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Reactions of Amino Acids on the Si(100)-21 Surface Pendar Ardalan,†,§ Guillaume Dupont,†,§ and Charles B. Musgrave*,‡ † ‡
Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States ABSTRACT: Reactions of amino acids on the Si(100)-21 surface have been investigated using the B3LYP hybrid density functional theory. Amino acids provide a diverse set of organic functional groups, several of which have not been studied previously for their reactivity on semiconductor surfaces. The amino acid common group is found to react through several low energy pathways, with O-H dissociation of the carboxyl group being the most kinetically favorable. Consequently, reactions of amino acids through the amine and carboxyl functionalities are not expected to be selective. The reactivity of several of the amino acids displays unique, and possibly useful, properties not exhibited by organic functionalities previously considered, while others react on Si(100)-21 analogously to their simpler organic analogues. Resonance effects significantly affect the reaction energetics of arginine, histidine, and tryptophan leading to reactivities qualitatively different from their analogous isolated functional groups. The most unique of these reactivities include pericyclic ene reactions of the imine functional group of arginine and the cyclic imine of the imidazole side-chain of histidine. Both of these reactions involve formation of Si-N dipolar (dative) bonds which are significantly stronger than any previously observed on Si(100)-21.
1. INTRODUCTION Organic modification of semiconductor surfaces enables the incorporation of organic functionalities onto semiconductor substrates to exploit their combined advantages to fabricate organic and semiconductor hybrid systems.1,2 The diversity of organic functional groups provides access to a wide variety of adjustable functions and properties, while semiconductor processing provides a technology for reliably and efficiently fabricating complex systems of integrated nanoscale electronic devices.3,4 The interest in the covalent attachment of organic molecules to group IV semiconductor surfaces has been partially driven by the expectation that the ability to controllably deposit a thin organic film onto a semiconductor surface by organic modification will have significant technological applications. Possible applications include hybrid organic-semiconductor molecular electronics, sensors, nanotechnology, and electronic and optical devices.4-7 One area of emerging interest is the fabrication of hybrid semiconductor-biological devices that couple the exquisite properties of biological molecules, such as proteins, with the modern fabrication capabilities of semiconductor technology.8-11 While biological molecules typically have unique and highly specific properties, they are themselves often large organic molecules, some of which, such as peptides, are composed of sequences of spatially oriented simple organic functional groups. Consequently, our growing capacity to attach organic molecules to semiconductor surfaces also enables the attachment of a variety of biological molecules to these same substrates that may result in films with unique or useful properties not exhibited by films of previously studied organic functionalities. The central question we address here is to what extent do the reactivities of amino acids on the Si(100)-21 surface display unique reactivities not exhibited by previously studied nonbiological organic functionalities? r 2011 American Chemical Society
Amino acids are of particular interest for several reasons. First, they are the building blocks of larger biological molecules, specifically peptides and proteins, which are generally not amenable to study using quantum chemical methods. Second, amino acids have functional groups in common with many organic molecules whose chemistries on Si(100)-21 and Ge(100)- 21 have previously been explored, including hydroxyls,12,13 amines,14-16 carbonyls,17 carboxylic acids,18 thiols,19 and aromatics.20-22 This allows the determination of the extent to which previously studied small organic molecules with analogous functionalities serve as models of the reactivity of their larger biological counterparts. Finally, amino acids provide organic functional groups which have not been previously investigated or which involve interactions with neighboring functional groups within the amino acid that make their reactions with the Si(100)-21 surface distinct from their simpler organic analogues. Although direct attachment of large polypeptides, such as proteins, to semiconductor surfaces will not be practical using vapor deposition techniques, methods that involve first functionalizing the surface with an amino acid to form an organic monolayer and then exposing this film to a solvated biomolecule might be capable of producing hybrid biomolecular and semiconductor systems. In this case, the amino acid acts as a linker molecule that not only binds the biomolecule to the substrate but also controls the semiconductor-biomolecule interface. Similarly, in the fabrication of organic molecular electronic devices, amino acids might be used to chemically and electronically couple the semiconductor to an active organic layer and thus control the stability and electronic properties of the interface. Received: December 2, 2010 Published: March 28, 2011 7477
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The Journal of Physical Chemistry C Although this work specifically explores the attachment of amino acids or their truncated analogues to Si(100)-21, it also provides insight into the principles that govern interactions of organics with semiconductors to suggest new directions for innovative approaches for organic functionalization of semiconductor surfaces. The effort to develop methods for organic functionalization of semiconductors has motivated a desire to understand the fundamental principles that govern this chemistry with the anticipation that this knowledge will help guide development of this field. Consequently, the theoretical investigation of semiconductor surfaces as organic reagents has been particularly active and has played an important role in not only elucidating the underlying principles responsible for the experimental observations but also predicting the behavior of these systems, establishing the detailed mechanisms of the surface chemistry, confirming experimental observations, and suggesting new types of reactions.1,2,5,9 Furthermore, theory is capable of predicting many properties that are not currently obtainable by experiment. For example, ab initio simulations provide a detailed description of the electronic structure of the reacting system from which a comprehensive picture of the principles that govern the energetics and thus the kinetics, thermodynamics, and reactivity of the system is obtained. This work is similarly motivated and aims to provide a detailed description of the reactions of amino acids on semiconductor surfaces to uncover the effects that govern their reactivity to determine to what extent they differ from those of previously studied nonbiological functionalities. We have investigated the reactions of amino acids with the bare Si(100)-21 surface using density functional theory (DFT). Although quantum chemistry is uniquely capable of describing the fundamental physics of these reacting systems, it is not currently practical for simulation of large molecules. Consequently, the results we report describe reactions between isolated amino acids and bare semiconductor surfaces. Furthermore, the effects of solvation are not included. Thus, because solvation plays a critical role in the behavior of large biological molecules, this work is not aimed at describing systems such as solvated proteins in their folded states. However, these calculations do serve as predictions for how isolated amino acids, including individual amino acids of polypeptides with localized surface interactions, and their organic analogues react on semiconductor surfaces. We also do not explore the attachment of amino acids to multiple reactive sites on the surface, unless those sites are on the same surface dimer. In a few cases, reactions of single functional groups across multiple dimers will be most favorable, while in other cases larger amino acids will react with multiple surface sites through multiple functional groups. Both cases are generally left to further investigation, although we occasionally comment on when specific reactions with multiple sites might be expected. This paper is organized as follows. We next describe the computational details of the simulations. We then report our results and follow with a discussion of those results for the reactions of the amino acids with the Si(100)-21 surface. The reactions of alanine and glycine are described first because they have unreactive side-chains, and so we use these two amino acids as models for the common group reactivity of the larger amino acids (except proline). We then describe the reactivity of the other amino acids grouped by their side-chain functional groups. We then conclude with a summary of the general principles uncovered in this work and highlights of the unique reactivities it predicts.
