INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, VOL. 42, 1625-1632 (1992)

Toward Designing Molecular-Electronics Devices: A Potential Significance of Highly Mobile

Equilibrium Interconversions Z D E N ~ K SLANINA*

Max-Planck-Institut fur Chemie (Otto-Hahn-Instrtut), Mainz, Germany

Abstract

Possible applications of computational molecular-engineering approaches to the design of bistable conformational systems, to be potentially employed in molecular electronics, have been analyzed in isomeric-thermodynamic terms. Constructing such systems led to (conflicting) requirements, viz. an easy interconversion of the two structures (the isomerization equilibrium constant close to unity). At the same time there is a need for both isomers to be sufficiently stable and mutually different (enthalpy-entropy compensation can still ensure the equilibrium-constant require- ment). Moreover, the equilibrium criteria have to be necessarily combined with considerations of kinetics. The design problems are illustrated on two model systems: Si6H6 isomeric species and deuterium- and hydrogen-bonded water dimers, HOD . OHD and DOH . OHD, respectively.

Introduction

Designing of molecular electronics systems represents [l] a challenging appli- cation field for computational chemistry. Phenomena under consideration [2,3] (e.g., intramolecular hydrogen transfer, cis-trans isomerization, and charge trans- fer) have been the subject of constant theoretical and computational interest. Bistable or multistable molecules, studied as a potential switch enabling infor- mation storage [4-61, can be treated as a particular application of chemical- isomerism concepts [7]. Design of an optimum molecular-electronics device can be developed, based on thermodynamic and kinetic isomerization criteria. The present article contains illustrations of the computational molecular engineering approach in its thermodynamic part.

Computational-Thermodynamic Framework

For a conformational system to be applicable as information storage it should exhibit a relatively easy interchange between two isomers (in both directions). In addition to the interconversion rates, the stability of both structures with respect

*Permanent address: The J. Heyrovski Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, DolejHkova 3, CS-182 23 Prague 8-Kobylisy, Czech and Slo- vak Federal Republic.

0 1992 John Wiley & Sons, Inc. CCC 0020-7608/92/0S1625-08$04.00

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to decomposition into other products is also important. Moreover, the isomers should be sufficiently different (i.e., different under a read sequence that will not destroy the information content). Such design requirements can be discussed in purely quantum mechanical terms; however, they can also be treated in statisti- cal terms of equilibrium and rate constants as complex (however condensed) functions of the molecular parameters. It is rather natural to consider the equi- librium constants before the rate constants, since the latter certainly are pos- sessing a more complex nature. (It does not contradict the fact that a real molecular-electronics system will work out of the thermodynamic-equilibrium regime.) In this report, we shall not deal with all the three aspects in full-we shall concentrate on their isomeric-thermodynamic part only.

Let us consider an isomerization (for simplicity treated as an ideal gas-phase system-vide infru):

A1 A2, (1)

described by its equilibrium constant K. Computational evaluation of the equi- librium constant (without input observed information, from first principles-i.e., from computed structural, energy, vibrational, and possibly other characteristics) has been mastered in recent years [7-91. The corresponding standard Gibbs en- ergy change AG; at temperature T can be decomposed in related enthalpy (in fact, energy and enthalpy changes for an isomerization are equal) and entropy changes:

(2)

The initially stated requirement of easy interconversions can be considered from both kinetic and thermodynamic points of view. In the latter case, it can be formulated in terms of comparable equilibrium isomeric populations, i.e.:

AG; = AH; - TAS;.

K = l (3)

or in the Gibbs function term:

AG: = -RT In K = 0, (4)

while the requirement of sufficient (structural) differences between isomers can be expressed in the entropy term as

[AS:[ %- 0 . (5 )

I A H ; ~ %- o (6)

However, the combination of Eqs. (4) and (5) yields also

(and, moreover, AH;AS: > 0). Clearly enough, Eqs. (4)-(6) mean a well-work- ing enthalpy-entropy compensation (with isomerizations, the enthalpy-entropy compensation concept is, in contrast to other reaction stoichiometries, quite straightforward-cf. [7]). Alternatively, in molecular terms, the potential energy

MOLECULAR-ELECTRONICS DEVICE DESIGN 1627

term is compensated for by excited vibrational levels (and possibly other conve- nient entropy contributions). Finally, from the temperature dependency of K,

d In K AH! dT RT2’

- (7)

and Eq. (6), it follows that the equilibrium constant for a potential bistable molecular-electronics system should exhibit rather pronounced temperature dependency.

Overall, a search should concentrate on isomeric pairs in which, at the work- ing temperature, the interconversion equilibrium constant is close to unity, but, however, the entropy terms of the two forms are sufficiently different. Systems obeying these criteria will exhibit a rather distinct temperature dependence of K in the neighborhood of the working point. Hence, we deal with highly mobile equilibria not only in the kinetic but also in the temperature sense.

