distance = 1.4 atomic units, to be compared with E=-1 at large kernel distance, thus with a dissociation energy of 0.17 Hartree. 

The total energy is the sum of the kinetic energy Ekin and potential energy Epot of the electrons together with the repulsion energy between the kernels. Ekin increases as the volume of electron density decreases, and Epot decreases as electrons get closer to the kernels. A standard view is that these are conflicting demands as concerns decreasing total energy. 

A physicist would say that the wave function describes two overlapping electron densities which do not need to be compressed and so can overlap in the region between the kernels and so decrease Epot with both electrons profiting from closeness to both kernels. Of course overlapping electrons increase Epot but a net gain comes out, is the idea. 

For a chemist overlapping or delocalised electrons is hard to accept because a physical presence in space of both kernels and electrons is the natural concept when building models of molecules. A chemist would say that the decrease of energy in the bond is mainly coming from the accumulation of non-overlapping electrons between the kernels, but that requires electron compression and the net gain is unclear. 

Here RealQM comes in to help the chemist by opening the possibility that the two electrons can meet with positive electron density and so avoid the cost of forcing electron density to be zero on the boundary to the region occupied by the electron thus increasing the kinetic energy. You can yourself follow the formation of the bond by RealQM in this p5js-code.

Notice in particular that the two electron densities meet between the kernels with non-zero density, thus combining favorable presence between the kernels without increase of kinetic energy, thus solving the puzzle! Or?

The prevailing confusion is expressed in the introduction the Chemical Bond (eds Frenking and Shaik):

• Lowering of the energy that establishes the bond is the result of a variational competition between the kinetic energy and potential energy. 
• On the other hand, there occurs an intricate interplay between various intra-atomic and interatomic interactions. These basic agents have, moreover, to accommodate electron correlation. It emerges that, in all cases, the driving force of covalent bond formation is the lowering of the kinetic energy gained by the delocalization of electronic waves over more than one atom. 
• This observation is only superficially discordant with the virial theorem which, as mentioned earlier, requires the molecule to have a higher total kinetic energy than the separated atoms. 
• The in-depth accounting of all interconnections between the various interactions shows that the information disclosed by the actual total kinetic and potential energies per se is insufficient for drawing any inferences regarding the origin of covalent bonding.

Modern physicists overpowered chemists in the 1930s by the heavy weight of quantum mechanics (demonstrated by the atomic bomb) claiming that the final word had been said and what remained was only to ”Shut up and calculate” according to heavy weight Dirac. 

But the quest of fundamental physics to unify all forces under string theory has not delivered and maybe this gives chemists an opening to molecular realism and then why not in the form of RealQM?