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2. COMPUTATIONAL DETAILS We describe the electronic structure of the reacting system using the B3LYP hybrid exchange density functional theory (DFT) method23-26 and expand the molecular orbitals in atomic Gaussian basis functions. The B3LYP method has been applied to study the reactions of a wide variety of functional groups on semiconductor surfaces and generally provides a good description of the system reactivity9,20,27-30 except in a few cases, for example, when stationary states possess multireference character, such as in the cycloaddition of benzene to the Si(100)-21 surface.31 This approach has been found to reproduce experiment and the results of high-level single-reference methods, such as quadratic configuration interaction singles and doubles and connected triples (QCISD(T)), relatively accurately.14 The Si(100)-21 surface is modeled with the Si9H12 one-dimer cluster, which consists of four layers of silicon atoms with the top layer containing the two Si dimer atoms. This simple cluster is designed to mimic the essential chemical reactivity of the 21 reconstructed Si(100) surface. Clusters have been used previously as models of surface reactive sites to predict reaction products on both the Ge and Si(100)-21 surfaces for systems such as amines,3,14,16,32,33 alkynes,34 ammonia,35-37 nitriles,38-41 and ketones27 and generally produce results consistent with experimental observations, except in cases where significant interactions extend beyond the cluster, for example, when strong Lewis bases dative bond to the surface.35,36,42,43 In these cases, the one-dimer cluster was seen to underestimate the adsorption energy calculated by larger clusters by ∼20%, although the nature of the reaction profile was unchanged. We use a mixed basis set scheme to more accurately describe the chemically active portion of the cluster while limiting the computational cost. Specifically, the 6-311þþG(d,p) basis set is used for the dimer atoms and atoms of the reacting amino acid, whereas the 6-31G(d) basis set is used to describe the subsurface and terminating hydrogen atoms. This scheme is designed to minimize computational cost while allocating additional basis functions to describe parts of the system that undergo significant modification to the electronic structure during reaction. It is important to note that in solutions of polar or protic solvents, as well as in crystalline phases, amino acids exist in their zwitterionic form.44-46 In the gas phase, however, amino acids are found in their neutral (nonionic) form.47-50 In the current work, gas phase reactions of amino acids with the Si(100)-21 surface are investigated, and hence we have modeled the amino acids in their neutral forms. In addition, we have employed truncated models to study the reactions of sidechains of arginine, tryptophan, tyrosine, and histidine at the Si(100)-21 surface (vide infra). These models will be described in detail in section 3. In contrast, the reactions of glycine, alanine, serine, threonine, and cysteine with the Si(100)-21 surface were studied using the complete amino acids. Structures were fully optimized without geometrical constraints on the clusters and were examined to determine whether unphysical distortions of the surface model occurred. Frequency calculations were used to verify that the minima and transition states (TS) have only zero and one imaginary frequency, respectively, as well as to determine the zeropoint energies of each state. All calculations were performed using the Gaussian 03 software package.51 3. RESULTS 3.1. Alanine and Glycine. Alanine and glycine are the simplest amino acids and also two of the most abundant in 7478
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Figure 1. Schematic potential energy surface of the N-H and N-C dissociation reactions of alanine on the Si9H12 one-dimer cluster.
Figure 2. Schematic potential energy surface of the O-H dissociation and CdO [2 þ 2] cycloaddition reactions of alanine on the Si9H12 one-dimer cluster.
protein structures. The common groups of all amino acids share two reactive groups: an amine and a carboxylic acid consisting of a carbonyl group and a hydroxyl group. In addition to the amino group, alanine and glycine possess a methyl and hydrogen sidechain, respectively. Consequently, because their side-chains are unreactive on Si(100)-21 alanine and glycine should exhibit nearly identical surface reactivity. Furthermore, because alanine is so simple we use it as a model for the reactivity of the common group on the Si(100)-21 surface. The reactivities of both the amine and carboxylic acid functional groups on Si(100)-21 have been investigated previously using small organic molecules.43,52-55 Thus, these calculations indicate the degree to which the neighboring functional group affects the energetics of the surface reactions of alanine on Si(100)-21. In polypeptides the amine and carboxyl groups form peptide bonds making them unavailable for reaction with Si(100)-21, and consequently the reactivity of the common group on Si is directly relevant to isolated amino acids only. We investigated several distinct possible adsorption states and reaction pathways of alanine’s common group on the Si(100)21 surface. The lone pairs of the amine, hydroxyl, and carbonyl
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groups can each act as Lewis bases to form dipolar (also known as dative) bonded molecular adsorbed states on Si(100)-21, which here acts as a Lewis acid. From these molecular adsorbed states, several desorption pathways are possible. We calculated seven local minima corresponding to the products of N-dipolar bonding, O-dipolar bonding through the O-H group, Odipolar bonding through the carbonyl oxygen, N-H dissociation, N-C dissociation, O-H dissociation, and [2 þ 2] cycloaddition across the carbonyl. The calculated energetics for these stable structures relative to the reactants are reported in Figures 1 and 2. We did not find low energy pathways for C-C or C-H dissociation, and consequently, we did not explore these reactions further. N-H Dissociation through the Amine Dipolar Bonded Adduct. The schematic potential energy surface (PES) for adsorption and reaction through the amine group is shown in Figure 1. The adsorption energy of the molecularly adsorbed alanine dative bonded through its amine N atom is 22.2 kcal/mol. Because amine dative bonded adsorbates on Si(100)-21 are stabilized by approximately 6 kcal/mol with respect to the onedimer model when charge is allowed to delocalize to neighboring bare dimers, we expect the adsorption energy of the alanine dative bonded state to be ∼28 kcal/mol.35,36,42 This stabilization should be similar for the amine dative bonds of the other amino acids. From the N dative bonded state two distinct dissociation pathways are found: one branch leading to the N-H dissociation product and one branch to the N-C dissociation product. The energy relative to the reactants of the transition state of the N-H dissociation reaction is -7.9 kcal/mol, which is 14.3 kcal/mol above the N dative bonded state. N-C dissociation is less kinetically favorable because its TS lies 12.5 kcal/mol above the reactants, and thus the barrier for this reaction is 34.7 kcal/mol. These results are consistent with results from previous studies of reactions of methylamines on Si(100)-2114,16,32 that showed that while the TS for N-H dissociation lies below the entrance channel the TS for N-C dissociation lies substantially above the energy of the reactants. Carboxylic Acid O-H Dissociation, Ene Reaction, and CdO [2 þ 2] Cycloaddition. The carboxylic acid of alanine can undergo several different reactions as shown by the schematic PESs in Figure 2. It can molecularly adsorb on Si(100)-21 via dipolar bonding through either of its two oxygens (Figure 2). The adsorption energies of the CdO dipolar bonded state (10.9 kcal/mol) and the O-H dipolar bonded state (8.3 kcal/mol) are consistent with previous studies.9,28,56,57 These dative bonds are weak relative to that of the amine dative bonded state, and consequently stabilization due to charge delocalization to neighboring dimers will be smaller. The CdO dipolar bonded state is calculated to be 2.6 kcal/mol stronger than the O-H dative bonded state, and although the difference in adsorption energies is similar to the size of the errors in the theoretical methods employed, we interpret this as a result of stronger Lewis base character of the CdO oxygen compared to that of the hydroxyl group in -COOH. A comparison of the gas phase proton affinities of these two donors reveals that the proton affinity of the CdO group oxygen is larger than that of the O of the -OH moiety in -COOH. O-H bond dissociation can occur from either the O-H or CdO dipolar bonded states as shown in both Figures 2 and 3. From the O-H dative bonded state, the O-H dissociation barrier (Figure 2) is 7.7 kcal/mol, and the overall reaction energy is -60.6 kcal/mol. We can compare these energies to those 7479
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Figure 3. Qualitative comparison of the transition states for O-H dissociation of the carboxyl group at the Si(100)-21 surface from the (a) CdO dipolar bonded state or (b) O-H dipolar bonded state.
