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. 

Why Is the H2O Molecule Bent?

Standard Quantum Mechanics stdQM presents the following geometry of the water molecule H2O:

We see covalent (2-electron) bonds between O and H leaving O with two lone electron pairs (depicted by dots) on top of O in the picture. The resulting accumulation of negative charge on one side of O is then claimed to cause the bending by repelling the H atoms towards the other side.

Is this a convincing argument? Not really, since the accumulation of the two lone pairs on one side instead of a symmetrical on opposite sides with a linear unbent configuration, is not explained. 

In any case, if a bent configuration is preferred before a linear, it must be because it has lower energy and this is also what RealQM shows (compare code linear and code bent), with a difference of about 0.1 Hartree. Also compare code with free boundary update.

We are then led to a different explanation of the lower energy for the bent configuration understanding that it brings the H atoms closer into a covalent bond without changing the bonds to O. Recall that the energy of H2 is 0.17 Hartree lower than that of two separate H atoms.

In RealQM the configuration of O is 2+4+2 with two valence electrons interacting with the two H atoms. 

In stdQM the configuration of O is 2+6 with thus six valence electrons of which only two bond with H, and the remaining four form the two lone pairs (with their mysterious bending effect).

PS Here is what ChatGPT has to say based on reading all texts of stdQM:

• The bent or angular shape of the water (H2O) molecule is a result of the arrangement of its atoms and the distribution of electron pairs around the central oxygen atom. Water consists of one oxygen atom and two hydrogen atoms. Oxygen has six valence electrons, and in the case of water, two of these electrons form covalent bonds with the hydrogen atoms, leaving four electrons as two lone pairs on the oxygen atom. 
• According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, electron pairs, whether bonding or non-bonding (lone pairs), repel each other. In water, the repulsion between the lone pairs of electrons is greater than that between the lone pairs and the bonding pairs. As a result of this increased repulsion, the two lone pairs of electrons position themselves closer together, pushing the bonding hydrogen atoms closer to each other. 
• This repulsion causes a distortion in the molecule’s shape, resulting in a bent or angular geometry where the H-O-H bond angle is approximately 104.5 degrees. Therefore, the bent shape of the water molecule arises from the repulsion between the lone pairs of electrons, which affects the arrangement of the hydrogen atoms, leading to a non-linear molecular structure.

We understand that this is not very convincing, which indicates the state of the art.