Computational studies of copper, silver, and gold alkanethiolates and alkaneselenates

Computational studies of copper, silver, and gold alkanethiolates and alkaneselenates

Journal of Molecular Structure: THEOCHEM 803 (2007) 103–113 www.elsevier.com/locate/theochem Computational studies of copper, silver, and gold alkane...

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Journal of Molecular Structure: THEOCHEM 803 (2007) 103–113 www.elsevier.com/locate/theochem

Computational studies of copper, silver, and gold alkanethiolates and alkaneselenates Jean M. Standard a

a,*

, Brian W. Gregory c, Brian K. Clark

b

Department of Chemistry, Illinois State University, Normal, IL 61790, USA Department of Physics, Illinois State University, Normal, IL 61790, USA Department of Chemistry, Samford University, Birmingham, AL 35229, USA b

c

Received 5 December 2005; accepted 29 September 2006 Available online 11 October 2006

Abstract Ab initio and density functional calculations have been performed for metal alkanethiolates and metal alkaneselenates containing one or three metal atoms of copper, silver, or gold. Alkanethiolates and alkaneselenates with alkane chains of one, three, and six carbons in length were considered. Equilibrium geometries, charge distributions, and HOMO–LUMO energy gaps were obtained. The objective of the study was to investigate invariant geometrical and electronic properties with respect to metal atom substitution, sulfur/selenium substitution, or alkane chain length. The study was carried out in order to help explain recent surface-enhanced electronic Raman scattering (SEERS) spectra of self-assembled monolayers of alkanethiolates on roughened gold surfaces. The observed SEERS transitions have been shown to be nearly independent of substitution of silver for gold, substitution of selenium for sulfur, and alkane chain lengths of 9–18 carbons. From the calculations, little change in the sulfur–carbon or selenium–carbon bond distances was observed as the metal ˚ as atom was varied from copper to silver to gold. On the other hand, the metal–sulfur and metal–selenium distances varied by over 0.2 A a function of metal atom. Significant differences also were observed for the charges of the metal atom and the sulfur or selenium atom. However, the charge of the carbon atom attached directly to sulfur or selenium was found to be invariant to metal or S/Se substitution for alkane chains greater than one carbon in length. Finally, the HUMO–LUMO gap was determined to be rather insensitive to metal atom and sulfur/selenium substitution.  2006 Elsevier B.V. All rights reserved. Keywords: Alkanethiolate; Alkaneselenate; Copper; Silver; Gold; Self-assembled monolayer; Ab initio; Density functional theory

1. Introduction Recently, new electronic transitions have been observed in surface-enhanced Raman spectra of self-assembled monolayers (SAMs) of alkanethiols on roughened gold surfaces [1–6]. In the experiments, samples of alkanethiol SAMs were prepared on electrochemically roughened gold surfaces and excited with laser radiation in the range of 1.7–2.0 eV. The observed Raman transitions were demonstrated to be independent of alkane chain length for alkane chains containing nine to 18 carbons, isotopic substitution *

Corresponding author. Tel.: +1 309 438 7700; fax: +1 309 438 5538. E-mail address: [email protected] (J.M. Standard).

0166-1280/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.09.029

(13C for 12C, D for H, and 34S for 32S), replacement of sulfur by selenium, and replacement of gold by silver [2,4,6]. This and other evidence suggested that the energy levels involved in the Raman transitions are electronic in origin; hence, the process giving rise to these transitions has been labeled surface-enhanced electronic Raman scattering (SEERS). A theoretical model based on extensions of nearly-free electron theory [7–10] and the method of images [11–14] was employed in order to describe the electronic energy levels responsible for the SEERS transitions. The theoretical model included an example surface roughness feature consisting of a step edge and a terrace. The dielectric overlayer created by the interaction of the alkanethiols with the metal