previously calculated for the analogous reactions with water. The calculated O-H dissociation barrier and reaction energy for water on Si(100)-21 are 1.6 and 62.8 kcal/mol, respectively. These energies are obtained using B3LYP/6-311G** single-point energies at BLYP/TZ94P geometries.56 The overall energy is similar because the reaction is isodesmic; that is, it preserves the number of each type of bond. However, the barrier is larger by 6.1 kcal/mol, most likely because of differences in the geometry, basis set, and reactivity of H2O and the O-H group of alanine. From the CdO dipolar bonded state, O-H dissociation is analogous to the electrocyclic ene reaction and has a barrier of only 0.2 kcal/mol (Figure 2). The low barrier for H transfer from the O-H group in the CdO adsorbed state is likely due to the conformationally favorable six-center TS (Figure 3a), whereas ring strain makes the four-center TS for hydrogen transfer from the O-H adsorbed state (Figure 3b) less favorable. We compare these results with those for the adsorption of formic acid on Si(100)-21 obtained by Lin and co-workers who also found a barrierless pathway for O-H dissociation in agreement with our result.57 However, the energy of -8.3 kcal/mol we calculated for the alanine O-H dipolar bonded adduct is 5.2 kcal/mol more stable than that obtained by Lin et al. for formic acid, while the O-H dissociation TS energies are different by 5.5 kcal/mol. Although some of the differences may be due to the difference in the level of theory employed, it might also result from interaction of the amine group of alanine with the O-H dative bond. The CdO double bond can directly undergo [2 þ 2] cycloaddition with the dimer leading to the formation of a four-membered ring (C-Si-Si-O). We found no barrier for this reaction, which is exothermic by 24.1 kcal/mol. However, this state can also be formed from the CdO dative bonded state in which case a barrier of 3.8 kcal/mol relative to the CdO dipolar bonded state is predicted, which therefore lies 7.1 kcal/mol below the entrance channel as illustrated in Figure 2. In either case, the low exothermicity makes the reverse barrier from the [2 þ 2] product to form the CdO dipolar bonded state only 17 kcal/mol, which thus makes the [2 þ 2] cycloaddition reaction reversible at moderate temperatures. We also calculated reactions of glycine with the Si(100)-21 surface. Glycine is similar to alanine but has a hydrogen atom in place of the side-chain methyl group. As might be expected, our results for glycine are essentially the same as those of alanine because alanine’s methyl group has only a minor effect on the interactions involved in the reaction. For example, the product energies obtained for alanine and glycine differ by at most 1.5 kcal/mol, and consequently, for both cases the main product
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is predicted to be that of O-H dissociation. This prediction agrees with experimental observations of glycine on Si(100)-21,8 which indicates that O-H dissociation is the major product while N-H dissociation is a minor product. 3.2. Serine, Threonine, and Tyrosine. O-H Dissociation of Alcohol Side-Chains. The side-chains of serine and threonine are a primary and secondary alcohol, respectively, whereas tyronsine’s side-chain is a phenol. Their reactivity is expected to be similar to that of the carboxylic acid hydroxyl group with the differences resulting from the effects of the neighboring carbonyl of the common group or aromatic ring of tyrosine’s phenol group. For example, the side-chain O-H groups have similar reactivity to that of the common group hydroxyl for O-H dipolar bonding and dissociation through the O-H dipolar bonded adduct. However, abstraction of the side-chain O-H hydrogen via the CdO dipolar bonded adduct has a large barrier and is endothermic, in contrast to H abstraction via the ene reaction of the common group (Figures 2 and 3a). In the case of serine and threonine, the two intervening carbon atoms between the sidechain hydroxyl and common group carbonyl do not allow the conjugation that stabilizes the TS and product of the ene reaction of the common group. Similarly, tyrosine’s intervening aromatic ring and two carbon atoms decouple the O-H and carbonyl groups. Consequently, serine, threonine, and tyrosine’s sidechain does not undergo O-H dissociation through the CdO dipolar bonded adduct. Instead, their side-chains react by O-H dissociation and therefore have reactivity analogous to that of alcohols on the Si(100)-21 surface. We calculate that serine’s side-chains will form an O-H adduct with an adsorption energy of 19.5 kcal/mol and an O-H dissociation barrier of 13.7 kcal/mol, which results in an O-H dissociated product with overall energy of -63.5 kcal/mol. The O-H adsorption energy for methanol reaction on Si(100)21 was previously predicted to be 12.1 kcal/mol and to undergo O-H dissociation through a 2.3 kcal/mol barrier.57 The OH dipolar bonded states of serine and threonine are likely more stable than that of the common group and methanol due to H-bonding the H of the -OH side-chain with the carbonyl or amine groups. Furthermore, unlike the O-H dipolar adduct of the common group, the side-chain O-H dipolar bonded adduct does not disrupt the carbonyl conjugation and forms a stable sixmembered ring. Similarly, the more stable O-H adduct and disruption of the six-member ring leads to a large O-H dissociation barrier. Tyrosine reactivity may be somewhat different because its side-chain contains an aromatic phenol group, which we model as 4-methyl-phenol. We calculate that tyrosine’s O-H group dissociates through a barrier of 2.3 kcal/mol and adsorbs with an adsorption energy of 8.1 kcal/mol. This compares to adsorption energies of 8.3 kcal/mol for the common group O-H adducts. The O-H adducts of tyrosine and the common group are destabilized due to the delocalization of the oxygen lone pair over the neighboring π systems. Although the reactivity of phenol on the Si(100)-21 surface has not been specifically considered previously, related functional groups have been studied. For instance, benzoic acid and aniline have both been shown to react on the Si(100)-21 surface through their respective substituents, the carboxyl and amine groups, leaving the aromatic ring unreacted. This is in contrast to benzene which reacts by either [2 þ 2] or [4 þ 2] cycloaddition to the Si-Si dimer, or in combinations of these reactions when attaching to neighboring dimers.58-61 Therefore, serine, threonine, and tyrosine are all predicted to react 7480
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Figure 4. Schematic potential energy surface of the reaction of the sidechain of cysteine on the Si9H12 one-dimer cluster. The inset shows the energies of different local minima with respect to the reactants for the reactions of cysteine at the Si(100)-21 surface. The energies of minima that result from analogous reactions involving alanine are shown in parentheses for comparison.
