Bohr's New Atomic and Molecular Structure

Top page ( correct Bohr model helium ).
H2   C-C, C=C   CH4, H2O. True radius
Two atomic calculator.,   Multi-atomic calculator.
True electron's motion.,   Metallic complex in bodies.
Glucagon structure   PDB protein interactions

What determine protein conformation ? (13/10/16)

Present quantum mechanics stops development of all science.

[ Molecular biological technology has made NO progress since 1970s. ]

(Fig.A-1) Development of molecular technology has stopped since 1970s.

You may often hear the news such as " molecular biology is progressing day by day. ".
But for example, we cannot deal with serious diseases such as cancer and various functional disorders at all.
The present molecular biological technologies dealing with DNA, RNA, PCR, cultured cells and knockout mice have been established in 1970s - 1980s.

Unfortunately, even in the 21st century, these old molecular technologies are still playing the leading role in leading-edge fields.
This is very strange.
These serious situations are caused by the fact that the unrealistic quantum mechanics ( chemistry ) can NOT be applied to molecuar technology at all.

(Fig.A-2) All living things can be made directly from elements themselves.

As you know, originally, all living things on the earth were just separated elements with no life.
And taking extremely long time, the nature on the earth has made all living organisms from elements.

This means it is possible that we can produce all living things from separated elements, and control them on the earth with some knowledge.
But now, we cannot do it ( even protist ) at all, and have made NO progress in atomic levels.

Comparing with very complicated human body, atomic structure is very simple, composed of electrons and nuclei.
This indicates various motion patterns of each electron determine and control various biological functions.
So we must discard problematic uncertainty principle (= Shut up and calculate ! ) as early as possible.

(Fig.A-3) Present science is going toward unrealistic and illusory fields.

In some science news and websites, we often see the news dealing with expanding universe, black holes, quantum computer, another dimensions and spin electronics.
Unfortunately, these pseudoscience are all illusions. ( See this page or this page. )
Actually, all developments of our science have stopped due to these unreal and unuseful things.
And special relativity is wrong, so standard model, string theory, and general relativity can NEVER be true theories.

We see the news such as Higgs has been found extremely many times.
But they NEVER explain the difference between infinite Higgs fields and "ether", and the concrete mechanisms of how each element can get masses ( "resistance" is contradictory , as shown on this page ).
So ordinary people and students with strong curiosity are very frustrated, I think.

Real two-electron and three-electron atomic strucure.

(Fig.1) "Real" two and three electron atomic structure.

Our new Bohr model has succeeded in calculating the Helium ionization energy more correctly than the quantum mechanical variational methods as shown on the Top page.
In this new successful Bohr model, the two electrons of the helium atom (He) are moving on the orbits of just one de Broglie's wavelength which are perpendicular to each other.
Because when the two electrons are on the same circular orbit, their 1 × de Broglie wave phases cancel each other out.
This model can explain the phenomena of Pauli exclusion principle correctly, because there is no space for the third electron ( of 1 × de Broglie wave ) to enter this new two-electron Bohr atom.

Surprisingly, this new atomic structure of Bohr's helium is applicable to all other two and three electron atoms ( ions ).

(Table 1) Calculation results of two electron atoms (ions).
Atoms r1 (MM) WN x 4 Circular orbit Result (eV) ExperimentError (eV)
He 3074.0 1.000000 -83.335-79.0037 -79.0051 0.001
Li+ 1944.5 1.000000 -205.78-198.984 -198.093-0.89
Be2+ 1422.0 1.000000 -382.66-373.470 -371.615-1.85
B3+ 1121.0 1.000000 -613.96-602.32 -599.60-2.72
C4+ 925.0 1.000000 -899.67-885.6 -882.1-3.50
N5+ 788.0 1.000000 -1239.8-1223.3 -1219.1-4.20
O6+ 685.3 1.000000 -1634.38-1615.44 -1610.70-4.74
F7+ 607.3 1.000000 -2083.3-2062.0 -2057.0-5.00
Ne8+ 544.5 1.000000 -2586.7-2563.0 -2558.0-5.00

(Fig.2) Two-electron Atomic Model ( He, Li+, Be2+, B3+, C4+ ... )
two-electron atom

The calculation results of Table 1 clearly show that the Fig.2 atomic model is true.
( Two 1 × de Broglie wavelength orbits are perpendicular to each other. )
As positive charges of ions are increased, the error becomes bigger, due to their unstability.

(Fig.3) Circular orbit of two-electron atoms
one-model

Circular orbit of Table 1 means the two electrons are at the opposite sides on the same one orbit like Fig.3.
Of course, Fig.3 model is wrong, because the opposite wave phases of their 1 × de Broglie waves cancel each other out.

