62 e4 162 1 0372 pa 0602 pb 0602 pc 0372

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: H
 The
secular
determinant
of
P
orbitals
 situated
on
carbon
atoms
and
normal
 to
the
plane
that
includes
the
 hydrogens
 ⎡ α − E β − ES ⎢ ⎢ β − ES α − ES ⎣ ⎤ ⎥ ⎥ ⎦ Hueckel
theory
makes
the
following
 assumpNons
 • The
overlap
integrals
(S)
are
zeroes.
 • Only
integrals
between
covalently
bound
carbon
(via
σ
bonds)
are
not
zero.
 • All
columbic
integrals
are
α
and
all
off
diagonal
(resonance
in
some
books)
are
β
 The
secular
matrix
for
ethene
therefore
simplified
to:

 ⎡ α−E β ⎢ α−E ⎢β ⎣ E =α ±β β <0 The
wavefuncNons
are
 ⎤ 2 ⎥ = (α − E ) − β 2 = 0 ⎥ ⎦ 1 ψ± = ( P1 ± P2 ) 2 Π
systems
(beyond
ethene)
 Butadiene
 The
secular
determinant
for
butadiene
 ⎛ α−E β 0 0 ⎜ α−E β 0 ⎜β ⎜ 0 β α−E β ⎜ ⎜ 0 0 β α−E ⎝ ⎞⎛ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎠⎝ c1 ⎞ ⎛ 0 ⎞ ⎟⎜ c2 ⎟ 0⎟ ⎟ =⎜ 0 ⎟ c3 ⎟ ⎟⎜ ⎠ ⎟ ⎜0⎟ c4 ⎠ ⎝ Energy
levels
and
wavefuncNons
 E1 = α + 1.62 β E2 = α + 0.62 β E3 = α − 0.62 β E4 = α − 1.62 β ψ 1 = 0.372 PA + 0.602 PB + 0.602 PC + 0.372 PD ψ 2 = 0.602 PA + 0.372 PB − 0.372 PC − 0.602 PD ψ 3 = 0.602 PA − 0.372 PB − 0.372 PC + 0.602 PD ψ 4 = −0.372 PA + 0.602 PB − 0.602 PC + 0.372 PD StabilizaNon
energy
of
the
π
...
View Full Document

Ask a homework question - tutors are online