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surface was described by two regions, the first representing the alkane chains and the second representing the headgroup region of the alkanethiols and the metal–sulfur bond. The electrons involved in the SEERS process were determined to exist in image potential surface states generated via an image force between the electrons and the step edge. Since the electrons experience no image force with respect to the terraces, they were able to move freely along the terraces [3–6]. Calculated electronic energy levels of the model system were obtained by numerical solution of the Schro¨dinger equation and were in excellent agreement with the experimental SEERS energy levels [3–6]. Furthermore, the dielectric constant of the alkane chain region determined from a grid search, e = 2.20 ± 0.04, agreed well with an empirical fit of the SEERS transitions [2] and with the experimental value of e = 2.25 for bulk close-packed alkane chains. The computer modeling studies also indicated that the image state electrons are localized in the headgroup region, in the vicinity of the sulfur atom of the alkanethiol or in the metal–sulfur bonding region. The mechanism of formation of the image states in these systems and the trapping of electrons in them is not known. Since the proposed model [3–6] suggests that the image state electrons are localized in the headgroup region, the electronic structure of the alkanethiol molecules binding to the metal surface must be elucidated in order to fully understand the origin of image state electrons in these systems. This objective may be accomplished through the use of quantum mechanical electronic structure calculations. Quantum mechanical calculations have provided detailed information about geometries, energies, and electron distributions for the interaction of alkanethiols, alkanethiolates, and other sulfur-containing molecules with copper, silver, and gold. Numerous previous studies have employed small clusters of metal atoms to study the alkanethiolate-metal interaction. For example, investigations by Vondrak et al. employed density functional methods to determine energies and electron distributions of individual alkanethiolate and other molecules bound to lithium and copper clusters containing one to three atoms [15,16]. These workers showed that the specific nature of the bonding interaction between the sulfur atom and the metal may be important in the design of nanoscale molecular electronic devices based on SAMs. Another recent study by Cho et al. [17] used ab initio Hartree-Fock methods to explore the binding of methylthiolate radical and other compounds to clusters containing one to three silver or gold atoms. They were able to correlate calculated vibrational frequencies with experimental Raman spectra. A slightly larger study by Kruger et al. [18] explored alkanethiolates with alkane chains of one to three carbons in length interacting with clusters of one to five gold atoms using Hartree-Fock, density functional, and advanced electron correlation methods. These workers found that the geometries obtained from density functional theory and the advanced correlation methods were quite consistent. Kruger et al.

also noted that the sulfur–gold bond is strongly directional in character and only a minor effect on alkanethiolate–gold binding energies was observed for an increase in the alkane chain from one to three carbons. There also have been many previous computational studies of the binding of alkanethiolates to metals that have employed large cluster models or slab models with periodic boundary conditions to represent the metal surface [19–30]. The first ab initio geometry optimizations of HS and CH3S interacting with silver and gold clusters containing up to 27 atoms were carried out by Sellers and coworkers [19]. Studies of a similar nature also have been performed by Beardmore et al. using density functional theory to probe CH3S binding to slightly smaller clusters of 17 gold atoms [20,21]. Both the Sellers and Beardmore studies found that the hcphollow site was the preferred adsorption site for CH3S on Au(111); however, more recent studies using slab models and periodic boundary conditions have found that bridge sites are preferred [22–30]. A recent investigation employing density functional theory with periodic boundary conditions focused on the deposition of methylthiolate on the Au(111) surface at both low and high coverages [28]. This computational study was the first one to obtain a c(4 · 2) structural arrangement of the thiolate molecules at high coverage, in accord with experimental data [31–34]. In addition, the calculated S–S distances of the alkanethiolate ˚ , were in dimer structures on the surface, 2.34 and 2.46 A reasonable agreement with the suggested experimental dis˚ [34]. Two other recent studies have focused tance of 2.2 A on the effects of alkane chain length on the SAMs and have determined that the adsorption energy increases with chain length and that binding of methylthiolate differs substantially from that of longer-chain alkanethiolates [29,30]. To date, there have been no systematic quantum mechanical studies of the effects of the type of metal or selenium/sulfur substitution on the structures, charge distributions, and energies of alkanethiolates binding to metal surfaces. Because the SEERS transitions observed experimentally [2–6] are nearly independent of these types of substitutions, it is important to elucidate the common features present in these systems in order to understand the electronic structure of the headgroup region and the possible origin of the image state electrons. In this work, in order to probe the nature of the metal– sulfur bonding interaction and the electronic structure of the headgroup region, ab initio and density functional calculations have been performed on copper, silver, and gold alkanethiolates and alkaneselenates with various alkane chain lengths. Results illustrating the effects due to alkane chain length, the substitution of selenium for sulfur, the type of metal, and metal cluster size are presented. In particular, the focus is on commonalities in interactions between individual alkanethiolates and alkaneselenates and the metals. Though it is outside the scope of the present work, there also may be additional common features observed in the structure and properties of a full selfassembled monolayer on a metal surface.