(Table 2) Calculation results of three electron atoms (ions).
Atoms r1 (MM) WN x 4 Result (eV) ExperimentError (eV)
Li 1949.0 1.000000 -203.033 -203.480 0.47
Be+ 1427.0 1.000000 -388.785 -389.826 1.04
B2+ 1125.0 1.000000 -635.965 -637.531 1.56
C3+ 928.0 1.000000 -944.46 -946.57 2.11
N4+ 790.5 1.000000 -1314.25 -1317.01 2.76
O5+ 688.0 1.000000 -1745.70 -1748.82 3.12
F6+ 609.4 1.000000 -2237.60 -2242.21 4.61
Ne7+ 546.0 1.000000 -2791.15 -2797.12 5.97

(Fig. 4) Three electron atomic model.

In the tree electron model, the radius of the outer 2S electron is Bohr radius × 4 in the lithium atom.
(Eq.1)

In other ions, divide it by (Z-2). Z means atomic number.
Because we consider the two inner 1S electrons are very close to the Z nucleus.
So the 2S electron is going around the +(Z-2) nucleus as if hydrogen-like atom.
In larger atoms, this approximation gives bigger errors as shown in Table 2.
( But we can say the atomic model of Fig.4 (and Fig.2) is true from these excellent results. )

Here we show ionization energies of various atoms ( experimental values ).

(Table 3) Ionization energies of the elements (eV).
(Experimental values.)
Atomic Name 1st 2nd 3rd 4th 5th 6th
Helium (He) 24.58741 54.41778 - - - -
Lithium (Li) 5.39172 75.64018 122.45429 - - -
Beryllium (Be) 9.32270 18.21116 153.89661 217.71865 - -
Boron (B) 8.29803 25.15484 37.93064 259.37521 340.22580 -
Carbon (C) 11.26030 24.38332 47.88780 64.49390 392.08700 489.99334

The sum of the last two large values of Table 3 mean the total energy of the two electron atoms (ions) in Table 1.
And the last three values mean the total energy of the three electron atoms (ions) in Table 2.
The ionization energies of 1S electrons ( red values of Table 3 ) are much bigger than other ionization energies.
This means that in various atoms, only two "1S" electrons are much closer to the nucleus than other electrons.
Of course, this is related to an integer times de Broglie waves.

Next we explain the energy value of the circular orbit of Fig.3 and Table 1.

(Fig.3)
one-model

Equating the centrifugal force to the Coulomb force, we have
(Eq.2)
centrifugal force
where r is the circular orbital radius (meter), m is the electron mass.
And "z" is atomic number.

The circular orbital length is supposed to be an integer (n) times the wavelength of the electron.
(Eq.3)

where h/mv is the de Broglie's wavelength.

The total energy E is the sum of the kinetic and the Coulomb potential energy of the two electrons, so
(Eq.4)

Solving the above three equations, the total energy E becomes,
(Eq.5)

Substituting the atomic number into z and n=1, we get the results of Table 1 (= circular orbit ).
This model gives larger ionization energies than the experimental results.
Because a single 1 × de Broglie wavelength orbit includes two electrons, which put their waves into disorder.

Bohr model two-electron atoms (ions).

(Fig.2) Two-electron Atomic Model ( He, Li+, Be2+, B3+, C4+ ... )
two-electron atom

In this section, we actually compute the ground state energy of Li+, Be2+ and B3+ using the same method as new Bohr's helium model.
See the Top page (He) about the detailed computing methods.
Here we use the next sample JAVA program ( or simple C language ).

JAVA program to compute two-electron atoms.
Simple C language program.

In this program, we use the new units of
(Eq.6)

From Eq.6, the acceleration is
(Eq.7)

In this program, we first input the atomic number Z (= 2, 3, 4, 5, ... or 10 ) .
Next we input the initial x-coordinate r1 (in MM) of electron 1 (see Fig.2), and the absolute value of the total energy E (in eV) of two-electron atoms.
At intervals of 1 SS, we compute the Coulomb force among the two electrons and the nucleus.
When the electron 1 is at (x, y, 0), the electron 2 is at (-x, 0, y).
So the x and y components of the acceleration (MM/SS2) of the electron 1 is,

(Eq.8) x and y components of the acceleration.

where the first term is by the Coulomb force between the nucleus and the electron 1, and the second term is by the force between the two electrons.
In light atoms such as helium and lithium, we use the reduced mass, rm =1/2 × (2me × nucleus)/(2me + nucleus). except when the center of mass is at the origin.
( See also reduced mass of three-body helium. )

We also calculate de Broglie's wavelength of the electron from the velocity ( λ = h/mv ) at intervals of 1 SS.
The number of that wave ( λ in length ) included in that short movement section ( the sum of them is WN ) is,

(Eq.9) Number of de Broglie's wave included in the short movement segment for 1SS.

where ( VX, VY ) are the velocity of the electron 1 ( in MM/SS ), the numerator is the movement distance (in meter) for 1 SS. the denominator is de Broglie's wavelength ( in meter ).

