Dipolar polarization binding energy of TTFTCNQ

Volurnc 50, nurnher 1

DIPOLAR

POLARIZATION

CHEMICAL PHYSICS LETTERS

BINDING ENERGY

IS August

1977

OF TTF-TCNQ

B.D. SILVERMAN, W.D. GROBMAN and 5.13.TORRANCE IBM Thomas J. IVatsotl Research Cetrter. Yorktorvrl I&I%

New York 10598, USA

Rcccivuci 3 May 1977

731~dipd.tr polnrifatwrl energy that arises from the dwtrx frcld miucod dipoles at the alornlc SlteF has been calculated cx -~-t-t-- TCNQ arid tound to IJ~ 0.09 I cv per donor-ducptor pair for the fuully charge transferred crystal. ?: his is, thcrcfore, a sigufuxnt mntrtbution to the binding energy, but is not mlfmcntly Img,c to account for the cui\tcnLc of the ch,~rge transterrcd ionic ground state of this crystal.

The relative stalitlity of an ionic or non-ionic ground state of organic charge transfer crystals has been the subject of previous discussion. McConnell et al. [l] have emphnslrcd that complexes fbrmcd with strong acceptors and donors do form crystals with charge transferred ground states and they have suggested a semiquantitative criterion to predict the energetic possibility of such a state. IF it takes an energy, 1-A. to form a charge transferred donor- acceptor pair, where I is the Ionization potential of the donor and A is the electron affinity of the acceppair must be sufficiently large tor, the Madelung energy (electrostatic crystal!inc energy), /:,,r, p er donor--acceptor to offset this; in other words 11&l > i--A.

(1)

Metlger [2-4 j * and ofhers [G-8 ] have calculated the classical Madelung energy of several TCNQ compounds. TCNQ comoounds, in general, arc ionic (charge transferred) and are found to be either msulating, scmiconducting or metallic at finite tcmpcratures [9]_ Since metallic organic salts arc unique, the srnnll number of metallic TCNQ salts has been extensively studied. Whereas the Madclung energy calculated for several simple insulating TCNQ salts [3] appears to satisfy eq. (l), the Madclung energy of the metaIlic salts, NMI’ 141 and TTP-TCNQ [2,6-s] IS found to be insufficient to stabilize charge transfer, namely cq. (1) is found not to hold. In particular, such a calculation for the metallic salt TTF-TCNQ, under the assumption of full charge transfer, has yielded Ehl sz 2 V compared with I-A z 4 V. Recent X-ray [IO] and neutron [ 11 lscattcring results have enabled one to infer that this salt is less than fully charge transferred, being closer to a state in which one electron is transferred for two donor--acceptor pairs than to a state in which one electron is transferred for each donor-acceptor pair. For this reason, the relevant Madelung calculations are for models involving partial charge transfer. Two such models have been examined, one in which the charge is distributed uniformly [2] aio17g the stack and one in which the charge is distributed in a highly correlated [2,7,8] manner (Wigncr crystal). The assumption of a correlated distribution, involving a charge carrier at every other site (p = :(2, where p is the average number of electrons transferred per donor-acceptor pair) dots indeed tend to minimize the Coulomb repulsion along the stack and hence provides the strongest binding. For this casz Tile absolute value of the Madelung energy per donor--acceptor pair is approximately equal to I-A. Recently

(tctracyanoquinodimethane)

* It IS dtfflcult to get a good estimate for the ioruzation energy of NMP. Met7ger’s calculation however yielded positive or nonbindmg energies for NiUP-TCNQ. Any positive ionrzation energy for NMP would thcreforc not satisfy cq. (1). Recent calculatlons, however, for NMP-TCNQ by Ukraimky et al. [S] IIWC yicldcd -2.4 eV per donor-acceptor pair for the fully charge tramferred crystal.

1.52

CHkhlICAL PHYSICS LETTCRS

Volume 50. number 1

The origin of the stability of the charge transferred ground state is therefore still open to question and there has been speculation concerning the contributions to the energy that have been neglected and that therefore stabiJim the ionic ground state of TTF-TCNQ. One such contribution discussed [2,6,12] has been the so called “polarization energy”. Even though crystalline TTF -TCNQ has inversion symmetry, belonging lo the crystal class l?21/c, each atom in the crystal is not at a center of synmetry. Such atoms ~111 then experience a local field due to the entire point charge array of the crystal and hence bocomc polarized_ The purpose of the present paper is to calculate the energy associated with this polarization. To distinguish this contribution to the energy from another contribution we will mention we ~111call it the dipolar polari/.atlon energy. Perhaps it should be emphasized that the point of the present paper is not to shed further hght on the issue of correlated versus noncorrelated wavefunctions for ‘M’F--TCNQ but to see if the dipolar polarizatmn can make a sufficiently significant contribution to the energy of this crystal so tllat cq. (1) is satisfictl at some value of the charge transfer. The dip&r polarization

