Theor Chem Acc (2015) 134:109
1 3
theorem has later been extended to any (quasi) 1D crystals
containing multiple types of atoms and more than one electron per atomic site, for reviews see Refs. [ 19 , 20 ]. The distortion toward the stabilized structure may also be based on
charge or spin density waves with a doubled periodicity as
compared to the geometric periodicity of the system.
In reality, 1D polymers form bunches and interact with
each other. The strength of this interaction also has an
effect on the applicability of Peierls’ instability theorem.
(CH) x appears to be a classic example of the original form
of Peierls’ instability theorem, as in reality the unit cell
consists of two CH units and alternating shorter and longer
C–C bonds are present along the polymeric backbone [ 21 ].
Bond-length alternation is present in (SN) x as well [ 22 ];
however, it is believed that the intermolecular interaction in
(SN) x is strong enough to suppress Peierls’ instability and
forces (SN) x to take up a specifi c geometry in which each
strand becomes a metal instead of a semiconductor [ 3 , 19 ,
23 – 26 ]. Therefore, the origin of metallicity in (SN) x is a 3D
effect of interchain interactions, and (SN) x is generally considered a 3D system instead of a loose set of 1D polymers.
Our recent work in the fi eld of ternary acetylides-based
semiconductors [ 8 , 27 ] directed the attention of the present
author toward acetylenic polymers with –M–C ≡ C– repeating units, where M may be a transition metal or a metalloid element, such as Te or Se, or sulfur. Several such
polymers exist in an alkali-doped form in ternary acetylides [ 28 ]. While the doped forms are mechanically stable,
the undoped ones are explosive. On the other hand, stable
organic compounds with –C ≡ C–(Te/Se/S)–C ≡ C– structural units have been known for decades [ 29 , 30 ]. The generalization of such chemical bonding systems into the corresponding polymers appears reasonable, but has not been
carried out yet. While the corresponding polymers with Te
or Se may be explosive, similar to transition metal acetylides, the one with sulfur, (–S–C ≡ C–) x , is potentially stable
at least to the degree of stability of (SN) x , which is known
to be explosive when heated to 240 ◦ C [ 31 ]. The explosivity of transition metal acetylides also varies, for example,
CuC 2 is a well-known explosive, while stable forms of
Cu 2 C 2 have been produced [ 32 , 33 ].
The investigation of the –S–C ≡ C– polymer is attractive
also because its synthesis should be straightforward, based
on existing synthesis methods on –C ≡ C–S–C ≡ C– compounds (see, e.g., Ref. [ 30 ] and reviews Refs. [ 34 – 36 ]).
Following these recipes, the reaction of dialkali acetylides
with sulfur dichloride is expected to result in the desired
polymer, according to
where A is conveniently Li or Na. Furthermore, this proposed polymer is also related to polyyne (carbyne), (–
C ≡ C–) x , the one-dimensional carbon-only chain with
(1)
xA 2 C 2 + xSCl 2 → (−S−C≡C−) x + 2xACl,
alternating single and triple bonds. While polyyne is very
unstable and the longest synthesized species contain only
about one hundred acetylenic units [ 37 – 41 ], embedding
S atoms between the –C ≡ C– units may be a way to create long stable polymers, with attractive materials properties. Ladder-type copolymers with acetylenic linking units
between main strands have been proposed by Kertesz et al.
[ 6 ] as a way of reducing the band gap of conjugated polymers, primarily that of (CH) x . Poly(para-phenylene sulfi de)
(PPS, [ 42 ]) is a similar polymer to the proposed (–S–C ≡
C–) x one, in as much as the sulfur atoms link para-phenylene groups (a benzene ring with two external links on
inversionally symmetric carbon sites) instead of acetylenic –C ≡ C– units. PPS is an industrially produced material, and it is synthesized by a polycondensation reaction
analogous to Eq. 1 with NaCl by-product. Recently, Duan
et al. developed a composite material consisting of polyyne
cross-polymerized with polysulfur links performing well as
cathode material in Li ion batteries [ 43 ]. The present study
focuses on predicting a few basic properties of the proposed (–S–C ≡ C–) x polymer, poly(sulfur acetylide).
2 Results and discussion
Density functional theory calculations using the QUANTUM
ESPRESSO program package [ 44 ] have been carried out using
the PBEsol [ 45 ] exchange–correlation functional with
ultrasoft pseudopotentials as provided with the program
package. Eighty Rydbergs wavefunction cutoff has been
applied. Structural optimization has been carried out until
the residual forces became smaller than 0.0001 Rydberg/
bohr and the residual pressure on the cell was smaller
than 1 kbar. Three different conformers and crystal packings of the (–S–C ≡ C–) x polymer have been explored. The
one with I4/mmm space group contains straight polymeric
strands of (–S–C ≡ C–) x , the one with P4/mma space group
has polymers with armchair conformation, and the one
with C2/m space group has polymers in zig–zag conformation. Figure 1 depicts the conformers, while Fig. 2 shows
the associated band structures. The band structure of the I4/
mmm crystal has been calculated for a unit cell containing
a single –S–C ≡ C– unit, using a 10 × 10 × 10 k-space grid.
The band structure of the P4/mma crystal has been calculated in a unit cell containing four –S–C ≡ C– units, using a
4 × 6 × 10 k-space grid. The band structure calculation of
the C2/m crystal used a cell with two –S–C ≡ C– units and a
5 × 6 × 10 k-space grid. The geometries of the given structures have been relaxed using the above defi ned k-space
grids.
