Chemistry Reference
In-Depth Information
In these conditions, the chemical field current (
11.15
) carries specific bonding par-
ticles that can be appropriately called as
bondons
, closely related with electrons,
in fact with the those electrons involved in bonding, either as single, lone pair or
delocalized, and having an oriented direction of moving, with an action depending
on chemical field itself
.
Nevertheless, another important idea abstracted from above discussion is that
going to search the chemical field
ℵ
no global gauge condition as (
11.16
) should
be used. Worth noting as well that the presence of the chemical field do not change
the Bohm quantum potential (
11.9b
) which is recovered untouched in (
11.13b
) thus
preserving the entanglement of interaction. With his there follows that in order the
de Broglie-Bohm-Schrödinger formalism and Eq. (11.6) to be invariant under gauge
U(1) transformation (
11.10
) a couple of gauge conditions the chemical field has to
fulfilled out of Eq. (11.13); they are respectively:
ℵ
R
2
∂
e
mc
∂
∂x
∂x
=
0
(11.18a)
e
c
2
∂t
+
∂x
∂x
=
e
c
∂
1
2
m
∂
e
mc
∂S
∂x
∂
+
0
(11.18b)
Now, the chemical field
is found through combining its spatial-temporal informa-
tion contained in Eqs. (11.18). From condition (
11.18a
) is getting that:
ℵ
ℵ
−
∇
R
·
−
j
∇
2
−
∇ℵ=−
−
j
R
(11.19)
where the vectorial feature of the chemical field gradient was emphasized on the
direction of its associated charge current (
11.15
) fixed by the versor
−
j(j
2
=1). We
will maintain such procedure whenever necessary for avoiding scalar to vector ratios
and preserving the physical sense of the whole construction as well.
Next, the gradient (
11.19
) is replaced in (
11.18b
) to obtain a single equation for
the chemical field:
−
∇
S
·
−
∇
S
−
∇
R
2
e
2
mc
R
m
∂
∂t
=
)
2
2
2
R
)
2
(
∇
ℵ
−
(
∇
ℵ
)
+
0
(11.20)
·
−
∇
(
∇
R
S
that can be further rewritten as
·
−
j
2
ρ
−
v
ρ
2
e
mc
∂
∂t
=
)
2
2
2
2
ρ
)
2
(
∇
ℵ
−
(
∇
ℵ
)
+
0
(11.21)
−
∇
·
−
j
(
∇
ρ
since calling the relations:
⎨
ρ
)
2
ρ
1
2
ρ
ρ
1
/
2
;(
∇
1
4
(
∇
R
)
2
∇
R
=
∇
=
ρ
1
/
2
;
−
∇
=
−
p
R
=
S
⇒
(11.22)
−
∇
·
−
∇
·
−
j
−
∇
ρ
·
−
j
−
p
⎩
2
ρ
1
/
2
S
−
∇
R
·
−
∇
S
=
S
