Electronic structures of carbon diselenide

Synthetic Metals, 29 (1989) F 2 0 7 - F 2 1 2

ELECTRONIC

MICHAEL

STRUCTURES

F207

OF C A R B O N D I S E L E N I D E

SPRINGBORG

NORDITA,

Blegdamsvej

17, D K 2100 K z b e n h a v n

Z

(Denmark)

ABSTRACT The first-principles, ical

polymers

and

on

molecular

unstable

CSe2.

it has two v a l e n c e two

conjugated ever,

by

Some

of

forms

the

of other

a n d one c o n d u c t i o n

An a l t e r n a t i v e

considering

interactions

atoms

earlier

proposed

CSe,

forms

is predicted.

K b a n d close It s h o u l d

between

two

that

as a s y n t h e t i c

for hel-

C2Se,

are

and CSeH

found

Special

to

be

emphasis

is

It is found that

to the Fermi

level,

therefore

of interest

f o r m of a p o l y m e r i c

it is d e m o n s t r a t e d

to be i n t e r e s t i n g

LMTO m e t h o d

CSe2,

with cis p o l y a c e t y l e n e .

configurations.

polymer.

full potential,

of p o l y m e r i c

structures

with similarities

(meta-)stable

and hydrogen believed

functional,

on various

and the e x i s t e n c e

put on a C2Se c o m p o u n d

exists

density

is a p p l i e d

such

be

CSe chain

chains

and there

and b e t w e e n

it is reactive.

Also

as a

is found.

this

How-

one

chain

compound

is

metal.

INTRODUCTION At the last mental

polymerizing papers

they

in

a

CSe2 without

performed

a

geometries

of CSe2,

[4].

Here,

'synthetic

number

the we

will

the

CSe, focus

of free forms

of

the

that

latter

some

of the various

a n d C2Se polymers.

In a d d i t i o n

some

upon

In two

reaction

polymerization

calculations

on

a

C2Se.

part.

conditions

of free selenium.

properties

of

and

experi-

obtained

and polymeric

first-principles

Most

[i] p r e s e n t e d

the m a t e r i a l

selenium

report

any contents

et al.

that

the

results

additional

we

will

results

on

on

be

polymers

we have

different have

nuclear

examined

published

polymers

a CSeH

elsewhere

which

from

a

of v i e w are of interest.

results

for charge t r a n s f e r

0379-6779/89/$3.50

of

point

for these p o l y m e r s

they

the e l e c t r o n i c

CSe 2 molecule.

metal'

We b e l i e v e

different [3]

Okamoto

They a r g u e d

consisted

paper

to e x a m i n e

and

of c o n f e r e n c e s

diselenide.

proposed

recent

to p o l y m e r i c

In order

polymer

series

on c a r b o n

CSe2 m o l e c u l e s

[1,2]

However, leads

of this

results

on carbon

selenium polymers

but also for other s e l e n i u m

to be of r e l e v a n c e

containing

conjugated

not only

polymers

and

salts.

© Elsevier Sequoia/Printed in The Netherlands

F208

IV.

I.

VIII.

V. X. iX.

Ui.

Vii.

XI.

Fig. i. S c h e m a t i c r e p r e s e n t a t i o n s of p o l y m e r i c CSe 2 (III, V, VI, X), CSe (I, II, IV, IX), C2Se (VII, VIII), and CSeH (XI). The s e l e n i u m atoms are shown as closed circles, the c a r b o n atoms as open circles, a n d the h y d r o g e n atoms as squares with crosses.

COMPUTATIONAL The

METHOD

details

where

[5].

of

The

approximation approaches decades. tions

are

Thereby

and

have In

parameter-free

with

here

is b a s e d

the

the

tial

is i n c l u d e d

gle,

periodic,

in

We shown

use of the helical

a basis

We assume

is

of

the

the

and the zigzag

cases

local

similar last

two

Although

full poten-

to be isolated,

quasi-one-dimensional

Special

else-

(LMTOs).

size.

potential

a

eigenfunc-

orbitals

limited

the p o l y m e r s

For these

in

over the

equations

muffin-tin set

presented

well-known

physics

of a m u f f i n - t i n

symmetry.

symmetry

state

linearized

with

been

formalism

sin-

systems

of the h e l i c a l

we

symmetry

symmetry.