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2. Computational methods In this work, metal alkanethiolates, MS(CH2)nCH3, and metal alkaneselenates, MSe(CH2)nCH3, M = Cu, Ag, Au, and n = 0, 2, 5, are considered. In addition to the compounds containing one metal atom, related systems of metal methylthiolates and metal methylselenates containing three metal atoms, M3SCH3 and M3SeCH3, M = Cu, Ag, Au, also have been studied. All the systems investigated in this work possess electronic ground states with singlet multiplicities. Full geometry optimizations of the metal alkanethiolates and metal alkaneselenates were performed at the Hartree-Fock (HF), density functional (B3LYP), and second-order Moller-Plesset (MP2) levels of theory. The Hartree-Fock results are included only in Supplementary materials. The frozen core approximation was utilized for the MP2 calculations. The basis set employed in the computations consisted of a standard 6-31+G(d) basis for H, C, S, and Se atoms and the LANL2DZ valence-only double zeta basis for Cu, Ag, and Au [35–37] augmented by a set of f-type polarization functions. The exponents of the f-type polarization functions were optimized at the MP2 level to produce the lowest energy for the metal dimer structures (Cu2, Ag2, Au2) at the experimental geometry. The LANL2 relativistic effective core potential was employed for the Cu, Ag, and Au atoms [35–37]. Vibrational frequency calculations were performed to verify each structure as a minimum on the potential energy surface. Charge distributions were obtained by carrying out Natural Population Analysis (NPA) [38]. The NBO 5.0 software package [39] was employed for the NPA analyses. The energies of the HOMO and LUMO of each of the metal alkanethiolates and metal alkaneselenates were determined from single point energy calculations of the cation and anion species at the equilibrium geometry of the neutral species. The HOMO energy was then computed as the difference in energy between the neutral and cationic species (i.e., the negative of the ionization potential), while the LUMO energy was obtained as the difference between the energies of the anionic and neutral species (i.e., the negative of the electron affinity). Most of the calculations were carried out on SGI O2, SGI Origin200, and Linux workstations at Illinois State University. Some of the larger calculations were performed using the IBM p690 cluster at the National Center for Supercomputing Applications in Champaign, Illinois. The Gaussian98 [40] and Gaussian 03 [41] software packages were utilized for all calculations.

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HOMO–LUMO energy gaps are considered. Next, the effects of alkane chain length on the geometries and properties of the metal alkanethiolates and metal alkaneselenates for compounds of the form MS(CH2)nCH3 and MSe(CH2)nCH3, M = Cu, Ag, Au and n = 0,2,5, are presented. Finally, the effects of metal cluster size on the results are investigated for compounds of the type M3SCH3 and M3SeCH3, M = Cu, Ag, Au. In the following discussion, distinctions are made between variations in geometrical and other properties that are considered significant and those that are considered insignificant with respect to metal atom substitution, substitution of selenium for sulfur, alkane chain length, and metal cluster size. For bond lengths, differences of more ˚ are considered significant while differences of than 0.1 A less than a few hundredths of an angstrom are considered insignificant. For bond angles, variations of several degrees (5–10) are considered significant while variations of less than 1–2 are considered insignificant. Differences in charge of more than 0.1 are considered significant and differences in charge of less than a few hundredths (0.02–0.03) are considered insignificant. Finally, variations of HOMO– LUMO gaps of more than 1 eV are considered significant and variations of less than 0.2–0.3 eV are considered insignificant. 3.1. MSCH3 and MSeCH3 compounds, M = Cu, Ag, Au 3.1.1. Equilibrium geometries The optimized geometry of AuSCH3 determined at the MP2 level of theory is shown in Fig. 1a. The geometries of compounds containing Cu and Ag as well as those containing Se are similar and are not shown. Selected geometrical parameters obtained at the B3LYP and MP2 levels for all the compounds containing one metal atom are presented in Table 1. Trends in geometries and properties with

