Chemistry Reference
In-Depth Information
By the subsequent employment of the Heisenberg time-energy saturated indetermi-
nacy at the level of kinetic energy abstracted from the total energy (to focus on the
motion of the bondonic plane waves)
h
t
=
¯
E
(10.33a)
2
m
√
2
mT
h
¯
p
=
mv
=
→
(10.33b)
t
the bondon Eq.(10.32) becomes
X
bond
2
m
h
t
=
¯
(2
πn
+
1)
h
(10.34)
¯
that when solved for the bondonic mass yields the expression
ht
2
1
X
bond
m
B
=
¯
1
)
2
,
n
(
2
πn
+
=
0,1, 2
...
(10.35)
which appears to correct the previous non-relativistic Schrödinger expression (Putz
2010
) with the full quantification. However, the Schrödinger bondon mass is here
recovered from the Dirac bondonic mass (10.35) in the ground state,
i.e.
, by set-
ting
n
0. Therefore, the Dirac picture assures the complete characterization of the
chemical bond through revealing the bondonic existence by the internal chemical
field symmetry with the quantification of mass either in ground or in excited states
(
n
=
N
).
Moreover, as always happens when dealing with the Dirac equation, the positronic
bondonic mass may be immediately derived as well, for the case of the chemical
bonding is considered also in the anti-particle world; it emerges from reloading the
square root of the Dirac chemical field—Eq. (10.27c) with a plus sign that will be
propagated in all the subsequent considerations, e.g., with the positronic incoming
plane wave replacing the departed electronic one of (10.29), until delivering the
positronic bondonic mass
≥
0,
n
∈
ht
2
1
X
bond
m
B
=
¯
1
)
2
,
n
˜
(
2
πn
−
=
0,1, 2
...
(10.36)
It nevertheless differs from the electronic bondonic mass (10.35) only in the excited
spectrum, while both collapse in the non-relativistic bondonic mass (10.38) for the
ground state of the chemical bond.
Remarkably, for both the electronic and positronic cases, the associated bondons
in the excited states display heavier mass than those specific to the ground state, a
behavior once more confirming that the bondons encompass all the bonding infor-
mation,
i.e.
, have the excitation energy converted in the mass-added-value in full
agreement with the mass-energy relativistic custom Einstein equivalence (Einstein
1905
).