RESULTS

have in

presented clusions. [3]

in solid

As

Schr6dinger-like

so-called

and helical.

have

functional

approximation.

used

in the calculations.

u s e d here

density

are e i g e n f u n c t i o n s

are the pure t r a n s l a t i o n a l

GENERAL

been

is a c h i e v e d

infinite,

make e x p l i c i t

method the

one-particle

expanded accuracy

functions

on

Born-Oppenheimer success

solving

great

the basis

the

method

are

applied Fig.

i.

the AS

elsewhere Some not

method already

on d i f f e r e n t

geometries

mentioned

detailed

[4], and we will

of the m o s t

included

in

a

in this

recently proposed

Fig.

1 but

will

of most account

of of

the the

structures results

section m a i n l y give the g e n e r a l nuclear

briefly

be

geometries mentioned

is con-

of p o l y m e r i c

CSe2

in

text

when

3.79 a.u.

when

the

appropriate. For the CSe 2 m o l e c u l e assuming

the

half-filled

molecule ~g orbital,

we find an o p t i m i z e d

to

be

linear

which makes

and

with

C-Se b o n d equal

a Jahn-Teller

C-Se

length bond

distortion

of

lengths.

likely.

It has

a

F209

Okamoto erizing metallic This

et al.

CSe2. with

can be

making C-Se

structure

Structure

et

stable

is the

the

al.

the

Iqbal

interatomic

greatly

This

between

these

results

As

a

consequence

found

angles

a stable

bonds

is

to

the

results

on

section

the

structure

m o r e details, Structure of

furthermore

removes

Since pairs

as

VIII

the

suggested

~ bonds.

parameters

Instead IX

could

structure

structure

IV we

will d i s c u s s

backbone. is the

structure pro-

structure

atoms

is

of

structures

the most

this c o m p o u n d

by

et

orbitals

contains

our

although

it could

consider

this

in

section. the

larger

to other parts

stable C:Se

form ratio

of the poly-

stable.

chains might the

with

a n d metallic.

the

IV are o n l y t w o f o l d

Varying

con-

[3]. A resonance

[i] to be I

the

C2Se 4 units

agreement

for that

al.

IV

and b o n d

further.

section

structure

C-Se

in

structure

next

a.u.

of i n t e r p r e t i n g

hexagon

most

structure

3.71

coordinated,

interact

interchain of the

the

lone

to f o r m l o c a l i z e d

distance

and keeping

isolated

chains

equal to 3.07 a.u. A l s o

we

all

found

for this

com-

m o r e details.

structure

X is the one p r o p o s e d

here.

However,

the f o u r f o l d

e a r l i e r by K o b a y a s h i coordination

of the

seems unrealistic.

of l e t t i n g

we

find

structure

considered

lengths

to be stable

fixed at the values

[6], a n d is not c o n s i d e r e d

s e l e n i u m atoms

we

A t h i r d way

by O k a m o t o

IX with C-C b o n d lengths section

We

interac-

III

second

more

III bond

in the

resembles

antibonding

The q u a s i - t w o - d i m e n s i o n a l

giving

it

of structure

structure

by the

of the b a c k b o n e

with

electronic

leave the d i s c u s s i o n

on n e i g h b o u r i n g

et al.

ture

will

atoms

a stable

the

For the

the

VII as a stable

We

atoms

and delocalized

of the

the backbone,

whereas

to be

in the p o l y m e r p r o b a b l y b e i n g

geometrical

parts

not parts

formed

seems

carbon

pound a following

with

the s t r u c t u r e

data.

Although

f r o m the

results

not

interact

in

disulfide.

p r o p o s e d by Iqbal et al.

VI

structure

EXAFS

is that

C2Se.

atoms

being

of the carbon

bonds other

[2] p r o p o s e

electrons

This

suggest

a n d will t h e r e f o r e

polymeric

mer.

and

their

this but

half-filled

f o r m of s t r u c t u r e

chain.

identical.

as recently

for

carbon

chain,

we will discuss

structure

account

Increasing

is an a n t i b o n d i n g

considering

structure

geometry

consider

Iqbal et al.