3. Results and discussion This study initially focuses on the behavior of the molecules with respect to substitution of metal atom and replacement of selenium with sulfur for the simplest metal alkanethiolate and metal alkaneselenate systems, MSCH3 and MSeCH3, M = Cu, Ag, Au. Effects on geometries as well as on properties such as charge distributions and

Fig. 1. Optimized geometries of (a) AuSCH3, (b) AuS(CH2)2CH3, and (c) AuS(CH2)5CH3 obtained at the MP2 level of theory.

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Table 1 Selected geometrical parameters of metal alkanethiolates and metal alkaneselenates containing one metal atom, M = Cu, Ag, Au, calculated at the B3LYP and MP2 levels of theory ˚) ˚) M–S(e) bond length (A S(e)–C bond length (A M–S(e)–C bond angle (degrees) Cu

Ag

Au

Cu

Ag

Au

Cu

Ag

Au

2.166 2.170

2.388 2.391

2.298 2.268

1.848 1.832

1.845 1.832

1.839 1.826

104.0 103.7

104.2 103.0

103.9 102.0

MS(CH2)2CH3 B3LYP 2.163 MP2 2.168

2.388 2.389

2.299 2.266

1.857 1.838

1.855 1.837

1.851 1.833

104.4 102.9

104.2 102.4

104.0 101.4

MS(CH2)5CH3 B3LYP 2.163 MP2 2.167

2.387 2.388

2.298 2.264

1.858 1.839

1.856 1.838

1.851 1.833

104.4 102.8

104.3 102.4

104.3 101.5

MSeCH3 B3LYP MP2

2.266 2.270

2.489 2.488

2.407 2.370

1.993 1.982

1.991 1.981

1.984 1.974

101.3 100.7

101.4 100.3

101.0 99.2

MSe(CH2)2CH3 B3LYP 2.265 MP2 2.268

2.489 2.486

2.407 2.369

2.007 1.990

2.004 1.989

2.000 1.984

101.4 100.0

101.7 99.8

101.5 98.8

MSe(CH2)5CH3 B3LYP 2.265 MP2 2.266

2.490 2.484

2.407 2.368

2.006 1.990

2.003 1.989

1.998 1.984

101.5 100.2

102.0 100.0

102.0 99.0

MSCH3 B3LYP MP2

respect to variation of metal atom and sulfur/selenium substitution also are illustrated in Fig. 2. One of the most interesting results found from the structural studies is that the S–C and Se–C bond lengths are nearly invariant with respect to metal atom substitution, ˚ longer than the though the Se–C bonds are about 0.1 A S–C bonds in all cases. For any given level of theory, the ˚ as S–C or Se–C bond lengths change by at most 0.009 A the metal atom is varied. Furthermore, there is little variation in the S–C and Se–C bonds as a function of level of theory. Across all the levels of theory, the S–C bond ˚ while the Se–C bond lengths range from 1.83 to 1.85 A ˚ . The S–C bond lengths lengths range from 1.97 to 1.99 A calculated in this work are comparable with the previous literature study of Cho et al., who obtained S–C bond ˚ for AgSCH3 and AuSCH3, lengths of 1.828 and 1.825 A respectively, at the HF level of theory [17]. Another intriguing finding from the structural studies is that there is very little variation in the M–S–C and M–Se– C bond angles as a function of metal atom. For any given level of theory, the M–S–C or M–Se–C bond angles change by at most 1.7 as the metal atom is varied. There is again little variation in these results with respect to level of theory. Though all the bond angles are very similar, the smallest bond angles are those of the Au-containing compounds, while the bond angles of the Cu- and Ag-containing compounds are comparable. The M–S–C bond angles in MSCH3 compounds computed in this work are similar to those determined in previous studies. Cho et al. [17] obtained M–S–C bond angles of 106.2 and 104.9 for AgSCH3 and AuSCH3, respectively, at the HF level of theory and Kruger et al. [18] determined an Au–S–C angle of