primarily by O-H dissociation, either through the common group carboxylic acid or their side-chain O-H groups. 3.3. Cysteine. Cysteine is similar to alanine, but with one of the methyl hydrogen atoms replaced by an S-H group, providing a reactive group that has not been explored extensively on Si surfaces. Thiols are analogous to O-H groups thus making cysteine the thiol analogue of serine. As with serine, the common group amine and carboxylic acid are not expected to affect the energetics of reactions at the S-H group. For example, we found structures and energetics for reactions involving the amine and carboxylic acid groups of cysteine similar to those of alanine and glycine, suggesting that the thiol has little effect on those reactions (Figure 4 inset). However, the thiol side-chain introduces two additional minima: cysteine molecularly adsorbed through a Si-S dative bond between sulfur and the electrondeficient down Si atom of the surface dimer and the S-H dissociation product (Figure 4). Formation of the dipolar bonded state is barrierless and exothermic by 13.3 kcal/mol. Dissociation of the S-H bond from the dative bonded state involves a barrier of 4.3 kcal/mol and is exothermic by 58.5 kcal/mol. Osgood et al. showed that methanethiol undergoes a similar S-H dissociation on the Si(100)-21 surface,19 although the energy of the adduct relative to the reactants is lower for cysteine (-13.3 kcal/mol) than for methanethiol (-9.1 kcal/mol).19 Similarly, the S-H dissociation TS energy relative to the reactants is also lower for cysteine (-9.0 kcal/mol) than for methanethiol (-6.5 kcal/mol).19 However, the differences between the energies we calculate for cysteine and the analogous reactions involving methanethiol are moderately small relative to the resolution of the methods and the differences in the levels of theory. For S-C dissociation, Osgood et al. found S-CH3 dissociation barriers greater than 30 kcal/mol for the organosulfur compounds they investigated.19 Thus, as in the case of methylamines, methyl group transfer to the neighboring dimer Si atom requires a large barrier, and consequently we do not describe this reaction further. Because the barrier for S-H dissociation is only 4.3 kcal/mol, we expect the formation of both O-H and S-H dissociation products, with O-H dissociation via the ene reaction dominating the product distribution at low temperatures. Furthermore,
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Figure 5. Schematic potential energy surface of Nb-Hb and Nc-Hc dissociation mechanisms for arginine as modeled by N-methylguanidine on the Si9H12 one-dimer cluster.
because the S-H functional group is two and three C atoms removed from the NH2 and O-H groups, respectively, cysteine might bridge between neighboring dimers through either dipolar bonds or covalent bonds resulting from O-H, S-H, and/or N-H dissociation, similar to this possibility for serine. We have left investigation of these bridged structures for a later study. 3.4. Arginine. Glycine, alanine, cysteine, and serine are the four smallest amino acids. In the case of most of the larger amino acids, their side-chain functional groups do not interact strongly with the carboxylic acid or amine common groups. Because quantum chemical calculations grow rapidly with system size, it is expedient to truncate the reacting molecule to only include the atoms of the reacting group and neighboring atoms. For example, in the case of arginine the common group and the reactive end of the side-chain are well separated. Consequently, we model the reactive end of the arginine side-chain as N-methylguanidine (Figures 5 and 6), whereas the reactivity of arginine’s common group is expected to be similar to that of alanine, as discussed above. We investigated several possible adsorption states and reaction pathways of arginine (as modeled by N-methylguanidine) on the Si(100)-21 surface. The side-chain of arginine has three nitrogen centers, an imine nitrogen and two amine nitrogens, which we label as Na, Nb, and Nc, respectively. The amine groups, including that of the common group not present in the Nmethylguanidine model, should behave similarly to the amine reactions discussed above and to those we have studied previously, although they may be affected by the resonance effects within the π-space of the guanidine group. On the other hand, the imine [2 þ 2] reactions of guanidine are unique from other [2 þ 2] reactions of amino acids. Furthermore, the imine dipolar bond to the surface may behave differently from the amine dipolar bond due to the electronic effects of the imine CdN double bond as suggested by the differences between the CdO and O-H dative bonds of alanine and their respective ene and O-H dissociation reactions. CdN [2 þ 2] Cycloaddition Reaction. We have calculated the reaction energetics for CdN [2 þ 2] cycloaddition to the weak π-bond of the Si(100)-21 dimer, the three Si-N dative bonded states, and the four N-H dissociation reactions (Figures 5 and 6). The CdN cycloaddition reaction is barrierless and, due to ring strain, only 26.1 kcal/mol exothermic, similar to 7481
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Figure 6. Schematic potential energy surface of the Na-Ha dissociation and ene reaction mechanisms for arginine as modeled by N-methylguanidine on the Si9H12 one-dimer cluster. The inset shows a resonance model representing the dative bonding of N-methylguanidine to the Si(100)-21 surface via its imine nitrogen atom.