energy has been calculated in two dilfcrcnt ways to muu:n~~c the chncc of cr~or. First, we have calculated the distribution of electric fields at the atomic sites that arise from rhc monopoldr charges on the individual atoms of the crystal. Assuming atomic polanrabilities, one can then sum the product of this polarizability with the square of the electric field over the atomic sites of the unit ccl1 to obtairl the dipolar polarization energy. This is cquivalcnt to summing the product of the clecrric field with the dlpolc nwmcnt over the atomic sites. Alternatively, one can use the dlstrlbution of dipoles to calculate the shift in electrostatic potcntial at each of the sites. The product of thisshift with the charge at each site can then bc summed over the unit ccl1 to yield the dipolar polarization energy. The exact agreement of the results obtained ill these two diffclcnt ways provides a check to eluninate several sources of posslblc error in the calculation. For the point dipole model WC have considcrcd, it is assumed that the induced dipoles arc localilcd on the atomic sites. The electric field IS therefore calculated at sites and atomic polarirnbilitics for the neutral atoms have been used. The values of thcsc atomic polarrzabilitrcs are listed 111table I_ Again, it should be emphasized that neutral atomic polarr7abihtics have been usccl. These do not differ appreciably in magnitude from the values obtained by assignment of atomic polarizabilnics from bond polarrzabilltlcs [ 141. If bond polarizabihtics arc used, howcvcr, the values of the electric field should be calculated at the bond center since t!le local field varies rapidly over the unit cell. A comparison of results obtained using the clectrlc field at the atomic sites or at the bond centers would be of interest [15]. We have also neglected changes in the number of electrons at the atomic sites of the ionized molecules. If these changes are simply used to correct the neutral atomic polarr7abilitics such corrections can he shown to be small [14]. At first thought, one might object to the USCof atomic polari7abilities of neutral atoms to describe the ionic.ed molecule since one might expect that the additional electron/hole on an acccptor/donol molecule could sigmficantly enhance the molecular polarizability by becoming delocalized over the extent of rllc molecule. Since the local field at the molecule has inversion symmetry about the molecular cctrtcr such dclocali;ration would, however, contribute to a moment of higher order than that of a dipoie and therefore not involve a molecular dunenslon linearly. Such molecular contribution to a higher order moment could be estimated with use of the energy lcvcls and wavefunctions of the molecule as wcil as the electric field distribution at the different atomic sites. In the present calculation this is not done. This electric field distribution has been calculated as arising from the fully charge transferred crystal with use tile

atoms

‘Table 1

Atomic polari~abilitlcs(Coulomb mctcr) from ref. [ 131

---

----

-------.--

------

-

Hydrogen --.- -- ____ 5.8 X 1O-42

---.---_-------

-

---.-

-_

-

-_

__

_

_

_

_

__ _

_____._

------------

Carbon

Nitrogen

Sulfur -----

1.6 x 1O-4’ -___-___

9.7 x 10-42 ___-----_--

3.1 x 10-41

._-_-__-_---

-

. --------_-

---_--

153

CHEMICAL PHYSICS LEITERS

Valumc 50, nurnbcr 1

15 August 1977

of one of the charge distributions considered by Mctzger.+ The crth component due to the distribution of point charges can be written E,(r’)

F’ S@) k~2k,i, exp (- n2q2k$+ 2nikll -f')

= -- (2iq/4ne,-,A)

i- [1-F(lr’-q-r,>

of the electric field at the point i

I/rl)l(~~-~,I-rorp)!lf’-r,-r,,l)

Ir’-q-

‘J-?