104.7 for AuSCH3 using plane wave DFT methods. From studies of AuSCH3 and other compounds, Kruger et al. note that the consistency of the calculated Au–S–C bond angles, ranging from 103–109 for the interaction of CH3S with between one and five gold atoms, indicates a strong directionality of the gold–sulfur interaction. In contrast to the common trends observed in the S–C/Se–C bond lengths and M–S–C/M–Se–C bond angles, the variation of M–S and M–Se bond lengths with metal ˚ atom is fairly significant. A difference of over 0.2 A between the Cu–S and Ag–S (or Cu–Se and Ag–Se) bond ˚ between Ag–S and Au–S (or lengths and around 0.1 A Ag–Se and Au–Se) bond lengths is observed. The Cu–S (or Cu–Se) bonds are the shortest while the Ag–S (or Ag–Se) bonds are the longest at all levels of theory. The finding that the Au–S bonds are shorter than the Ag–S bonds is in accord with the previous computational study of Cho et al., who obtain Au–S and Ag–S bond distances ˚ , respectively, for MSCH3 at the HF of 2.327 and 2.438 A level of theory [17]. As noted by Sellers and coworkers, the shorter Au–S bond distance relative to Ag–S is in part due to relativistic effects [19]. 3.1.2. Charge distributions and bonding Atomic charges were computed for the metal alkanethiolates and metal alkaneselenates using Natural Population Analysis [38]. The charges of selected atoms determined at the B3LYP and MP2 levels of theory are presented in Table 2. A nearly invariant quantity in the charge distributions of MSCH3 and MSeCH3 with respect to variation of metal atom and sulfur/selenium substitution is the charge of the

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less polar, with a charge on Au of 0.2–0.5 and a charge on S or Se of 0.1 to 0.4. Thus, the M–S and M–Se charge separation is similar for Cu- and Ag-containing compounds but is substantially lower for Au-containing compounds. The substantial differences in charge distributions for the silver and gold compounds are somewhat surprising given the similarities of the image state models for silver and gold alkanethiolates [3–6]. 3.1.3. HOMO–LUMO energies The energies of the HOMO and LUMO of the MSCH3 and MSeCH3 compounds, M = Cu, Ag, Au, were calculated at the B3LYP and MP2 levels of theory as described in Section 2. The HOMO and LUMO energies along with the HOMO–LUMO energy gaps of each compound are presented in Table 3. For the MSCH3 and MSeCH3 compounds, the HOMO– LUMO gaps are fairly constant as a function of metal type or substitution of selenium for sulfur. For example, at the MP2 level the HOMO–LUMO gap ranges from 6.5 to 7.1 eV for MSCH3 and from 6.4 to 6.8 eV for MSeCH3 as the metal atom is varied from copper to gold. The silver compounds exhibit the smallest and the gold compounds the largest HOMO–LUMO gaps. The primary difference between the sulfur and selenium compounds is that the HOMO–LUMO gaps tend to be slightly larger for the sulfur compounds; for example, at the MP2 level the HOMO– LUMO gaps of the sulfur compounds are 0.15, 0.13, and 0.25 eV larger than those of the corresponding copper, silver, and gold alkaneselenates. Fig. 2. Illustration of the effects of metal atom and sulfur/selenium substitution on (a) bond lengths, (b) natural atomic charges, and (c) HOMO–LUMO energy gaps of MSCH3 and MSeCH3. The results shown were obtained at the MP2 level of theory. The solid lines correspond to results for MSCH3 and the dashed lines correspond to results for MSeCH3. No difference between the sulfur- and selenium-containing compounds is observed on the scale of the plot in (c) for the HOMO and LUMO energies.

carbon atom, which exhibits differences between copper, silver, and gold compounds of at most 0.02 at a given level of theory. In addition, the carbon atom charge is reasonably invariant with respect to substitution of selenium for sulfur: the carbon charge of the selenium compounds is only 0.04–0.05 higher than the carbon charge of the sulfur compounds. In contrast to the carbon charge, the charges of the metal and the sulfur/selenium atoms vary substantially. The metal and sulfur/selenium charges decrease by up to 0.3 as the metal atom is varied from Cu to Au. The calculated natural atomic charges indicate that the metal–sulfur and metal–selenium bonds in the Cu and Ag compounds are quite polar, with a positive charge on the metal atom ranging from 0.5 to 0.7 and a negative charge on the S or Se atom ranging from 0.3 to 0.6. The metal–sulfur and metal–selenium bonds in the Au compounds are slightly