our results for CdN [2 þ 2] cycloaddition of nitriles on the Si and Ge(100)-21 surfaces.38,62 N-H Dissociation Reactions of the Side-Chain Amines. The amine dative bonded states of arginine have adsorption energies (see Figure 5) 2-5 kcal/mol lower than those previously calculated for amines and ammonia on Si(100)-21, due to the disruption of resonance within the guanidine functional group upon forming the dative bond.14,16,35,36 The barriers to amine N-H dissociations of the side-chain have slightly larger energies than the N-H barrier for alanine and other amines.35,36 Thus, the arginine N-H dissociations of the amine groups are only slightly less kinetically favorable than N-H dissociation of the common group amine because the imine group has only a minor effect on the reactivity of the neighboring amine N-H bonds once the resonance within the guanidine functional group is disrupted by the amine dipolar bond to the surface. Furthermore, N-H dissociation is within ∼2 kcal/mol of that of the common group amine (Figures 1 and 5). In contrast, the Si-N dipolar bond formed between arginine’s imine N of the guanidine functional group of the side-chain is quite unlike the dative bonds of the two amines. Imine Dative Bonding, N-H Dissociation, and Ene Reactions. Adsorption of arginine to form a dipolar bonded surface adsorbate through the imine N lone pair (Figure 6) results in an adsorption energy of 41.3 kcal/mol. The dipolar interaction involves the donation of the N lone pair of CdN to the dangling bond orbital of the down Si atom of the dimer and is significantly stronger than any previously observed Si-N dipolar bond. For example, ammonia and methylamine dative bonds on Si(100)-21 have energies of 23-29 kcal/mol.14,16,35,36 Furthermore, nitriles, which might at first be expected to have Si-N bonds similar to imines, have dative bonds of only ∼14 kcal/mol.38 Consequently, the significantly stronger imine Si-N dative bond indicates that it is likely qualitatively different from other Si-N dative bonds on Si(100)21. An analysis of the structural changes of guanidine on adsorption through the imine lone pair confirms this and provides insight into the nature of this interaction. The dative N-Si bond energy of the imine N atom of the guanidine functional group relative to that of simple alkyl amines on Si(100)-21 can be attributed to the stronger Lewis base character of the imine N of guanidine relative to the donor
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properties of the N of simple alkyl amines. This can be analyzed by computing the gas phase proton affinities of the nitrogens of the imine and amines of guanidine and of methylamine. The proton affinity (computed using B3LYP/6-31G(2d, p)) of the guanidine imine is larger than the proton affinities of the amine N's in guanidine and methyl amine by 31.0 and 27.5 kcal/mol, respectively, and can be explained using a simple resonance model as shown in Figure 6 (inset) in which the larger proton affinity of the imine N can be attributed to additional stabilization gained from extensive delocalization of the positive charge from the imine N to the neighboring amine N’s. Because adsorption to form the imine dative bond is a Lewis acid-base reaction, the ability to delocalize is similarly manifested in the stronger adsorption energy of the imine adduct. Examination of the imine dipolar bonded adduct geometry and the changes in the bond lengths of arginine’s guanidine sidechain upon adsorption reveal that its interaction with the surface through the imine is not simple dipolar bonding. Furthermore, upon adsorption arginine’s CdNa double bond lengthens to 1.33 Å, which is intermediate between a CdN double bond (∼1.28 Å) and a C-N single bond (∼1.4 Å). However, the C-N single bonds also lengthen when their N centers form dative bonds to the Si surface, signifying the disruption of resonance in the guanidine moiety, which in turn reduces the amine dipolar bond strengths. We also find that in the imine N-Si dipolar bonded state the C-Nb bond decreases to 1.33 Å, which is intermediate between that of a C-N single and double bond, indicating that they are of intermediate bond order. In fact, it has the same length as CdNa. On the other hand, the C-Nc bond length is unchanged. Furthermore, the Si-N dipolar bond length is 1.87 Å, significantly shorter than typical Si-N dative bonds (2.05 Å) while somewhat longer than Si-N covalent bonds (1.78 Å). Consequently, the N-Si bond might be more accurately interpreted as a bond of mixed covalent and dipolar character. The equivalent C-N bond lengths of the dipolar bonded state indicate the stabilization gained by the delocalization of the positive charge as described earlier. We also observe that the distance between the hydrogen atom bound to Nb and the bare Si dimer atom is 2.32 Å, indicating a H bond which further adds to the stability of the adsorbed state. From the imine adsorbed state, two distinct dissociation pathways involving H transfer to the bare Si atom of the dimer are possible: Na-H bond dissociation and Nb-H dissociation where the H transfer completes the electrocyclic ene reaction. The barriers for these two pathways differ appreciably: the barrier for the Na-H dissociation is 24.7 kcal/mol, whereas the barrier for the Nb-H dissociation by the ene reaction is only 5.3 kcal/mol. The latter is thus the most kinetically favorable pathway for reactions of the guanidine side-chain. The two dissociations are exothermic by 57.0 and 57.4 kcal/mol, respectively. An examination of the geometry of the ene product indicates that the quantum mechanical resonance in the π-space observed in the molecularly adsorbed state is maintained. Furthermore, a detailed examination of the electronic structure of the ene product and molecularly adsorbed imine adduct shows that this resonance effect couples to the electronic structure of the Si(100)-21 surface. 3.5. Tryptophan. [4 þ 2] and [2 þ 2] Cycloadditions Reactions. Tryptophan’s side-chain is composed of the aromatic and highly conjugated indol group, which we model as 3-methyl-1-Hindol (Figure 7). Because 3-methyl-1-H-indol is strongly conjugated, reactions involving electrons in the π-space of the rings incur an energy penalty for disrupting the resonance. We considered several distinct adsorption states and reactions pathways 7482
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Figure 7. Schematic of the potential energy surface of the N-H dissociation reaction of the side-chain of tryptophan (as modeled 3-methyl-1-H-indol) and side-chain of histidine (as modeled 5-methyl1-H-imidazole) on the Si9H12 one-dimer cluster.
