Ground-state properties of the PtBr neutral Mx chain compound

3 3 64

Synthetic Metals, 55-57 (1993) 3364-3369

GROUND-STATE PROPERTIES OF THE PtBr NEUTRAL MX CHAIN COMPOUND M. A L O U A N I a,b, R.C. ALBERS °, J.M. WILLS °, and M. SPR/NGBORG c aLos Alamos National Laboratory, Los Alamos, New Mexico 87545 (U.S.A.) bDepartment of Physics, The Ohio State University, Columbus, Ohio (U.S,A.) CFakult/i.t fiir Chemie, Universit/it Konstanz, Konstanz, Germany

ABSTRACT We present first-principles all-electron local-density-approximation (LDA) electronic-structure calculations of the neutral halogen-bridged transition-metal linear-chain compound (MX chain system) Pt2Brs(NH3)4; the results agree well with the experimental lattice dimerization, band gap, and the Raman breathing mode. INTRODUCTION The MX materials provide an important testing ground for low-dimensional materials. Besides their mixed valence character and strong electron-electron and electron-phonon interactions, they often have competing charge-density-wave and spin-density wave ground states, which are sensitive to tuning by chemical substitutions, pressure, or doping [1-8]. In this paper we present first-principles calculations that provide a detailed understanding of the electronic structure of the MX chain compound Pt2Brs(NH3)4 (denoted PtBr). We have found an intricate interplay between crystal structure and electronic structure. In particular, the dimerization in this material can be explained by a Peierls mechanism acting on the only bands near the Fermi energy, a single set of Pt-Br one-dimensional bands. The ligand structure plays a crucial role. For example, the ammonia (NH3) ligands, which do not affect the one-dimensional conducting properties of this system, remove important nonbonding platinum-d orbitais that would otherwise prevent the observed dimerization. The Br ligands give rise to two-dimensional bonding. Thus, even though the important electronic structure near the Fermi energy that controls the electronic properties of this material is one dimensional, PtBr can be described as a set of strongly bonded sheets with a relatively weak intersheet bonding. These calculatit)ns can be modeled by a modified two-band Su-Schrieffer-Heeger model (SSH) that has currently been used phenomenologically to describe the MX systems[5], and provide first-principles values for the model's parameters. CRYSTAL STRUCTURE The MX materials form in linear chains with alternating transition-metal atoms (M=Ni, Pd, Pt) and halogen atoms (X=C1, Br, or I) along the chains. Different types of ligand structure can surround the chains and the whole matrix forms in a three-dimensional crystal with the chains aligned parallel to each other. The typical unit cell consists of two MX units, arranged so that the two neighboring X atoms move in closer to one of the M atoms. This dimerization is responsible for an alternating valence character of the transition-metal atoms because of the strong electronegativity of the X atoms. 0379-6779/93/$6.00

© 1993- Elsevier Sequoia. All fights reserved

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The MX Pt2Brs(NH3)4 studied here has a llgand structure consisting of two Br atoms and two ammonia molecules, which surround each Pt atom in a square planar geometry perpendicular to the chain axis. The experimental x-ray data for the crystal structure, which has not been able to distinguish between the two valence states of the Pt atoms, give the result that the undistinguished Pt atoms form in a body-centered orthorhombic structure with lattice parameters: a=8.23 ~, b=7.76 ~, and c=5.55 ,~. Figure 1 shows the crystal structure of an MX system. The ordering of the dimerized chains with respect to each other in the three-dimensional lattice is not known experimentally. In our calculation we have ordered the chains to minimize the number of atoms in the unit cell. This leads to a monoclinic Bravals lattice with twice the number of atoms as the undimerized structure; the basis vectors are:

M(IV)

• ",2'-2

V-'q" •

,, 1

~

x(2)

X(2)

(a/2, -b/2, c/4), (el2, b/2, c/4),

and (0, 0, c).