3.2. Effect of alkane chain length The effects of increasing the alkane chain length on the structures, charge distributions, and HOMO–LUMO gaps of the metal alkanethiolates and metal alkaneselenates were investigated for compounds with one metal atom (copper, silver, or gold) and containing alkane chains of one, three, and six carbons in length. Representative optimized structures of AuS(CH2)2CH3 and AuS(CH2)5CH3 obtained at the MP2 level of theory are shown in Figs. 1b and c. Results for selected equilibrium bond lengths and angles of the compounds computed at the B3LYP and MP2 levels of theory are presented in Table 1 and atomic charges are presented in Table 2. Note that the charge of the carbon atom presented in Table 2 is for the atom directly attached to the sulfur or selenium. The HOMO and LUMO energies are presented in Table 3 along with the HOMO–LUMO energy gaps. The calculations indicate that increasing the alkane chain length has little effect on the geometries of the compounds. For example, very little variation is observed in the metal–sulfur bond lengths as a function of alkane chain length in the metal alkanethiolates: a slight decrease ˚ in the metal–sulfur distance is of less than 0.004 A observed as the alkane chain length increases. Similar results are observed for metal–selenium bond lengths in

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Table 2 Selected atomic charges for metal alkanethiolates and metal alkaneselenates containing one metal atom, M = Cu, Ag, Au, calculated using Natural Population Analysis at the B3LYP and MP2 levels of theory Charge of M

Charge of Ca

Charge of S(e)

Cu

Ag

Au

MSCH3 B3LYP MP2

0.524 0.620

0.503 0.605

0.267 0.309

0.420 0.505

0.392 0.481

0.175 0.207

0.827 0.823

0.832 0.827

0.841 0.840

MS(CH2)2CH3 B3LYP MP2

0.537 0.635

0.515 0.621

0.279 0.317

0.434 0.511

0.405 0.488

0.189 0.208

0.589 0.595

0.593 0.600

0.604 0.614

MS(CH2)5CH3 B3LYP MP2

0.534 0.635

0.511 0.620

0.276 0.314

0.435 0.510

0.404 0.487

0.190 0.205

0.585 0.593

0.589 0.596

0.600 0.611

MSeCH3 B3LYP MP2

0.482 0.595

0.455 0.580

0.229 0.277

0.348 0.458

0.313 0.434

0.101 0.148

0.870 0.864

0.876 0.869

0.885 0.882

MSe(CH2)2CH3 B3LYP 0.490 MP2 0.607

0.467 0.592

0.230 0.285

0.363 0.466

0.333 0.443

0.111 0.154

0.621 0.626

0.626 0.631

0.637 0.644

MSe(CH2)5CH3 B3LYP 0.488 MP2 0.607

0.461 0.592

0.229 0.282

0.364 0.465

0.327 0.443

0.112 0.151

0.617 0.623

0.623 0.627

0.633 0.641

a

Cu

Ag

Au

Cu

Ag

Au

The charge of the carbon atom directly attached to sulfur or selenium is reported.

Table 3 HOMO and LUMO energies and HOMO–LUMO gap for metal alkanethiolates and metal alkaneselenates containing one metal atom calculated at the B3LYP and MP2 levels of theory HOMO (eV) Cu