(2)

This expression has been obtained by taking the negative derivative with respect to r: of the expression for the potentldl energy gin by Tosi [161. q IS the electronic charge and e. is the permittivity of free space. All other qullntities _have been defined in the article by Tosi. Rapid convergence of the sums is ensured by making use of the Ewald method. Table 2 gives the calculated values of the electric field at the atomic sites. The square of these field values times the corresponding polari7ability gives the dipolar polarization energy when this product is summed over the unit cell. The dipolar polarization binding cncrgy per donor-acceptor pair is obtained, however, only after the self-energy associated with each independent molecule is subtracted from the result obtained by cvaluating eq. (2). This self-energy is obtained by calculating the dipolar polarization energy of each molecule when the source of the electric field at each site arises from only the charges on the free molecule. Calculations for a less than fully charge transferred crystal will in general result in lower electric fields at the atomic sites and hence yield a polarization energy that is lower than that calculated for the fully charge transferred crystal. The value of the dipolar polarization energy obtained in this man&r is 0.091 CV per donor-acceptor pair. A preliminary value of this energy had been given [2] as 0.63 eV. One therefore finds that the dipolar polarization energy makes a significant contnbution to the binding of the crystal. This contribution is, however, no greater than that expected from dc!ocaiization of the electrons/holes along the stack (kinetic energy). In table 3 WChave The small v31listed four contributiol.J to the binding energy of a fully charge transferred crystal of TTF-TCNQ. ues of all such contributions to the energy other than the Madelung energy and ionization energy therefore suggests that the mixed valence character of TTF-TCNQ and perhaps other metallic salts could be required to reduce intrastack repulsion to allow the crystal to form [S]. $ We

have used the charge distribution Idbclcd Q, for TCNQ- by Mctzger and Bloc!1in rcC [2]. We have chosen this chaqc distribution since it provided the largest Madelung binding cncrgy of all the TCJNQ- charge distributions mvestigated in ref. [2], 11Gmcly -2.34 v.

Tfiblc 2 tlectric tieldc (V/m) -___.

at the

atomic sites a) __ ___- ____ - - __

F'X I CNQ -_A_---_.-------_C (8) 4.09 x 108

C0? C(1) C(6) C(4) C(5)

-8.28 x 3.55 x -2.03 x -1.62 x

108 10s IO9 10’0

1.62X lOLo

4

EY

-7.09x -7.03 x 2.07x -2.54 x 6.25 x

__ __

108 108 10’ 109 10”

7.36 x 10’

___

-

TTF

_____

1.69x 1.39x 5.54 x 6.44 x 1.79 x

__-----.-.-

10’ 108 10s lo8 10’0

6.39 x 10’

N(1)

-2.89 x log 3.66 x 10’ 1.14 x 10’0 N(2) 6.31 x 10’ 4.38 x 10’ 3.61 x 10’ 1.17 x 10’0 -1.12x 10” -6.38 X 10’ )I@) -1.15 x 1O’O -1.08,x 10’ 2.18x 10’ H(9) ----.----_-__-- - --. --- ---a) Atomic designations and positions arc given in ref. [ 17 1. 154

-_.-----

-

-

--_-s-w---EY

-E,

S(l) S(2) C(1) C(2) C(3)

- 1.22 x 10’0 1.55 x 10’0 3.10 x 109 6.36 X 10’ 6.54 x IO”

1.52X 10s 6.13 X IO’ 2.50x 109 1.62X 109 2.97 x 10s

11(I)

-1.01 x 10’0

-1.86 x 109

7.27 X lo9

--2.01 x 109

8.58 x 109

f!(2)

__.-

._-_-EX

-.--

2.09x 1O’O

-_ -

-

3.63 x 10’ 1.33 x 109 -3.60 X 10’ -7.39 x 108 4.56 X lo8

V01ume 50, number Tztble 3 Contributions

---

1

to the binding

__-__-__.-.-.-- -_-_--__

CHEMICAL

__-_

bfadclung

polarrzation

kinetic

or covalent

-_

_______

(2’( Viqj>

atomic

__

--

___I.-__.

clcctrogtatic (Xi qfif) (2t)

- _.-_

15 August

__--_

_-

--_

-_

_

Orgin _.__- -_- -_ _ _-_ --_ -.__ -__ __. --. molecular crier~y rcqu~ed to transfer one electron