Figure 1. Crystal structure of M2X6(NHa)6. The dimerization is chosen such that the lattice is monoclinic with the basis vectors given by: ( a / 2 , - b / 2 , c/4), (a/2, b/2, c/4), and (0, 0, c). Here M = Pt, X(1) is the Br along the chain, X(2) is the Br ligand, and the triangles are the ammonia molecules.

M(II) NH 3

METHOD OF CALCULATION, RESULTS, AND DISCUSSION All calculations presented in this paper used an all-electron full-potential linear muffin-tin orbital (LMTO) method [9], which requires no shape approximations for either the potential or the charge density. We used the yon Barth-Hedin form [10] for the local exchange-correlation potential. We have considered a single PtBr Chain as well as structures with and without the ligands. We have found that all the llgands were required to generate the insulating dimerized ground state with the strong Peierls distortion that is observed experimentally. The calculated static band gap was about 1.15 eV, which is in good agreement with the 1.5 eV experimental band gap found for the charged PtBr system [2]. As expected, the Pt-Br bonding in the chains is dominated by the strong coupling between the Pt d3z~-r2 and the Br Pz orbitals. Also, the bands above and below the gap had, respectively, a strong Pt(II) and Pt(IV) character, which is consistent with conventional notions of a "charge-transfer gap." In Fig. 2 we show our LDA calculation of the total energy as a function of dimerization. The minimum of the total energy occurs at a dimerization of 4%, compared to the 4.8 and 5.2% found experimentally [5] (we define dimerization as the ratio of the off-center distance of the Br atom to the P t - P t distance). The curvature of the energy versus dimerization curve at the minimum energy provides an estimate for the effective phonon energy of a Raman-active breathing mode (whereby two Br chain atoms oscillate in and out in phase around the Pt atom). The calculated phonon

3366 i

1.6

1.2

i

i

2

6

t

>

o.8 LJ

<8 0.4

0.0

-10

-6

-2

10

(%) Figure 2. Total energy of Pt2Brs(NH3)4 as a function of dimerization ratio in (%). The full curve is with all the ligand structure and the dashed curve is without the NHa ligands. The dot-dash curve is the fit to the model using next neighbor tight binding parameters. The calculated Raman breathing mode is 22.8 meV compared to 22.7 meV experimental value.

frequency is 22.8 meV compared to the experimental values 21.7 and 21.5 meV for the neutral and charged PtBr systems [5]. The modified SSH model used by Bishop and coworkers [1-2] to described the properties of the MX system is a tight-binding single-chain model, with the onsite transition-metal energy and the hopping parameters linearly dependent on the degree of dimerization (electron-phonon coupling). Only two orbitals are considered important: a single d3z2_~2 orbital on the Pt sites and a single pz orbital on the Br sites along the chain. All other orbitals and ligand structures are assumed to play a passive role and are implicitly included in the elastic energy of the model (see below). We have fit our LDA results to a slightly generalized version of this model for the electronic contribution to the energy that is given by:

H = F_.tA,c+oc,o + ,,(c+oc,+, + b.c.) + C,(cT~c,+~ + h c)]

(1)

Ia

where

Al = ( - l y e o - ~(/Xt+1 + AI-I) + ~[(/xl+1 -/xt)2 + (/xl - Ai-1)2], Bt = -to + a(At+1 - / x l ) + a'(Ai+1 -/xt)2, C~ = t , + 7t(Al+2 - At) + 7/(At+2 - At)2,

Here M and X occupy even and odd sites, respectively. The onsite terms A~, The nearest-neighbor terms Bt and the second-nearest-neighbor hopping terms C~ contain electron-phonon contributions,