of 3-methyl-1-H-indol on Si(100)-21 as tryptophan may undergo several different reactions, including [2 þ 2] and [4 þ 2] cycloadditions to both the phenyl and pyrrole rings. Reactions with the phenyl ring are expected to be less energetically favorable because of its aromaticity. On the other hand, the pyrrole ring although conjugated is not aromatic. Furthermore, [4 þ 2] reactions are usually more exothermic than [2 þ 2] reactions because of the ring strain of the four-membered ring of the [2 þ 2] product.1,2 However, [2 þ 2] cycloaddition between the dimer and the CdC bond of the pyrrole ring is 18.8 kcal/mol exothermic. while the [4 þ 2] reaction between the dimer and the pyrrole ring is only 2.3 kcal/mol exothermic. The [2 þ 2] product is more stable because although the [2 þ 2] reaction forms a strained four-membered ring it only disrupts the conjugation of the pyrrole ring, whereas the [4 þ 2] reaction breaks the resonance in both the phenyl and pyrrole rings. In addition to cycloaddition reactions with the pyrrole ring, both [4 þ 2] and [2 þ 2] reactions involving the phenyl ring are possible. These reactions are generally not favorable, unless they involve binding to multiple surface dimers. Similarly, the reactivity of the phenyl ring is lower than that of the amino acid common group. Consequently, we have not examined reactions with the phenyl ring of tryptophan further. N-Si Dipolar Bonding and N-H Dissociation. In addition to cycloaddition reactions, tryptophan may also adsorb onto the surface through a N-dipolar bonded state between the N atom of the pyrrole ring and the electron-deficient Si dimer atom (Figure 7). The dipolar bonded state lies 6.1 kcal/mol below the reactants. Compared to other Si-N dative bonds described here and in previous studies, this interaction is weak. For instance, the energy of the N-dipolar bonded state of alanine is predicted to be -22.2 kcal/mol on the one-dimer cluster. The Si-N dipolar bonds on bare Si(100)-21 are approximately 6 kcal/mol stronger when neighboring dimers in the dimer row are included in the cluster model;35,36 however, the dative bond of tryptophan will remain substantially below that of other Si-N dative bonds involving amine-like N centers. We can again explain the weak interaction as a result of the loss of resonance of tryptophan’s indol side-chain where the pyrrole N atom lone pair participates in the delocalized π-space, but rehybridization of the N lone pair from sp2 to sp3 and formation of the N-Si dipolar bond disrupt the resonance.
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From the dipolar bonded state, N-H dissociation occurs with a transition state energy of 1.2 kcal/mol above the vacuum level and thus a reaction barrier of 7.3 kcal/mol, and the overall reaction is 54.3 kcal/mol exothermic (Figure 7). Thus, the sidechain of tryptophan is predicted to react on Si(100)-21 by N-H dissociation. These results are consistent with the results of previous studies on the reactivity of pyrrole on Si(100)-21.33 In that case we found that the dipolar bond was only 0.6 kcal/mol, and consequently the pyrrole dipolar bonded adduct is not stable. The pyrrole barrier and N-H dissociation energy of 7.0 and 52.6 kcal/mol are similar to those of tryptophan’s side-chain we report here despite the higher degree of conjugation in indol relative to pyrrole.33 3.6. Histidine. The aromatic nitrogen-heterocyclic imidazole side-chain of histidine provides a unique functionality whose reactivity on Si(100)-21 has not been previously explored. We model the side-chain by truncating the amino acid common group at the R carbon to obtain 5-methyl-1-H-imidazole (Figure 7). We investigated several distinct possible adsorption states and reaction pathways of 5-methyl-1-H-imidazole on the Si(100)-21 surface. Histidine’s imidazole ring includes two qualitatively different nitrogen centers: an imine nitrogen and an amine nitrogen. The lone pair of the amine N is delocalized over the ring and comprises part of the ring π-system. On the other hand, the lone pair of the imine nitrogen is orthogonal to the ring π-space and thus does not participate in the ring aromaticity. Consequently, two distinct dative bonded states are expected: one similar to the N-Si dative bond of pyrrole and one somewhat similar to the N-Si dative bond of arginine, but here involving a cyclic imine N atom. Furthermore, we examine N-H dissociation, CdN and CdC [2 þ 2] cycloaddition, and [4 þ 2] cycloaddition. For dipolar bonding by N lone-pair donation to the electrophilic Si atom of the dimer we find two dissimilar results. Adsorption at the amine-like N center is not stable as we were unable to locate a minimum. This is because dipolar bonding through this N disrupts the resonance in the ring, analogous to the effect in pyrrole and tryptophan. On the other hand, adsorption through dipolar bonding of the imine N lone pair to the Si down atom produces two similar stable structures with the rings lying in the same vertical plane as the dimer, but differing by a 180° rotation of the adsorbate about the N-Si bond. Both adducts involve dipolar bonds of -28.4 and -30.1 kcal/mol, ∼57 kcal/mol stronger than amine dipolar bonds on Si(100)-21. N-H dissociation via transfer of the alpha H from the more stable isomer to the neighboring Si dimer atom (see Figure 7) involves a TS lying 10.5 kcal/mol below the entrance channel and is exothermic by 26.9 kcal/mol. Consequently, this state is not expected to be a major product. The cyclic imine dative bonded adsorbed state is thus predicted to be the most stable product of the reaction of histidine’s imidazole side-chain with Si(100)-21. Considering that this state involves dipolar bonding between the Si dimer and the N lone pair of a conjugated imine, it is analogous to the imine N-Si adsorbed state of arginine. Therefore, this product is expected to be the most stable state. However, we note that although this N-Si bond is stronger than N-Si dative bonded states of amine N centers it is substantially weaker than the Si-N bond of the noncyclic imine of arginine’s side-chain. [2 þ 2] cycloaddition to the Si dimer π-bond leads to the formation of four-membered rings. We find CdN [2 þ 2] cycloaddition to be 10.7 kcal/mol exothermic and CdC [2 þ 2] cycloaddition to be 15.6 kcal/mol exothermic. In both cases, the 7483
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The Journal of Physical Chemistry C formation of the four-membered ring adds constraints to a bond that is already involved in a ring, thus leading to substantial ring strain. These [2 þ 2] products are approximately 15-20 kcal/mol less stable than CdN and CdC [2 þ 2] products on Si(100)-21 that do not involve disrupting resonance in the ring.63,64 We find a similar result for the imidazole [4 þ 2] cycloaddition, which we find to be 19.0 kcal/mol exothermic. Although the five-membered ring adds less ring strain to the system than the four-membered ring, the product still involves significant strain and disruption of ring resonance. Consequently, the reaction is only slightly more exothermic than the [2 þ 2] reactions.