_ -__ charge trnnster me-

LLTTCRS

1977

energy of TTF+‘XNQ-

IhZgy rnolccular

PHYSICS

energy of crystal of charged

increase in elcctrost.rtic thl: molecules

-_

energy ofdelocalination

__

_-_

-

energy

v-Y_.__

---

_bctwecn

-_

-____

_ -_ ____ -ITT: and *lCNQ

‘T?‘F+ and ‘IC’NQ-

due to pol,&ation

__

___

ValUC ___-44.2 cv

--___

-2.3

eV

of the dtomq composing -0.09

_-

of clcctrons

..-

---

along the stacks

.-

_.___

---__

--

___

eV

- 0.25 ev

--__

-

.-

The contribution to the “polarization cncrgy” that we have just discubscd we have called the “dil>olar polarizaenergy”. This is to distinguish it from what we wit1 call the “monopolar polarization energy”.We had prcviously calculated the charge redistribution on the molecules when placed in the crystalline environment. This work was done in connection with core level shifts and rhc interpretation of photocmission peaks observed in ‘I’TF-TCNQ [18].Th’ IS ch*dr g e redistribution will result in :I correction to the Madelung energy that one calculates with the use of free molecular charges. WC will call thiq correction to the Madelung energy the “monopolar polarization energy” and have found that this contribution amounts to several tenths of volts. Relteratir!g then, the three sources of electrostatic binding energy arlsc in the following manner. The Madclung energy lcsults from the interaction between the atomic charge (monopoles) assigned from 11free or independent n~oleculc calculation. The bipolar polarization energy arises from the interaction of these charges with the clcctric field induced dipoles at tl~e atomic sites. The monopolar polarization energy icprescnts the correction to the Madelung energy wl~cn the atomic charges on the molecules readjust as charge rcdistributcs self-consistently [lSJ on each molecule m the presence of the electrostatic environment of the crystal. TTF-TCNQ can then bc cxpectcd to marginally satisfy eq. (1) if It is assumed that the electrons aiong a stack are highly correlated [I J and the sources of polarizatmn energy discussed in this paper arc also added to the left side of cq. (1). The oxistcncc of such correIation5, even If dynamic, is still open to question. Finally it may be difficult to estimate the binding energy per unit volume of TTF- TCNQ since the actual value may be small compared with the accuracy of the calculations discussed. It would be of interest, however, to show by experiment that the alkah TCNQ salts are more stable than TTF-TCNQ and NMP-TCNQ. tion

References [ 11 P.L. Nordlo, Z.(i. Soos and 1t.M. McConnell, Ann. Rev. l’hys. Chcm. 17 (1966) 237; ILM. McConnell, 13.M. Hoffman anti R.hf. Mctlger, Proc. Nat1 Acad. Sci. US 53 (1965) 46. 121 R.M. hfetqer and A.N. Bloch, J. Chcm. Phys. 63 (1975) 5098. \3] R.M. Metzgcr, 3. Chcm. Phys. 63 (1975) 5090. 141 R.M. Mctzger, J. Chcm. Phys. 57 (1972) 2218. [S) 1.1. Ukrainsky, V.E. Klymcnko and A.A. Ovchinnikov, preprint ITP-7.589C. Academy of Sclencc!, of the Ilkraini;in SSI~ Instrtutc for Thcoretic.il Physics. [6] A.J. Epstein, N.O. L~par~, D.J. Sandman and P. Nlelscn, Phys. Rev. L)13 (1976) 1569. [7) V.E. Klymenko, V.Ya. Krivnov, AA. Ovchinnikov, 1.1. Ubrainsky and A-F. Shvcts, On the Charge Transfer States of QuasiOne-Dimensional Donor-Acceptor Crystals, Preprint ITP-75-t%, Kiev (1975). [S ] J-H. Torrance and R-D. Silverman. Charge Transtcr +nd Ionic Bonding in Organic SOWS with Scjiregatcd Sto._ks, Pbys Rev,, submitted for publication. (91 1-F. Shchegolev, Phys. Stat. Sol. A12 (1972) 9. [IO] F. Dennyer, R. Corn&. A.P. Garlto and A.J. Hecger, Phys. Rev. Letters 35 (1975) 445; S. Kagoshima, T. Ishiguro and II. Anzai, unpublished. [ 111 J1.A. Mook and C.R. Watson Jr., Phys. Rev. Letters 36 (1976) 801. [ 121 A.P. Garito and A.3. Heegcr, Accounts Chcm. Res. 7 (1974) 232.

Volume

50, number

1

CHEMICAL

PHYSICS

LE77XRS

[13 J R.R. Teachout and R.T Pack, Atomic Data 3 (I “7 1) 195. [ 141 12-L. Bush, Phys. Rev. B12 (1975) 5698. [IS] B.D. S~lvcrmin, to be published. 1161 M.P. Toti, in: Soild state physics, Vol. lG, cds. P. Scitz. D. Turnbut and H. Ehrenrclch [ 17 ] 13.Kistcnmacher ct 31. Acta Cryqt. R30 (1974) 763. [ 18 1 W.D. Grobman and ED. Sdvcrman, Solid State Commun. 19 (1376) 3 19.

156

15 August

(Academic

Press, NcW York,

1977

1967).