Isomeric conversion can alternatively be treated in terms of isomerism contri- butions to thermodynamics, recently introduced and applied to various systems [7-91. The treatment starts with isomeric mole fractions wi, for a two-component system in thermodynamical equilibrium given [7] (in terms of the isomeric parti- tion functions qi) by

while wz = 1 - w1 (R denotes the gas constant). The index 1 is usually assigned to the structure that is more stable in the low-temperature region. The wi terms measure the relative stabilities of the two isomeric structures (however, they say nothing about their decompositions to other products). Equation (8) was primar- ily designed for gas-phase conditions; however, it can also be applied [7] to other environments, supposing the partition functions are adjusted accordingly. More- over, a substantial cancellation operates on the right side of Eq. (8), ensuring a wide transferability of the results even without any adjustment. In particular, low vibrational frequencies are especially important in connection with Eq. (8). Their treatment is essentially the same in both the gas- and condensed phases, though the frequency values can be significantly shifted by solvation effects in some cases. Let us mention for completeness that sometimes a simplification of Eq. (8) is used, viz. the so-called simple Boltzmann factors w! (i.e., complete neglection of the rotational-vibrational contributions):

I 1 w 1 = 1 + exd-AE/(RT)]’ (9)

[AH: and A E in Eqs. (8) and (9) denote the ground-state and potential energy changes, respectively, induced by isomerization (1). In other words, AH: is the standard enthalpy change for the reaction at the absolute zero temperature.]

The isomerism contributions to thermodynamic functions, SX,, are intro- duced as correction terms that are to be added to the thermodynamic value be- longing to the pure isomer 1 in order to obtain an overall value of the function X,

1628 SLANINA

i.e., the value belonging to the equilibrium isomeric mixture. For example, it holds for the isomerism contribution to heat capacity in the two-component sys- tem [lo]:

where SC,,,, stands for the so-called isofractional isomerism contribution to heat capacity :

S C , , , = W 2 ( C j 2 - C;d, (11)

in which C j i denotes the standard heat capacity at constant pressure of the i-th isomer. The full isomerism contribution to heat capacity (10) is called the relax- ation contribution as it presupposes relaxation of the component population with a temperature change [lo].

Two Illustrative Examples

The first example deals with the isomeric system Si6H6. Computational studies of its potential hypersurface [ll, 121 proved the existence of three different local energy minima-hexasilaprismane (4), hexasilabenzene (&), and hexasila- Dewar benzene (G). On the potential energy hypersurface, hexasilabenzene is located [12] about 41 kJ/mol above hexasilaprismane, while the Czv structure is still some 100 kJ/mol above hexasilabenzene (so that for thermodynamic pur- poses the system can be well treated [13] as a two-component one). Figure l sur- veys the isomeric interplay, showing quite fast relative stability interchange. The interchange is equally well seen at the w, (however, the simple Boltzmann factors w,’ fail completely in this respect), the SC,,,, as well as the C; levels. Interest- ingly enough, the overall standard heat capacity at constant pressure C; reaches, close to or in the area of the fast relative-stability changes, considerably high val- ues. In fact, it can be considered as a rather favorable, stabilizing factor.

Isomeric species containing hydrogen bonds are considered as another possible candidate for designing molecular-electronics devices. There are several interest- ing systems of that type described computationally [7]. Actually, even one of the most popular simple hydrogen-bonded species, the water dimer, can be employed for the purpose in spite of the fact that no isomerism was proved in the system. Using isotopic labeling, two different, isomeric water-dimer structures can be created, viz. HOD * OHD and DOH * OHD, differing in the hydrogen isotope involved in the hydrogen bond.

The system was described by means of flexible water-water potentials of MCY-type [14-161. They originate from the famous MCY intermolecular poten- tial suggested by Matsuoka et al. [15]. Later on, Lie and Clementi [17] created the so-called MCY L potential by combining the MCY I1 intermolecular potential (i.e., the potential based on intermolecular electron correlation [l5]) with a quar- tic potential of a free water molecule from quantum-chemical evaluation [HI. As

MOLECULAR-ELECTRONICS DEVICE DESIGN 1629

5- 75

1 9

25

d

E" 2 150 2 \ - U 100 10

t

t *0°

0 - - E"