4. DISCUSSION Among the pathways we have calculated, the most energetically favorable reactions are O-H dissociations. However, because the N-H dissociation and CdO [2 þ 2] cycloaddition reactions are also energetically favorable and have small or no barriers, we expect that the reaction of alanine on Si(100)-21 should lead to a distribution of products resulting from these reactions. Consequently, the orientation of the amino acid as it adsorbs on the dimer and the dynamics of the collision are critical factors in determining the actual products resulting from reaction of its common group with the surface. However, these results indicate that the O-H dissociation product should be the most likely because it has low forward barriers and is thermodynamically stable, while N-H dipolar bonded surface adducts will likely be a minority product. Resonance affects the reactivities of several amino acids causing them to be significantly different from analogous reactions that do not involve resonance. The most striking example is the strength of arginine’s dative bond to the Si(100)-21 dimer which is predicted to be ∼18 and 27 kcal/mol larger than the analogous dative bonds of nonaromatic or cyclic amines and nitriles, respectively. This increase in bond strength is attributed to the ability of arginine to delocalize charge over the resonating π bonds in its guanidine side-chain. Aromaticity also significantly affects the reactivity of tryptophan where the [2 þ 2] cycloaddition of the CdC of the pyrrole ring is favored over the [4 þ 2] cycloaddition despite the ring strain. Here, the [4 þ 2] cycloaddition disrupts the resonance of both the phenyl and pyrrole rings, whereas the [2 þ 2] reaction only breaks the conjugation of the pyrrole ring. Similarly, tryptophan’s Si-N dative bond is relatively weak due to participation of the N lone pair in the π-space of the pyrrole ring. Similarly, disruption of resonance weakens the Si-N dative bond of histidine’s cyclic amine to the Si(100)-21 dimer to make it unstable. On the other hand, the ability of histidine to delocalize charge over its resonating π-space analogous to arginine results in a Si-N dative bond 5-7 kcal/mol stronger than that of amines. Isoleucine, leucine, and valine have alkane side-chains which are unreactive on the Si(100)-21 surface. Thus, their only reactions are those of the common group, and consequently they have the same reactivity on Si(100) as alanine and glycine. Therefore, like alanine, isoleucine, leucine, and valine will only react via their common group, and thus the conclusions we obtained for alanine also apply to isoleucine, leucine, and valine; the dominant reaction will be O-H dissociation. The side-chains of aspartate and glutamate are simple carboxylic acids, and consequently, reactions at the side-chain carboxyl are similar to those of the common group carboxyl calculated using alanine and glycine. Consequently, aspartate and
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glutamate are expected to react preferentially by O-H dissociation and may also react with the surface through multiple reactive groups. On the other hand, the side-chains of asparagine and glutamine are terminated by amide groups where an amine neighbors a carbonyl group. The reactivity of amides on the Si(100)-21 surface has not been studied previously. Our results for reactions at amines and carbonyls indicate that these groups will preferentially undergo N-H dissociation on the surface. We have left examination of the reaction of the amide groups of asparagine and glutamine to a later study. The side-chain of lysine consists of a four-carbon atom alkane chain terminated with an amine group. Accordingly, the reactivity of the side-chain is expected to be the same as that of amines, which we have previously explored and also described above with the exception that lysine is capable of reacting with the surface simultaneously through both the side-chain amine and either the common group amine or carboxyl groups when they are not involved in peptide bonds. The barrier for the N-H dissociation is approximately 15 kcal/mol, and thus this reaction is less favorable than O-H dissociation of the carboxyl. The side-chain of proline is pyrrolodine and consists of a ring with an amine center. We have investigated the reactivity of pyrrolodine previously and found that it forms a 25.2 kcal/mol Si-N dative bond on Si(100)-21 and undergoes N-H dissociation with a barrier of 13.3 kcal/mol.33 These results for the cyclic amine mimic those of noncyclic amines, and thus the reactivity of proline’s side-chain is essentially the same as that of noncyclic amines. The side-chain of phenylalanine consists of a phenyl group. The reactivity of benzene on the Si(100)-21 surface and similar aromatic compounds has been studied extensively. Previous results show benzene to be unreactive on Si(100)-21. Thus, the sidechain of phenylalanine is expected to be unreactive on Si(100)21, and so phenylalanine only reacts with the Si(100)-21 surface through its common group.58-61 The side-chain of methionine consists of a simple thioester. Osgood et al. have determined that simple sulfides adsorb through S-Si dative bonds. However, while S-H bonds dissociate on Si(100)-21, S-C bonds do not as they have dissociation activation barriers of approximately 30 kcal/mol.19 Consequently, because the adsorption energy through Si-S dative bonding is only approximately 13 kcal/mol, and S-C bonds will most likely not dissociate, any methionine that adsorbs into the Si-S dative bonded state is expected to interconvert to more stable dative bonded adsorbates involving the amine or carboxyl groups and subsequently dissociate, either by O-H or N-H dissociation.