Only

changes

n e c t e d b y C-C d o u b l e bonds,

not

is

stable.

are e s s e n t i a l l y

which

a modified

moreover

between results,

atoms

can

semiconducting

structure

selenium

the s e l e n i u m

V a n d VI

this

there

-C-C-Se-Se-

important

104 ° . In a f o l l o w i n g

Structure

it

unstable.

semiconductor,

I have e x a c t l y

of p o l y m e r i c

-C-Se-C-Se-

atoms

in

of

that

compound

distance.

for this

CSe2.

is a p e r i o d i c

and

Se-Se

indicate

the

a small-gap

for s t r u c t u r e

that

as a p e r i o d i c

likely m a k i n g the s t r u c t u r e

and

and the

recently

distance

increased

backbone.

atoms

also

of p o l y m e r i c

et al.

thus m a k i n g

into

analogue

However,

carbon

can be d e s c r i b e d

posed by

it

geometries

selenium

[3] p r o p o s e d

configuration

interaction

changes

c o m p o u n d w h e n polym-

calculations

likely to be found.

semiconducting.

between

our

antibonding.

II is not

III

I as an i n t e r m e d i a t e

as due to a too small

helical

remains

structure

Iqbal

C-Se

none of the e x a m i n e d

it to be tion

structure

configuration

planar

an a n t i b o n d i n g

interaction

bands

[i] p r o p o s e the

interpreted

the

Since

III

For

two p o l y m e r i c

imagine XI. find

letting

Fixing an

the results

chains the

of s t r u c t u r e

structure

the g e o m e t r i c a l

optimized

C-H

in m o r e details

bond

IV

IV interact

strucatoms

parameters

of the CSe b a c k b o n e

as of

length

approximately

of

section.

with

giving hydrogen

in a later

interact

2.2

a.u.

We

F210

(b)

-3.0

-60 ~

(a) 02

g

~ > ~

o~

--::2:1:1:

-60

-12.o -ls.o

==

7o

~_

-,,.0~

~

7s

w

-21.o

© ~ ~ o

.ao 8s .9.o -9.5

o2

-24.0 ~ . ~ ' ~ o = -270

~..o4 .o5

-30.0 .03

.02

01

O0

01

02

03

0.0

Bond length difference (a.u,)

(d)

-

(c)

-0o ~

0.5 k

-~oo -o 3 - o 2 - o l Bond l e n g t h

1.o

co Ol difference

o~

03

(a.u.)

(e)

.,

Fig. 2. V a r i o u s p r o p e r t i e s of structure VII. (a) Total e n e r g y p e r C2Se unit as a function of b o n d length d i f f e r e n c e relative to the u n d i m e r i z e d structure. (b) The b a n d structure of the u n d i m e r i z e d structure. The d a s h e d line represents the Fermi level. (c) The p o s i t i o n s of the ~ states near the Fermi level. Shown are the top of the v a l e n c e bands at the zone center [~(~2,k=-0)] and zone edge [E(~2,k=l)] and the b o t t o m of the c o n d u c t i o n b a n d at the zone center [g(~3,k=-0)]. The gap is b e t w e e n the u p p e r curve and the uppermost of the two lower curves. (d), (e), and (f) The e l e c t r o n d e n s i t y of the ~2 b a n d at k=-0 (d) a n d at k=l (e) and the ~3 b a n d at k=0 (f) in a plane p a r a l l e l to that of the nuclei but the d i s t a n c e 2.0 a.u. from that. C o n t o u r values are 0.02, 0.01, 0.005, 0.002, and 0.001 a.u. The d a s h e d lines represent the n u c l e a r backbone.

