Chemistry Reference
In-Depth Information
dynamics of warm-dense-matter and plasma formation, functional molecular biol-
ogy, and protein structure prediction, among others.
In this chapter, we describe some of our progress in theory, methods, compu-
tational techniques, and tools towards first-principles-based multiscale, multipar-
adigm simulations, in particular, for systems that exhibit intricate chemical
behavior. We map the document over the hierarchical framework depicted in
Fig.
1
, threading the description from QM up through mesoscale classical
approximations, presenting significant and relevant example applications to dif-
ferent fields at each level.
2 The Role of QM in Multiscale Modeling
QM relies solely on information about the atomic structure and composition of
matter to describe its behavior. Significant progress has been made in the develop-
ment of QM theory and its application, since its birth in the 1920s. The following
sections present an overview of some parts of this evolution, describing how it
provides the foundations for our first-principles-based multiscale, multiparadigm
strategy to materials modeling and simulation.
2.1 The Wave Equation for Matter
Circa 1900 Max Planck suggested that light was quantized, and soon after, in 1905,
Albert Einstein interpreted Planck's quantum to be photons, particles of light, and
proposed that the energy of a photon is proportional to its frequency. In 1924, Louis
de Broglie argued that since light could be seen to behave under some conditions as
particles [
1
] (e.g., Einstein's explanation of the photoelectric effect) and at other
times as waves (e.g., diffraction of light), one could also consider that matter has the
same ambiguity of possessing both particle and wave properties. Starting with de
Broglie's idea that particles behave as waves and the fundamental (Hamilton's)
equations of motion (EOM) from classical mechanics, Erwin Schrodinger [
2
]
developed the electronic wave equation that describes the space- (and time-)
dependence of quantum mechanical systems [
3
], for an n-particle system as
"
#
h
2
X
n
2
2
m
i
þ
r
h
@
@
Vr
1
;
ð
r
2
:::
r
n
;
t
Þ
c
ð
r
1
;
r
2
:::
r
n
;
t
Þ ¼
i
t
c
ð
r
1
;
r
2
:::
r
n
;
t
Þ;
(1)
i¼
1
where the term in brackets corresponds to a linear operator that involves the kinetic
(first term) and potential (second term,
V
) energy operators that act over the
systems' wavefunction,
, and the right-hand side the quantized energy operator,
corresponding to the full energy of the system, acting on the same wavefunction.
C
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