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The Nature of the Chemical Bond of Hydrogen-Type Molecules and Molecular Ions

THE DIHYDRINO MOLECULAR ION H 2 2c '  a0 

427

FORCE BALANCE OF THE DIHYDRINO MOLECULAR ION

Force balance between the electric and centrifugal forces of H 2 1/ 2  is given by Eq. (11.115) where p  2 2 pe 2 2 (11.316) D D 2 2 me a b 8 0 ab 2 which has the parametric solution given by Eq. (11.83) when a  a0 (11.317) The semimajor axis, a , is also given by Eq. (11.116) where p  2 . The internuclear distance, 2c ' , which is the distance between the foci is given by Eq. (11.111) where p  2 . 2c '  a0 (11.318) The semiminor axis is given by Eq. (11.112) where p  2 . 3 a0 2 The eccentricity, e , is given by Eq. (11.113). 1 e 2 b

(11.319)

(11.320)

ENERGIES OF THE DIHYDRINO MOLECULAR ION

The potential energy, Ve , of the electron MO in the field of magnitude twice that of the protons at the foci (   0 ) is given by Eq. (11.117) where p  2 8e 2

Ve 

a  a 2  b2

(11.321) 8 0 a 2  b 2 a  a 2  b 2 The potential energy, V p , due to proton-proton repulsion in the field of magnitude twice that of the protons at the foci (   0 ) is ln

given by Eq. (11.120) where p  2 Vp 

2e 2

8 0 a 2  b 2 The kinetic energy, T , of the electron MO is given by Eq. (11.119) where p  2

2 2

T

(11.322)

a  a2  b2

(11.323) me a a  b a  a 2  b2 Substitution of a and b given by Eqs. (11.317) and (11.319), respectively, into Eqs. (11.321-11.323) and using Eqs. (11.19111.193) with p  2 gives 2

2

ln

Ve 

16e 2 ln 3  239.16 eV 8 0 a0

(11.324)

Vp 

4e 2  54.42 eV 8 0 a0

(11.325)

T

8e 2 ln 3  119.58 eV 8 0 a0

(11.326)

ET  Ve  V p  T  Eosc

  2e 2   3   4 0  2aH  ET  22  2  2 me  e 1  2 (4 ln 3 1 2 ln 3)    8 a  me c 2 0 H    22 16.13392 eV   23  0.118755 eV   65.49 eV

(11.327)

        1 k   2   

(11.328)

where Eqs. (11.324-11.326) are equivalent to Eqs. (11.122-11.124) with p  2 . The bond dissociation energy, ED , given by Eq. (11.198) with p  2 is the difference between the total energy of the corresponding hydrino atom and ET given by Eq. (11.328): ED  ET ( H 1/ p )  ET ( H 2 1/ p )  22  2.535 eV   23  0.118755 eV   11.09 eV

(11.329)

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Volume 2: Chapters 11-14  

The solution of the 26 parameters of hydrogen molecular ions and molecules from two basic equations, one to calculate geometric parameters a...

Volume 2: Chapters 11-14  

The solution of the 26 parameters of hydrogen molecular ions and molecules from two basic equations, one to calculate geometric parameters a...

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