Theor Chem Acc (2015) 134:109
1 3
In general, anything is a Peierls’ distortion that moves an
unstable (quasi) 1D system of atoms from a metallic ground
state to a semiconductor one. The application of the term
“Peierls distortion” is favored here by the present author,
because—unexpectedly—the linear structure is metallic.
Would the linear structure be nonmetallic, the term “Peierls
distortion” could not be used and the distortion should be
explained simply by the favored hybridization of the sulfur atom in the given bonding system. While linear H 2 S
or HC ≡ C–S–C ≡ CH has degenerate ground states, such
ground states cannot be called metallic for the lack of band
structure in isolated molecules, and therefore, they can be
associated neither with Peierls distortion, nor with Jahn–
Teller distortion, the latter of which does not apply for linear molecules at all. All previously known cases of Peierls’
distortion happened along normal modes involving bond
lengths only, or by charge/spin density waves. In the present case, Peierls’ distortion happens along a different type
of normal mode that involves only bond angles.
It is clear from the above analysis that Peierls’ distortion
is realized through C–S–C angle bending in the (–S–C ≡
C–) x polymer. This is not surprising as the S atom is known
to strongly prefer taking up two, four or six valences, and
in the present situation, it could take up more than two
valences only if at least one of its neighboring –C ≡ C– units
would convert to cumulenic =C=C= structure instead of
the acetylenic –C ≡ C– one. The feasibility of such a conversion typically depends on the end units of the –C ≡ C– chain
and is energetically unfavorable in the present situation
when the end units are sp 3 hybridized S atoms. While in
(SN) x the N strongly prefers to have three valences and thus
can to some degree force the sulfur to take up three or four
valences in some of the possible resonance structures [ 47 ],
the –C ≡ C– unit is much less able to enforce more than two
valences on sulfur in the present situation, as mentioned
above. This also implies that there is virtually no opportunity for S–C bond-length alternation in (–S–C ≡ C–) x .
In the straight polymer, the hybridization of S changes
to sp 1 establishing a continuous conjugation of carbon and
sulfur p x and p y orbitals and some of sulfur’s d orbitals
allowing for signifi cant π -electron donation from sulfur to
antibonding orbitals of the C ≡ C bond, as mentioned also
above. This conjugation is also present at the bent C–S–C
angles though to a lesser degree, through hyperconjugation
of carbon π -orbitals and sulfur sp 3 lone pairs and d orbitals.
Even though charge or spin density wave would theoretically be possible as an alternative of C–S–C angle bending
for Peierls’ distortion, it is not realized in the conformers
studied here.
Methods to enforce the metallic straight conformation
may involve external pressure or strain, transition metal
(M) salts that complex and cross-link the –S–C ≡ C– polymers through S–M–S bridges, substrates that favor (–S–C ≡
C–) x crystallization in the straight conformers, e.g., surfaces of transition metal compounds with suitable lattice
parameters. Even though the energy required to straighten
the C–S–C angles (2.6 eV per repeating unit) is high as
compared to thermal energy at room temperature, it is still
relatively low to the energy of phase transitions accessible
in diamond anvil cells. Such phase transitions involve the
compression of oxygen to a metallic solid [ 48 ] or the compression of carbon dioxide to a quartz like crystal [ 49 ]. To
the best of the knowledge of the present author, there is no
other conjugated polymer that would become metallic from
semiconductor by a moderately energetic stretching as in
the case of the present (–S–C ≡ C–) x polymer.
Chemical doping of (–S–C ≡ C–) x is also possible to control its conductivity, similar to other conjugated polymers.
Controlled distribution of the torsional angles around the
polymeric backbone may also be possible, similar to (CH) x
which was shown to crystallize in helical conformations in
the presence of chiral nematic liquid crystals [ 50 ]. A particularly interesting helical conformer would consist of helical turns composed of approximately four –S–C ≡ C– units
as the equilibrium bent C–S–C angle is only slightly larger
than 90 ◦ . Similar to the composite polyyne-sulfur materials recently proposed by Duan et al. [ 43 ], mentioned above,
the presently proposed (–S–C ≡ C–) x polymer may also fi nd
application as electroactive material in batteries, and this
potential will be analyzed in a forthcoming paper.
3 Summary and conclusions
A simple new conjugated polymer, poly(sulfur acetylide)
with –S–C ≡ C– repeating units, has been proposed on the
basis of density functional theory calculations. The new
polymer is predicted to be metallic in a straight conformation, while it is a semiconductor with ≈ 1.6 eV band gap
when bent at the C–S–C angles. It appears to be unique
among conjugated polymers by its ability to become metallic when straightened out along a bending coordinate on the
polymeric backbone, albeit the process requires a relatively
large, 2.6 eV energy per repeating unit. Owing to its relative simplicity, potentially easy synthesis through polycondensation and close relationship to other fundamentally
important conjugated polymers, such as (SN) x , (CH) x and
(–C ≡ C–) x , and to the great variety of synthetic opportunities and materials properties that can be associated with
it, the experimental exploration of this new polymer is
proposed.
Acknowledgments The author of the present study gratefully
acknowledges countless valuable discussions and an enduring support
and mentorship to Professor Péter Surján, to whose 60th birthday this
Festschrift is dedicated. Károly Németh started research on the fi eld
of theoretical design of small band gap conjugated polymers in 1990
203
Reprinted from the journal
1 3
In general, anything is a Peierls’ distortion that moves an
unstable (quasi) 1D system of atoms from a metallic ground
state to a semiconductor one. The application of the term
“Peierls distortion” is favored here by the present author,
because—unexpectedly—the linear structure is metallic.