DIMERIZING By

cis

STRUCTURE

replacing isomer

cis-trans the

of

We e x a m i n e d types

bond

with

of

lengths

C-C

bonds

and

the

that

cis-trans

found about

for 0.

relative

(double)

bonds

It is t h e r e f o r e

keeping

C-C-C

isomer

the

bond

total

Furthermore, the

For

VII

with

this

it

two h y d r o g e n is

parallel

surprising

atoms

the

that

the

well-known

to the p o l y m e r

that

Iqbal

et

al.

axis

is

[2] pro-

(trans-cis) isomer to be the stable form.

the

the

of structure

obtained.

this q u e s t i o n b y v a r y i n g the d i f f e r e n c e

obtained

metastable.

atom is

the shorter

configuration.

pose the other

two

selenium

polyacetylene

isomer

stable

VII

each

angles

energies

is the

average at

per

stable

fixed 3.70

at

a.u.

C2Se

unit

form,

but

between 2.65 and

shown that

the

a.u.

form,

and

the

two

minima

in Fig.

the

are

of the

the

C-Se

120 °, respectively, 2a.

trans-cis

it is seen that the top of the b a r r i e r

undimerized

lengths

Fixing

not

We

isomer

in b e t w e e n located

we

notice is

is not

syrm~etric

F211

(a)

(c)

(b)

0.0

0.0

I

%6

-5.0 a.5

-5.0

(~u6

0.0

0,0

X.2

-5.0

-5.0

~

(Ju4

Z2 ~]

-10.0

-10.(

-15.0

-15.C

z~j

(~g4

(~u3

tUJ

-15.1

o

a,2

-25.0

~

-20.q

-20.0

0.0

-25.q

0.5

,

i

0.0

1.0

Fig.

The

band

structures

of

the

of

the

those

of

close

to the Fermi

the

rest

the two K levels to the Fermi of s i m i l a r present

three

those

states

conduction

that

three

~ bands

near

types

of

REACTIONS

interact carbon

that

are

shown

are

slightly

interesting

in Fig.

I.

in Fig.

to n o t i c e

We depict

2b.

(The

different

from

that

all

states

2c the p o s i t i o n

the

states

carbon

other

p

hand

exclusively

Fermi

VII

level,

contributing polaronic

to

The

the

of

an

p

of

two

the

excitations

but band

on b o t h carbon

band

near

gap

at

the

non-negligible

maximum

at

the

The b o t t o m and s e l e n i u m The

Fermi

polymers

zone

of the sites.

existence

configurations,

the

for c o n j u g a t e d

con-

the

maximum

also

compound.

(meta-)stable

orbitals

is almost

Finally,

character.

interesting

results

has in the

of d i m e r i z a t i o n .

valence

valence

to the

isomer

level

much.

components

of s e l e n i u m

is

vary

as a function

characters.

large

In c o n t r a s t

cis-trans

[7] the

of the c o n d u c t i o n

band

indirect

different

has

level

and

of of

proposes

show a particu-

IV

of the

structure

coordinated.

with e a c h

interchain

In Fig.

to b e i n g

On

OF S T R U C T U R E

twofold

2b

(c) of Fig.

for this polymer.

The e x i s t e n c e only

Fig.

of the dimerization.

valence

structure

atoms

the w e l l - k n o w n

lar richness

is here

The p o s i t i o n

the

have

the

(b), and XI

structure

for

(Fig. 2f) has large components

believe

that

gap.

of

2d)

We

two

It

IX

on cis p o l y a c e t y l e n e

is almost

band

0.5

zone c e n t e r a n d the single K level at the zone edge close

components. 2e)

undimerized

as a f u n c t i o n

(Fig.

d

(Fig.

0.0

k

(a),

structure

2).

f r o m b e i n g direct

selenium edge

at the

level

center

1.0

are of ~ symmetry.

calculations

whereas

changes The

level

case the s m a l l e r

stant,

zone

of Fig.

IV

-25.0 1.0

-25.

0.5

of s t r u c t u r e

parameters

-15.0 -20.0

k

3. B a n d s t r u c t u r e s

geometrical

~

02

-20.

k

see

-I0.0

-10.(

When

IV seems being

other

a n d the f i n d i n g

distance

of 3.07 a.u.

3a a n d Fig. structure

found to be metallic.

IV

surprising

synthesized

since the

of the stable

confirms

the

chains geometry

carbon

atoms

might

therefore

IX w i t h

the b a n d structures

of the two

is

be

whereas

However,

to

a

a carbon

this.