300 7

o n U

-

100

---. --- ---

__---- __---

I I I

500 1000 1500 20 3

Figure 1. Temperature evolution of the Si6H6 (hexasilaprismane and hexasilaben- zene) isomeric system. Top part: Equilibrium mole fractions w, and simple Boltz- mann factors wl (dashed curves); the two decreasing curves (i.e., one solid and one dashed) belong to hexasilaprismane. Middle part: Isomerism contributions SC,,, and SCp,v,~ (dashed curve) to heat capacity (related to hexasilaprismane as the refer- ence species). Bottom part: The standard heat capacity at constant pressure C,"., of hexasilaprismane (dashed curve) and the overall term C," belonging to the Si6H6

pseudospecies.

there are three other parametric modifications of the MCY intermolecular part available (MCYI [15], B [19], MCYC [20]), altogether four flexible potentials are considered (coded by MCY-X, where X = L, I, or C, or simply by -B). Table I surveys energetics of the water-dimer isotopomer formation. Figure 2 presents

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TABLE I. Survey of the (HD0)z formation energeticsa evaluated in the flexible MCYL-type potentials.

Potential Process Potential energy A E Ground-state energy AH:.i

MCY-L 2 HDO = HOD. OHD 2 HDO = DOH. OHD

2 HDO = DOH. OHD

2 HDO = DOH. OHD

2 HDO = DOH. OHD

MCY-I 2 HDO = HOD OHD

-B 2 HDO = HOD. OHD

MCY-C 2 HDO = HOD. OHD

-25.01 -25.01 -24.33 -24.33 -23.93 -23.93 -25.68 -25.68

- 18.24 - 17.54 - 17.95 -17.30 -17.73 -17.09 -18.63 -17.90

"In kJ/mol; the potential term is the same for both isotopomers within the Born-Oppenheimer approx imat ion.

the isomeric interplay evaluated within the flexible MCY-L potential. In a qualitative respect, the picture resembles the findings of Figure 1; however, the magnitude of the effects is considerably smaller. Moreover, the temperature maximum in the overall Cj term is missing. Table I1 shows the positions of the wi crossings and maxima in the isomerism contribution to heat capacity. The re- sults are surprisingly similar in all the four potentials, which strengthens reliabil- ity of the prediction.

In conclusion, it has been shown that highly mobile isomeric systems could meet requirements of molecular electronics. However, interest has been focused on the temperature mobility of the isomeric equilibria rather than on their ki- netic mobility. Vibrational motions of atomic nuclei and their temperature exci- tation play a crucial role in creating the temperature mobility. With respect to the computational demands, only simple model systems could be discussed (for which experimental data for verification are, unfortunately, so far lacking). A deeper insight, however, requires details on the interconversion mechanisms and, thus, a complete reaction-rate treatment. It can be understood as another impetus for theoretical studies of systems and phenomena of molecular electronics.

Acknowledgments

The study was carried out during a research stay at the Max-Planck-Institut fur Chemie (Otto-Hahn-Institut) supported by the Alexander von Humboldt- Stiftung. The support as well as the valuable discussions with Professor Karl Heinzinger and the kind hospitality of him, of his group, and of the Max-Planck- Institut fur Chemie are gratefully acknowledged. Last but not least, the con- structive and stimulating referee comments are highly appreciated.

MOLECULAR-ELECTRONICS DEVICE DESIGN 1631

75

50

25

4

3

2

1

0

- 1

500 lo00 1500 2Ooo - T(K) Figure 2. Temperature evolution of the (HDO)* (HOD . OHD and DOH . OHD) MCY-L isomeric system. Top part: Equilibrium mole fractions wi and simple Boltz- mann factors w i (dashed line); the decreasing curve belongs to HOD. OHD. Middle part: Isomerism contributions SC,, and SC,,, (dashed curve) to heat ca- pacity (related to HOD . OHD as the reference species). Botton part: The standard heat capacity at constant pressure Cj,j of HOD . OHD (dashed curve) and the over-

all term Ct belonging to the (HD0)z pseudospecies.

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TABLE 11. Characterization of some distinguished temperature pointsa of the (HD0)2 equi- librium isotopomeric mixture.

MCY-L 36.4d

MCY-I 33.8d

-B 33.0d

MCY-C 38.0d

549

532

539

63 1

89.6 50.0 89.7 50.0 89.7 50.0 89.6 50.0

0.09

0.08

0.08

0.09

-0.40

-0.38

-0.35

-0.36

4.38 -0.40

4.34 -0.37

4.35 -0.34

4.38 -0.35

43.7 87.2 43.4 86.8 43.8 87.1 44.2 89.8

"Either wi crossing or maximum in the isomerism contribution to heat capacity SC,,, (cf. Fig. 2). bRelated to HOD. OHD isotopomer as the reference species. T h e standard heat capacity at constant pressure of 1 mole of the two-membered equilibrium

dLocal temperature maximum of the SCp,l term. isomeric mixture of the (HD0)2 species.

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Received November 14, 1990 Accepted for publication May 7, 1991