The band structures in Fig. 2 indicate that the straight
polymers (space group I4/mmm) are metallic, while
the zig–zag (C2/m) and armchair (P4/mma) ones are
200
Reprinted from the journal
1 3
theorem has later been extended to any (quasi) 1D crystals
containing multiple types of atoms and more than one electron per atomic site, for reviews see Refs. [ 19 , 20 ]. The distortion toward the stabilized structure may also be based on
charge or spin density waves with a doubled periodicity as
compared to the geometric periodicity of the system.
In reality, 1D polymers form bunches and interact with
each other. The strength of this interaction also has an
effect on the applicability of Peierls’ instability theorem.
(CH) x appears to be a classic example of the original form
of Peierls’ instability theorem, as in reality the unit cell
consists of two CH units and alternating shorter and longer
C–C bonds are present along the polymeric backbone [ 21 ].
Bond-length alternation is present in (SN) x as well [ 22 ];
however, it is believed that the intermolecular interaction in
(SN) x is strong enough to suppress Peierls’ instability and
forces (SN) x to take up a specifi c geometry in which each
strand becomes a metal instead of a semiconductor [ 3 , 19 ,
23 – 26 ]. Therefore, the origin of metallicity in (SN) x is a 3D
effect of interchain interactions, and (SN) x is generally considered a 3D system instead of a loose set of 1D polymers.
Our recent work in the fi eld of ternary acetylides-based
semiconductors [ 8 , 27 ] directed the attention of the present
author toward acetylenic polymers with –M–C ≡ C– repeating units, where M may be a transition metal or a metalloid element, such as Te or Se, or sulfur. Several such
polymers exist in an alkali-doped form in ternary acetylides [ 28 ]. While the doped forms are mechanically stable,
the undoped ones are explosive. On the other hand, stable
organic compounds with –C ≡ C–(Te/Se/S)–C ≡ C– structural units have been known for decades [ 29 , 30 ]. The generalization of such chemical bonding systems into the corresponding polymers appears reasonable, but has not been
carried out yet. While the corresponding polymers with Te
or Se may be explosive, similar to transition metal acetylides, the one with sulfur, (–S–C ≡ C–) x , is potentially stable
at least to the degree of stability of (SN) x , which is known
to be explosive when heated to 240 ◦ C [ 31 ]. The explosivity of transition metal acetylides also varies, for example,
CuC 2 is a well-known explosive, while stable forms of
Cu 2 C 2 have been produced [ 32 , 33 ].
The investigation of the –S–C ≡ C– polymer is attractive
also because its synthesis should be straightforward, based
on existing synthesis methods on –C ≡ C–S–C ≡ C– compounds (see, e.g., Ref. [ 30 ] and reviews Refs. [ 34 – 36 ]).
Following these recipes, the reaction of dialkali acetylides
with sulfur dichloride is expected to result in the desired
polymer, according to
where A is conveniently Li or Na. Furthermore, this proposed polymer is also related to polyyne (carbyne), (–
C ≡ C–) x , the one-dimensional carbon-only chain with
(1)
xA 2 C 2 + xSCl 2 → (−S−C≡C−) x + 2xACl,
alternating single and triple bonds. While polyyne is very
unstable and the longest synthesized species contain only
about one hundred acetylenic units [ 37 – 41 ], embedding
S atoms between the –C ≡ C– units may be a way to create long stable polymers, with attractive materials properties. Ladder-type copolymers with acetylenic linking units
between main strands have been proposed by Kertesz et al.
[ 6 ] as a way of reducing the band gap of conjugated polymers, primarily that of (CH) x . Poly(para-phenylene sulfi de)
(PPS, [ 42 ]) is a similar polymer to the proposed (–S–C ≡
C–) x one, in as much as the sulfur atoms link para-phenylene groups (a benzene ring with two external links on
inversionally symmetric carbon sites) instead of acetylenic –C ≡ C– units. PPS is an industrially produced material, and it is synthesized by a polycondensation reaction
analogous to Eq. 1 with NaCl by-product. Recently, Duan
et al. developed a composite material consisting of polyyne
cross-polymerized with polysulfur links performing well as
cathode material in Li ion batteries [ 43 ]. The present study
focuses on predicting a few basic properties of the proposed (–S–C ≡ C–) x polymer, poly(sulfur acetylide).
2 Results and discussion
Density functional theory calculations using the QUANTUM
ESPRESSO program package [ 44 ] have been carried out using
the PBEsol [ 45 ] exchange–correlation functional with
ultrasoft pseudopotentials as provided with the program
package. Eighty Rydbergs wavefunction cutoff has been
applied. Structural optimization has been carried out until
the residual forces became smaller than 0.0001 Rydberg/
bohr and the residual pressure on the cell was smaller
than 1 kbar. Three different conformers and crystal packings of the (–S–C ≡ C–) x polymer have been explored. The
one with I4/mmm space group contains straight polymeric
strands of (–S–C ≡ C–) x , the one with P4/mma space group
has polymers with armchair conformation, and the one
with C2/m space group has polymers in zig–zag conformation. Figure 1 depicts the conformers, while Fig. 2 shows
the associated band structures. The band structure of the I4/
mmm crystal has been calculated for a unit cell containing
a single –S–C ≡ C– unit, using a 10 × 10 × 10 k-space grid.
The band structure of the P4/mma crystal has been calculated in a unit cell containing four –S–C ≡ C– units, using a
4 × 6 × 10 k-space grid. The band structure calculation of
the C2/m crystal used a cell with two –S–C ≡ C– units and a
5 × 6 × 10 k-space grid. The geometries of the given structures have been relaxed using the above defi ned k-space
grids.
The band structures in Fig. 2 indicate that the straight
polymers (space group I4/mmm) are metallic, while
the zig–zag (C2/m) and armchair (P4/mma) ones are
200
Reprinted from the journal