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since the coefficients contain a power-law dependence on the distance between the relevant atoms in terms of At, the deviation of the atoms from their positions in the undimerized structure. The zero of energy was chosen to be midway between the metal- and halogen-atom symmetric-geometry onsite energy levels (+eo). a, at, ~3, 13t, "7, and 7 t are all electron-phonon parameters, which couple the atomic positions through the Ai to the electronic structure. We have done a least-squares fit of Eq. 1 to the four LDA bands that have the most Pt da~2_,.~ and Br Pz character along the chain direction (FZ). Although nearest-neighbor interactions provide a reasonably good representation of these LDA bands, small second-neighbor terms are needed to correct for the slight asymmetry between the upper and lower bands. The fit provides values for e0, to, a, a',/3, and/3'. We have calculated this set of parameters for each separate dimerization and from a simultaneous global fit to all four different dimerizations we used (0, 2, 4, and 5.5 %). We have found that the parameters of the individual least-squares fits differ at most by 3% from the respective global fit parameters except for /3M which is found to be relatively small and has scattered values. We have found that the quadratic approximation for t and e with the secondneighbor tight-binding approximation matches the LDA eigenvalues very well, although even the finear nearest-neighbor least-squares fit is excellent. In Table 1 the column labeled "quadratic" is our best fit to Eq. 1. In addition, to give a feeling for the sensitivity of the parameters to the fitting procedure, we also give a second fit in the column labeled "linear" and a third fit called linear-nearst neighbors. For the linear fit the quadratic terms in A were eliminated. Finally, in the last two columns, labeled "emp. (1)" and "emp. (2)," are two recent empirical fits by Gammel et

al. [2] and by Huang [13] to various experimental data.

TABLE 1: Model Hamiltonian parameters as obtained from quadratic (in A), linear, and nearest-neighbor tight-binding fit to the LDA results (first three columns) and two empirical fits to experimental data (last two columns).

2~o

to

,~

c~'

~M

~M

~x

tMM

tXX

7M

7M

quadratic

2.3

1.5

2.3

0.4

0.1

0.5

0.2

0.2

0.0

0.1

0.0

finear

2.4

1.5

2.4

0.0

0.2

0.0

0.0

finear-NN

2.3

1.5

2.4

0.3

emp.(1) a

1.0

1.3

2.2

0.2

emp.(2) b

2.4

1.4

1.9

0.8

~Empirical values used for the charged PtBr system from Gammel et al. [2] bEmpirical values used for the charged PtBr system from Huang et al. [13] (the K M X spring constant was also needed - a value of 6.28 eV//~. 2 was used).

3368 A comparison of the two gives the sensitivity of the empirical fits to various experimental data. Huang's empirical fit uses all the input data as in Ref. 2 in addition to the experimental Raman and infrared frequencies. As shown in Table 1 our a priori LDA predictions for the parameters of the SSH model agree well with last empirical fit which uses more experimental data. In addition to the electronic energy, there are also elastic energies required to describe the dimerization, which are given by:

E.,o.,,o=-~1 ~

• K~(:,,+,-

At)20+j)

+-~1 ~

I,j=0,1

g ~MM~::'~,+~- :.~,+.--:"+')

(2)

/,j=0,1

The M-X spring coefficients K(~)X and M-M spring coefficients "'MMr"(J)model whatever other aspects of the electronic and ligand structure that are not included in the simple electronic Hamiltonian. To be consistent with the electronic model we have similarly generalized the elastic energy beyond the harmonic approximation to include quartic terms.

J'MX, we cMculated the total LDA energy as a function To extract the elastic coefficients u(J) of dimerization, while holding the Pt-Pt distance fixed at its experimentally determined value. These coefficients were determined by fitting Eq. 4 to the elastic energy obtained by subtracting the electronic energy Eq. 1 from the LDA total energy. A similar procedure was followed to obtain

KMM and KtMM, except that additional calculations were required, where different values of the Pt-Pt distance were used while the dimerization was held fixed at 4 %. We found ~r:(°) ' M X --- 0.68 e v / A L K ( ~ ) = 4 9 . 4 9 eV//~', KMM (o) =6"58 eV//~2, "~MM-r,'(') 3.85 eV//~ 3. -

For the undimerized case, we have done calculations both with and without the ammonia ligand structure. We have found that the important one-dimensional bands that we fit to the SSH model are nearly identical to each other for these two cases, which suggests that the ammonia ligands play no role in determining the conducting properties of these important bands. Instead, their main role seems to be to remove from the Fermi energy the nonbonding d orbitals that point in the direction of the ammonia ligands. Once this is done, the Peierls mechanism is effective in producing a dimerized ground state.