Here, the estimated electron's orbit is divided into more than one million short segments for the calculation.
When the electron 1 has moved one quarter of its orbit and its x-coordinate is zero, this program checked the y-component of the electron 1 velocity ( last VY ).
When the last VY is zero, two electrons are periodically moving around the nucleus on the same orbitals.

So, only when -0.0001 < last VY < 0.0001 ( MM/SS ) is satisfied, the program displays the following values on the screen, r1, VY, preVY ( VY 1 SS ago ), and (mid)WN ( total number of de Broglie's waves contained in one quarter of the orbit ).
( "Wrong Ene" means the total energy of circular orbits given by Eq.5. )

[ Lithium ion ( Li+ ) computing results. ]

(Table 4) Results of r1 and WN in which last VY is zero in Li+.
E (eV) r1 (MM) WN WN x 4
-194.0 1995.0 0.253191 1.012764
-196.0 1974.0 0.251895 1.007580
-198.0 1954.0 0.250620 1.002480
-198.984 1944.5 0.250000 1.000000
-200.0 1935.0 0.249364 0.997456
-202.0 1916.0 0.248126 0.992504
-204.0 1897.5 0.246907 0.987628

Table 4 shows the results of r1 and WN in which last VY is zero at various energy levels of Li+.
So when the total energy of Li+ is -198.984 eV, the number of de Broglie's waves contained in one orbits becomes just 1.000000.
The experimental value of Li+ energy is -198.093 eV.
The error is only -0.89 eV ( 0.4 %).
So it can be said that also in the lithium ion ( Li+ ), the orbital planes of the two electrons are almost perpendicular to each other.

[ Beryllium ion ( Be2+ ) computing results. ]

(Table 5) Results of r1 and WN in which last VY is zero in Be++.
E (eV) r1 (MM) WN WN x 4
-367.0 1447.0 0.252194 1.008776
-369.0 1439.0 0.251510 1.006040
-371.0 1431.0 0.250831 1.003324
-373.47 1422.0 0.250000 1.000000
-375.0 1416.0 0.249490 0.997960
-377.0 1409.0 0.248827 0.995308
-379.0 1401.0 0.248169 0.992676

Table 5 shows the results of r1 and WN in which last VY is zero at various energy levels of Be2+.
So when the total energy of Be2+ is -373.47 eV, the number of de Broglie's waves contained in one orbits becomes just 1.000000.
The experimental value of Be2+ energy is -371.62 eV.
The error is only -1.85 eV ( 0.4 %).
So it can be said that also in Beryllium ion ( Be++ ), the orbital planes of the two electrons are almost perpendicular to each other.

[ Boron ion ( B3+ ) computing results. ]

(Table 6) Results of r1 and WN in which last VY is zero in B+++.
E (eV) r1 (MM) WN WN x 4
-596.0 1133.0 0.251322 1.005288
-598.0 1129.0 0.250902 1.003608
-600.0 1125.0 0.250482 1.001928
-602.32 1121.0 0.250000 1.000000
-604.0 1118.0 0.249652 0.998608
-606.0 1114.0 0.249240 0.996960
-608.0 1110.0 0.248830 0.995320

Table 6 shows the results of r1 and WN in which last VY is zero at various energy levels of B3+.
So when the total energy of B3+ is -602.32 eV, the number of de Broglie's waves contained in one orbits becomes just 1.000000.
The experimental value of B3+ energy is -599.60 eV.
The error is only -2.72 eV ( 0.4 %).
So it can be said that also in Boron ion ( B+++ ), the orbital planes of the two electrons are almost perpendicular to each other.

Bohr model three-electron atoms (ions).

(Fig.4) Three-electron atomic model
lithium model

Next we try three-electron atoms (ions).
For example, lithium atom has two electrons in 1S orbital, and one electron in 2S orbital.
The two electrons of 1S state are attracted to the 3e+ nucleus strongly, so they are much closer to the nucleus than the 2S electron.
So approximately, we can suppose the 2S electron is moving around the e+ nucleus ( +3e - 2e = +e ) on the circular orbit of the two de Broglie's wavelength.
(This means that we can use the equations of the hydrogen atom in 2S electron approximately.)
2S electron of the ions with atomic number Z is considered to be rotating around ( Z-2 ) nucleus as hydrogen-like atoms.

According to the Bohr model, the radius (Rb) of the two de Broglie's wavelength orbit is 4 × Bohr radius, as follows,
(Eq.10)

This Rb is 2.1167 × 10-10 meter ( = 21167 MM ) .