Would the linear structure be nonmetallic, the term “Peierls
distortion” could not be used and the distortion should be
explained simply by the favored hybridization of the sulfur atom in the given bonding system. While linear H 2 S
or HC ≡ C–S–C ≡ CH has degenerate ground states, such
ground states cannot be called metallic for the lack of band
structure in isolated molecules, and therefore, they can be
associated neither with Peierls distortion, nor with Jahn–
Teller distortion, the latter of which does not apply for linear molecules at all. All previously known cases of Peierls’
distortion happened along normal modes involving bond
lengths only, or by charge/spin density waves. In the present case, Peierls’ distortion happens along a different type
of normal mode that involves only bond angles.
It is clear from the above analysis that Peierls’ distortion
is realized through C–S–C angle bending in the (–S–C ≡
C–) x polymer. This is not surprising as the S atom is known
to strongly prefer taking up two, four or six valences, and
in the present situation, it could take up more than two
valences only if at least one of its neighboring –C ≡ C– units
would convert to cumulenic =C=C= structure instead of
the acetylenic –C ≡ C– one. The feasibility of such a conversion typically depends on the end units of the –C ≡ C– chain
and is energetically unfavorable in the present situation
when the end units are sp 3 hybridized S atoms. While in
(SN) x the N strongly prefers to have three valences and thus
can to some degree force the sulfur to take up three or four
valences in some of the possible resonance structures [ 47 ],
the –C ≡ C– unit is much less able to enforce more than two
valences on sulfur in the present situation, as mentioned
above. This also implies that there is virtually no opportunity for S–C bond-length alternation in (–S–C ≡ C–) x .
In the straight polymer, the hybridization of S changes
to sp 1 establishing a continuous conjugation of carbon and
sulfur p x and p y orbitals and some of sulfur’s d orbitals
allowing for signifi cant π -electron donation from sulfur to
antibonding orbitals of the C ≡ C bond, as mentioned also
above. This conjugation is also present at the bent C–S–C
angles though to a lesser degree, through hyperconjugation
of carbon π -orbitals and sulfur sp 3 lone pairs and d orbitals.
Even though charge or spin density wave would theoretically be possible as an alternative of C–S–C angle bending
for Peierls’ distortion, it is not realized in the conformers
studied here.
Methods to enforce the metallic straight conformation
may involve external pressure or strain, transition metal
(M) salts that complex and cross-link the –S–C ≡ C– polymers through S–M–S bridges, substrates that favor (–S–C ≡
C–) x crystallization in the straight conformers, e.g., surfaces of transition metal compounds with suitable lattice
parameters. Even though the energy required to straighten
the C–S–C angles (2.6 eV per repeating unit) is high as
compared to thermal energy at room temperature, it is still
relatively low to the energy of phase transitions accessible
in diamond anvil cells. Such phase transitions involve the
compression of oxygen to a metallic solid [ 48 ] or the compression of carbon dioxide to a quartz like crystal [ 49 ]. To
the best of the knowledge of the present author, there is no
other conjugated polymer that would become metallic from
semiconductor by a moderately energetic stretching as in
the case of the present (–S–C ≡ C–) x polymer.
Chemical doping of (–S–C ≡ C–) x is also possible to control its conductivity, similar to other conjugated polymers.
Controlled distribution of the torsional angles around the
polymeric backbone may also be possible, similar to (CH) x
which was shown to crystallize in helical conformations in
the presence of chiral nematic liquid crystals [ 50 ]. A particularly interesting helical conformer would consist of helical turns composed of approximately four –S–C ≡ C– units
as the equilibrium bent C–S–C angle is only slightly larger
than 90 ◦ . Similar to the composite polyyne-sulfur materials recently proposed by Duan et al. [ 43 ], mentioned above,
the presently proposed (–S–C ≡ C–) x polymer may also fi nd
application as electroactive material in batteries, and this
potential will be analyzed in a forthcoming paper.
3 Summary and conclusions
A simple new conjugated polymer, poly(sulfur acetylide)
with –S–C ≡ C– repeating units, has been proposed on the
basis of density functional theory calculations. The new
polymer is predicted to be metallic in a straight conformation, while it is a semiconductor with ≈ 1.6 eV band gap
when bent at the C–S–C angles. It appears to be unique
among conjugated polymers by its ability to become metallic when straightened out along a bending coordinate on the
polymeric backbone, albeit the process requires a relatively
large, 2.6 eV energy per repeating unit. Owing to its relative simplicity, potentially easy synthesis through polycondensation and close relationship to other fundamentally
important conjugated polymers, such as (SN) x , (CH) x and
(–C ≡ C–) x , and to the great variety of synthetic opportunities and materials properties that can be associated with
it, the experimental exploration of this new polymer is
proposed.
Acknowledgments The author of the present study gratefully
acknowledges countless valuable discussions and an enduring support
and mentorship to Professor Péter Surján, to whose 60th birthday this
Festschrift is dedicated. Károly Németh started research on the fi eld
of theoretical design of small band gap conjugated polymers in 1990
203
Reprinted from the journal