CONCLUSIONS AND SUMMARY In conclusion, we have found that LDA correctly predicts dimerization for the conducting polymer MX compound Pt2Brs(NH3)2. A single band at the Fermi energy dominates the physics of this system and allows the Peierls mechanism to be effective in causing a dimerized ground state. The relevant LDA bands have an approximately nearest-neighbor form (small deviations from the expected cosine k dependence along the chain) and the correct one-dimensional character. While no data exists for the neutral MX chain we have studied, our parameters agree well with those that Bishop et al. have fit to experiments involving charged MX systems.

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ACKNOWLEDGEMENTS We thank A. R. Bishop and J. W. Wilkins for useful discussions. This research was supported in part by the US Department of Energy under Contract No. DE-AC02-76ER00881, and in part by the DOE - Basic Energy Sciences, Division of Materials Sciences. We acknowledge also travel money from NATO. Florida State and Livermore Cray-YMP computer time was provided by DOE. REFERENCES 1 S.M. Weber-Milbrodt, J. Tinka Gammel, A. R. Bishop, and E. Y. Loh, Jr., Phys. Rev. B 45 6435 (1992). 2 J. T. Gammel, A. Saxena, I. Batistie, A. R. Bishop, and S. R. Phillpot, Phys. Rev. B 45 6408 (1992); J. T. Gammel, S. M. Weber-Milbrodt, E. Y. Loh, Jr., and A. R. Bishop, J. Synthetic Metals 29 F161 (1989). 3 H . J . Keller, in Extended Linear Chain Compounds, Vol. 1, edited by J. S. Miller (Plenum Press, New York, 1982), p. 357. 4 R . J . H . Clark and R. E. Hester, in Infrared and Raman Spectroscopy (Wiley Heyden, NY, 1984), Vol. 11, p. 95. 5 H. J. Keller, B. Keppler, G. Ledezma-Sanchez, and W. Steiger, Acta Crvst. 37 674 (1981); L. Degiorgi, P. Waehter, M. Haruki, and S. Kurita, Phys. Rev. B 40 3285 (1989). 6 K. Toriumi, Y. Wada, T. Mitani, S. Bandow, M. Yamashita, and Y. Fujii, J. Amer. Chem. Soc. 111 2341 (1989); K. Toriumi et al., Mol. Cryst. Liq. Crvst. 181 333 (1990); H. Okamoto. K. Toriumi, T. Mitami, and M. Yamashita, Phys. Rev. B 42 10381 (1990). 7 R. J. Donohoe, S. A. Ekberg, C. D. TaJt, and B. I. Swanson, Solid State Commun. 71 49 (1989), and references therein. 8 M. Tanaka, S. Kurita, T. Kojima, and Y. Yamada, Chem. Phys. 91 257 (1984). 9 J.M. Wills (unpublished); M. Springborg and O. K. Andersen, J. Chem. Phys.87 7125 (1987). 10 U. Von-Barth and L. Hedin, J. Phys. C 5 1629 (1988). 11 Swanson and coworkers (private communication) have not yet been able to grow big enough single crystals of neutral PtBr to measure its ground state properties. However, we believe that the neutral and charged PtBr are sufficiently similar in their properties that comparisons between our theoreticM predictions and results for charged PtBr are appropriate. 12 M. Alouani, R. C. Albers, J. M. Wills, and M. Springborg, submitted to Phys. Rev. Lett. 13 X.Z. Huang, unpublished.