3b we depict found

are

semiconductor

we have only v a r i e d the i n t e r c h a i n

compounds.

structure distance

IX

We is

in the

F212 calculations this m i g h t ground

for

structure

change

state

might

only d i f f e r i n g lel might

it into have

and

performing

alternating

in w h e t h e r

be n e a r l y

IX

a semiconductor. C-Se

the s e l e n i u m

degenerate.

For

a

full

geometry

Of p a r t i c u l a r bond

lengths,

where

atoms are d i s p l a c e d

such

a compound

optimization

interest the

two

parallel

polaronic

for

is it that

the

geometries

or antiparal-

excitations

can be

of importance. Comparing when

the

unique ~g2

Figs.

chains

3a a n d 3b it is e a s y to i d e n t i f y interact

identification

Alternatively,

the

For

which

then

atoms

CSe to

for

the splittings the

O3+~4

like ~i-9~i+Oui

bands

where

such

a

important

difference

is that the

structure

IX,

a total

chain.

we depict

with two p a r t l y

of four,

as

of

important

former

O 5 bands

of

bands

and since

upon

the

giving

C-C

We

found

in Fig.

(not

difference

An

presented

isolated an

and C-H

optimizing

finally

modifying

distance The

of

struc-

the C-Se b o n d occupied

change

this

C-Se b o n d lengths

are b o t h O a n d ~ levels

We

approached

structures.

in o n l y one p a r t l y could

involves

chain

equilibrium

However,

result

atom

polyacetylene.

trans

3c the b a n d

Dimerizing

there

a t o m to e a c h carbon

with

close

band, into

a

with a

to the Fermi-

s h o u l d be interesting.

hybridizing

latter.

the

filled bands.

half-filled.

excitations

one h y d r o g e n

similarities

backbone

the

geometry

has

Since the d i m e r i z a t i o n

solitonic

The most

the

(empty)

attaching

structure

the

is e x a c t l y

periodicity

of the

filled

of

The most

and the C - S e - C b o n d angles might

semiconductor.

level

of

this

is m e t a l l i c

lengths

This

hydrogen

a.u.

ture

almost

one can imagine XI.

geometry

gradually 2.2

exception

interaction.

as in s t r u c t u r e fixed

the

not is possible).

(~u4) b a n d b e c o m e s

bonding

(with

between

Figs.

3(a)

with the h y d r o g e n

analysis here)

of

the

and

charge

demonstrates

3(c)

orbitals

is that

splits

densities

that

the

of

other

the O 4 b a n d

into the

the O3 and orbitals

changes

only

of are

small. A structure structure bridging results

r e c e n t l y p r o p o s e d by Iqbal et al.

IX.

In this

-Se-Se(see

the two

units

[4])

are

indicate

chains

of type

inserted

only little

and the Se2 units p r o p o s i n g

[3] shows m a n y s i m i l a r i t i e s

IV are not

between

the

interaction

the structure

directly

carbon between

with

connected,

atoms.

However,

the chains

of type

but our IV

to be unstable.

REFERENCES 1

Y.

Okamoto,

L.

S.

Choi,

Z.

Iqbal,

and

R.

H.

Baughman,

Synt.

Met.,

15

(1986)

265. 2

Z.

Iqbal,

man, 3

Z.

Y. Khanna,

Y. Okamoto, Iqbal,

Chem.

S.

Phys.,

4

M. Springborg,

5

M. S p r i n g b o r g

6

A.

Kobayashi,

Kosugi, 7

T. 88

S. Murthy,

Correale, (1988)

F.

J. S. Szobota,

J. Chem.

Reidinger,

C. Maleysson,

Phys.,

85

R.

Baughman,

H.

(1986)

R. H.

Baugh-

4019. and

Y.

Okamoto,

J__~

4492.

submitted. a n d O. K. Andersen, N.

H. Kuroda,

M. Springborg,

N.

and L. S. Choi,

Sasagawa,

Y.

J. Chem.

Sasaki,

and H. Kobayashi,

Phys.

Rev.

B, 33

K.

Chem.

(1986)

Phys.,

87

Asakura, Lett.,

8475.

(1987) T.

1985

7125.

Yokoyama, (1985)

I.

H.

Ishii,

N.