And the energy level of n =2 becomes, (using the energy levels of the hydrogen atom)
(Eq.11)

The two electrons of 1S state are avoiding 2S electron, so we fix the 2S electron at ( 0, - Rb / √2, - Rb / √2 ) as shown in Fig.4.
(Fig.4 shows the relative positions, But actually, this 2S electron is rotating around the nucleus slower than the 1S electrons.)

Like two-electron ions, when the electron 1 is at (x, y, 0), the electron 2 is at ( -x, 0, y ). So the distances among the particles are,
(Eq.12)

where ra is the distance between the electron 1 and the nucleus,
rb is between two 1S electrons, and rc is between the electron 1 and 2S electron, respectively.

The x component of the acceleration (m/sec2) of the electron 1 is ( Li case ),
(Eq.13)

In the same way, the y component of the acceleration (m/sec2) of the electron 1 is,
(Eq.14)

Then we compute the number of de Broglie's waves contained in one quarter of the 1S orbit like two-electron ions.

JAVA program ( three-electron atoms ).
Simple C language program.

In this program, we first input atomic number Z = 3, 4, 5, 6, 7, 8, 9, or 10. ( Li Z=3, Ne7+ Z=10 )
Next we input the initial x-coordinate r1 (in MM) of electron 1, and the absolute value of the total energy E (in eV) of three-electron atoms (ions).
From the inputted values, this program outputs the y component of electron 1 velocity after a quarter of its orbit, and WN (the number of de Broglie's waves included in one quarter of the orbital).
"Rbb" means the radius (MM) of 2S electron.

[ Lithium ( Li ) computing results. ]

(Table 7) Results of r1 and WN in which last VY is zero in Li.
E (eV) r1 (MM) WN WN x 4
-197.0 2010.0 0.253889 1.015556
-199.0 1990.0 0.252579 1.010316
-201.0 1969.0 0.251290 1.005160
-203.033 1949.0 0.250000 1.000000
-205.0 1930.0 0.248770 0.995080
-207.0 1911.0 0.247538 0.990152
-209.0 1892.0 0.246324 0.985296

Table 7 shows the results of r1 and WN in which last VY is zero at various energy levels of Li.
So when the total energy of Li is -203.033 eV, the number of de Broglie's waves contained in one 1S orbit becomes just 1.000000.
The experimental value of Li energy is -203.48 eV.
The error is only 0.447 eV ( 0.2 %).
So it can be said that also in Lithium ( Li ), the orbital planes of the two 1S electrons are almost perpendicular to each other.

[ Beryllium ion ( Be+ ) computing results. ]

(Table 8) Results of r1 and WN in which last VY is zero in Be+.
E (eV) r1 (MM) WN WN x 4
-383.0 1450.0 0.251968 1.007872
-385.0 1442.0 0.251282 1.005128
-387.0 1434.0 0.250602 1.002408
-388.785 1427.0 0.250000 1.000000
-390.0 1422.0 0.249593 0.998372
-392.0 1415.0 0.248926 0.995704
-394.0 1407.0 0.248265 0.993060

Table 8 shows the results of r1 and WN in which last VY is zero at various energy levels of Be+.
So when the total energy of Be+ is -388.785 eV, the number of de Broglie's waves contained in one 1S orbit becomes just 1.000000.
The experimental value of Be+ energy is -389.826 eV.
The error is only 1.041 eV ( 0.2 %).
So it can be said that also in Beryllium ion ( Be+ ), the orbital planes of the two 1S electrons are almost perpendicular to each other.

Various atoms and molecules by new Bohr model.

In this section, we show the various atoms and molecules by new Bohr model.
These models are only approximation for now.
So I'm grad if some specialists try to get more correct and "real" images about the various atoms and molecules.

Let's stop believing vague wave function "blindly" to develop "real" science.
Schrodinger wave function can NOT give the clear model of helium and other atoms.
( This is a main reason why the wave function gives only probability and many-world concept becomes dominant. )
So from the beginning, the quantum mechanical helium, which we can NOT understand, does NOT stand on the same stage as Bohr model.

(Atoms.)
Bohr model Lithium (Li). Bohr model Beryllium (Be).
Bohr's Carbon - (visualization). Bohr's Oxygen - (visualization).
Bohr's Fluorine and Nitrogen. Bohr model Neon - (visualization).

(Molecules.)   Proof of Virial Theorem.
Bohr's hydrogen molecule (H2). Bohr's hydrogen molecule ion (H2+)
True nature of CH4, H2O molecular bonds (13/3/6).
True nature of C-C and C=C molecular bonds. (13/3/18)

True atomic radius. (13/3/28)
Various two atomic combination calculator.(13/4/12)
Multi-atomic molecule calculator. (13/5/10)
Bohr's Covalent bonds (CH4,H2O,NH3). Bohr's C=C,O=O bonds.
Visualization of Bohr's water (H2O).

to

2010/7/28 updated. Feel free to link to this site.