Chemistry Reference
In-Depth Information
role by elucidating the fundamental properties of chemical bonds and relating it to
the performance of materials under extreme conditions.
To study such systems, our group has developed the eFF [
59
,
90
,
91
]approximation
to QM, which can simulate moderate excitations (tens to hundreds of electron volts)
that vary sharply over space and time, in large systems (tens of thousands of atoms)
where strong couplings between nuclei and electrons exist, and chemistry occurs. In
eFF, electrons are represented by wave packets, and nuclei by classical point charges
moving in the time-varying field of the electrons (Ehrenfest dynamics). The overall
electronic wavefunction is represented by a Hartree product of spin orbitals, where
each orbital is a single Gaussian wave packet with size (
s
) and position (
x
):
r
Y
;
2
p
s
;
i
s
i
1
s
i
2
Cð
r
Þ/
exp
ð
x
i
Þ
exp
ip
x;i
r
(12)
i
where
p
x
and
p
s
correspond to the conjugate translational and radial momenta,
respectively, which represent the translational motion and radial expansion/shrinking
of the wave packet over time. To account for the orbital orthogonality imposed by the
Pauli principle, a spin-dependent Pauli repulsion potential is included in the Hamil-
tonian, which increases with the overlap between the wave packets (see Fig.
8
).
The eFF method is similar to previous wave packet molecular dynamics
(WPMD) approaches, but differs in the form of the Pauli potential, which we
derived to account for the effect of pairwise orthogonalization on the kinetic energy
of orbitals; with this change, the scope and accuracy of previous approaches is
greatly extended. The only other terms present in eFF are interactions between
charge distributions from classical electrostatics, and a kinetic energy term for the
electron wave packets derived from QM, which provides the “kinetic energy
pressure” that prevents electrons from collapsing to a point:
m
e
X
i
h
2
E
KE
¼
3
2
s
i
;
(13)
where
m
e
corresponds to the electron mass. From these simple terms, a rich array of
chemical phenomena emerges - separation of core and valence electrons into
Fig. 8 Pauli repulsion
between two electrons with
size
s ¼
1 bohr, as a function
of their separation,
r,
and
spin. These curves are
described with three universal
parameters adjusted to give
reasonable structures and
energies for CH
4
,C
2
H
6
, LiH,
and B
2
H
6
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