5. CONCLUSIONS We have used DFT to predict the reactivity of amino acids toward the Si(100)-21 surface to study how their reactivities on semiconductor surfaces might differ from those of other organic functionalities. We have found that several amino acids possess unique reactivities that have not been previously reported, including resonance effects that govern the reactivities of arginine, histindine, and tryptophan with the surface. In particular, Lewis acid-base interactions between arginine’s and histidine’s imine functional groups with the Si(100)-21 surface dimer are significantly strengthened by resonance effects. This initial study is restricted to exploring the reactions of isolated amino acids on a single dimer of the Si(100)-21 reconstruction of the Si(100) 7484
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The Journal of Physical Chemistry C surface, although reactions across multiple dimers are expected to be important in several cases. Nevertheless, because amino acid reactions on Si(100)-21 are localized for the most part each functional group behaves as it would in a truncated form if the truncation is designed to include the significant interactions. On the other hand, the dipolar bond interactions with the surface reported herein are generally expected to be underpredicted when neighboring bare dimers are present in the same dimer row. We have found that the amino acid side-chains have little affect on the common group reaction energetics and similarly that the common group has little affect on the reactivity of the side-chains on Si(100)-21. Resonance effects significantly affect the reactivity of arginine, tryptophan, and histidine. Arginine’s guanidine side-chain exhibits a unique and remarkable reactivity on the Si(100)-21 surface. It molecularly adsorbs with its guanidine functional group imine forming a 41.3 kcal/mol N-Si dipolar bond that is significantly stronger than any other previously studied N-Si dipolar bond and which should be even more stable if neighboring bare dimers are present. Although the adduct is stable against desorption, the dative bonded adduct can undergo a low barrier N-H dissociation where the H transfer completes the electrocyclic ene reaction. Histidine also has an imine, although as part of an imidazole heterocycle that might be expected to behave analogously to the imine of arginine. In fact, the imine N-Si dipolar bond is ∼8 kcal/mol stronger than those of amines although still ∼11 kcal/mol weaker than that of arginine. Resonance also qualitatively affects the reactivity of tryptophan causing the [2 þ 2] cycloaddition of the CdC of the pyrrole ring to be favored over the [4 þ 2] cycloaddition because the [4 þ 2] cycloaddition disrupts the resonance of both the phenyl and pyrrole rings whereas the [2 þ 2] reaction only breaks the conjugation of the pyrrole ring. Aromaticity similarly affects the [2 þ 2] and [4 þ 2] cycloadditions of histidine, which are ∼15-20 kcal/mol less exothermic and produce products that are relatively unstable relative to their conjugated diene counterparts. We found that amino acid common groups are most likely to react on single dimers via O-H dissociation from either the O-H or the CdO dative bonded states with the barrier from the CdO dative bonded state being nearly zero, while the barrier via the O-H dative bonded state is 7.7 kcal/mol. Although the N-H dative bonded state is more stable than the O-H or CdO dative bonded states, the N-H dissociation barrier is larger than the barriers to O-H or CdO [2 þ 2] cycloaddition. Although this barrier is larger than both O-H dissociation barriers, it is still substantially below the entrance channel, and thus some N-H dissociation may occur. Although C-N dissociation leads to the most stable dissociated product, it has a large barrier and is thus not expected to be active. On the other hand, although CdO [2 þ 2] cycloaddition proceeds with no barrier, it is relatively unstable due to ring strain. Cysteine is predicted to undergo S-H dissociation mediated through an S-H dative-bonded state and to behave analogously to organothiols on Si(100). Similarly, tyrosine, serine, and threonine react on Si(100)-21 like alcohols and undergo O-H dissociation. Although the aromatic ring of tyrosine can stabilize the O-H dissociation barrier by radical stabilization, it is itself unreactive on Si(100). In several cases we have found amino acids that undergo unique and potentially useful reactions that have not been previously reported. The most noteworthy of these are those involving arginine’s and histidine’s imine functional groups.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Author Contributions §
These authors contributed equally to this publication.
’ ACKNOWLEDGMENT We gratefully acknowledge the support of the Semiconductor Research Corporation Materials Structures and Devices MARCO Center, the Office of Naval Research, and Stanford’s Center for Integrated Systems and Initiative for Nanoscale Materials and Processing. We also appreciate the scientific discussions and technical aid of Dr. Joseph Han, Dr. Collin Mui, Dr. Ankan Paul, and Dr. Ye Xu. ’ REFERENCES (1) Bent, S. F. Surf. Sci. 2002, 500, 879. (2) Filler, M. A.; Bent, S. F. Prog. Surf. Sci. 2003, 73, 1. (3) Lu, X.; Lin, M. C. Int. Rev. Chem. 2002, 21, 879. (4) Whaley, S. R.; English, D. S.; Hu, E. L.; Barbara, P. F.; Belcher, A. M. Nature 2000, 405, 665. (5) Loscutoff, P. W.; Bent, S. F. Annu. Rev. Phys. Chem. 2006, 57, 467. (6) Peelle, B. R.; Krauland, E. M.; Wittrup, K. D.; Belcher, A. M. Langmuir 2005, 21, 6929. (7) Estephan, E.; Larroque, C.; Cuisinier, F. J. G.; Balint, Z.; Gergely, C. J. Phys. Chem. B 2008, 112, 8799. (8) Lopez, A.; Heller, T.; Bitzer, T.; Richardson, N. V. Chem. Phys. 2002, 277, 1. (9) Ardalan, P.; Davani, N.; Musgrave, C. B. J. Phys. Chem. C 2007, 111, 3692. (10) Hamers, R. J.; Hovis, J. S.; Lee, S.; Lin, H. B.; Shan, J. J. J. Phys. Chem. B 1997, 101, 1489. (11) Kasemo, B. Surf. Sci. 2002, 500, 656. (12) Bitzer, T.; Richardson, N. V.; Schiffrin, D. J. Surf. Sci. 1997, 382, L686. (13) Casaletto, M. P.; Zanoni, R.; Carbone, M.; Piancastelli, M. N.; Abella, L.; Weiss, K.; Horn, K. Surf. Sci. 2000, 447, 237. (14) Mui, C.; Han, J. H.; Wang, G. T.; Musgrave, C. B.; Bent, S. F. J. Am. Chem. Soc. 2002, 124, 4027. (15) Wang, G. T.; Mui, C.; Musgrave, C. B.; Bent, S. F. J. Phys. Chem. B 2001, 105, 3295. (16) Mui, C.; Wang, G. T.; Bent, S. F.; Musgrave, C. B. J. Chem. Phys. 2001, 114, 10170. (17) Wang, G. T.; Mui, C.; Musgrave, C. B.; Bent, S. F. J. Phys. Chem. B 2001, 105, 12559. (18) Filler, M. A.; Van Deventer, J. A.; Keung, A. J.; Bent, S. F. J. Am. Chem. Soc. 2006, 128, 770. (19) Zhu, Z.; Srivastava, A.; Osgood, J.; R., M. J. Phys. Chem. B 2003, 107, 13939. (20) Konency, R.; Doren, D. J. Surf. Sci. 1998, 417, 169. (21) Taguchi, Y.; Fujisawa, M.; Takaoka, T.; Okada, T.; Nishijima, M. J. Chem. Phys. 1991, 95, 6870. (22) Gokhale, S.; Tischberger, P.; Menzel, D.; Widdra, W.; Droge, H.; Steinruck, H. P.; Birkenheuer, U.; Gutdeutsch, U.; Rosch, N. J. Chem. Phys. 1998, 108, 5554. (23) Becke, A. D. J. Chem. Phys. 1993, 98. (24) Hohenberg, H.; Kohn, W. Phys. Rev. B 1964, 1, 36B864. (25) Kohn, W.; Sham, L. Phys. Rev. A 1965, 140, 1133. (26) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (27) Wang, G. T.; Mui, C.; Musgrave, C. B.; Bent, S. F. J. Phys. Chem. B 1999, 103, 6803. (28) Wang, G. T.; Mui, C.; Musgrave, C. B.; Bent, S. F. J. Am. Chem. Soc. 2002, 124, 8990. 7485
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