LUMO (eV) Ag

Au

Cu

HOMO–LUMO gap (eV) Ag

Cu

Ag

Au

1.353 1.055

7.110 6.909

6.819 6.549

7.132 7.092

1.140 0.833

1.362 1.067

6.924 6.796

6.637 6.447

6.930 6.966

0.944 0.669

1.149 0.848

1.364 1.070

6.867 6.752

6.584 6.404

6.869 6.925

8.243 7.952

0.902 0.671

1.105 0.842

1.365 1.107

6.911 6.758

6.635 6.424

6.878 6.845

7.610 7.192

8.061 7.831

0.923 0.692

1.128 0.868

1.370 1.114

6.740 6.646

6.482 6.324

6.691 6.717

7.551 7.116

8.005 7.793

0.932 0.701

1.137 0.875

1.369 1.115

6.685 6.604

6.414 6.241

6.636 6.678

MSCH3 B3LYP MP2

8.009 7.530

7.924 7.348

8.485 8.147

0.900 0.620

1.105 0.799

MS(CH2)2CH3 B3LYP MP2

7.857 7.451

7.777 7.281

8.292 8.033

0.933 0.655

MS(CH2)5CH3 B3LYP MP2

7.811 7.421

7.733 7.252

8.233 7.995

MSeCH3 B3LYP MP2

7.814 7.429

7.740 7.273

MSe(CH2)2CH3 B3LYP 7.663 MP2 7.338 MSe(CH2)5CH3 B3LYP 7.616 MP2 7.305

the metal alkaneselenates. The S–C and Se–C bond lengths and M–S–C and M–Se–C bond angles also are nearly invariant with respect to alkane chain length, with ˚ slight increases in the bond lengths of at most 0.016 A and slight variations in the angles of at most 1 as the alkane chain length increases.

Au

The charges of the metal and sulfur atoms are nearly independent of alkane chain length in the metal alkanethiolates. Variations in the metal and sulfur charges of no more than 0.019 are observed as a function of alkane chain length. For example, the metal charge of the metal alkanethiolates at the MP2 level of theory increases by 0.015,

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0.015, and 0.005 for Cu, Ag, and Au, respectively, as the alkane chain length increases from one to six carbons in length. The charge of the sulfur exhibits even less variation than that of the metal atom as the alkane chain length increases. Once the alkane chain becomes two or more carbons in length, little variation of the charge of the carbon atom attached directly to sulfur or selenium is observed, though as the alkane chain increases from one to three carbons, a difference in carbon charge of 0.2 is observed. This effect is primarily due to the number of hydrogen atoms attached to each carbon atom. In all the compounds, the charge of a carbon atom in a methyl group is 0.8, while the charge of a carbon atom in a methylene unit is 0.6. When the alkane chain grows from three to six carbons, the difference in carbon charge is less than 0.004. Similar behavior in the charge distributions is noted for the metal alkaneselenates as the alkane chain length is increased. The HOMO–LUMO gaps also show very little variation with alkane chain length. The HOMO–LUMO energy gap changes by no more than 0.2 eV as the alkane chain is increased from one to six carbons. For example, the HOMO–LUMO energy gap computed using the MP2 level of theory for the Au-containing alkanethiolates drops from 7.09 to 6.97 to 6.93 eV as the alkane chain increases from one to three to six carbons, a decrease of only 0.16 eV, with most of the change occurring from one to three carbon atoms. The HOMO–LUMO results for the other metal alkanethiolates and the metal alkaneselenates are similar. 3.3. Effect of metal cluster size The effects of increasing the size of the metal cluster on the structure, charge distribution, and energies of the metal alkanethiolates and metal alkaneselenates have been investigated for compounds containing one and three metal atoms. Since it was demonstrated in the previous section that lengthening the alkane chain has little effect on the structure, charge distributions, and HOMO–LUMO gaps of the compounds, results presented in this section focus on metals interacting with methylthiolate radical, CH3S, or methylselenate radical, CH3Se. Furthermore, only structures in which the metal atoms are arranged in a triangular geometry are considered in this work. Recent computational studies have verified that a triangular geometry corresponds to the lowest energy conformation of Cu3 [42–45], Ag3 [46–49], and Au3 [10,42,50–52]. 3.3.1. Equilibrium geometries Two stable conformations of the M3SCH3 and M3SeCH3 compounds, M = Cu, Ag, Au, have been located. Representative optimized structures of the two conformations of Au3SCH3 obtained at the MP2 level of theory are presented in Fig. 3. Optimized geometries of Cu3SCH3, Ag3SCH3, and the metal alkaneselenates are very similar to those shown in Fig. 3. Selected geometrical parameters of the two stable conformers of M3SCH3 and M3SeCH3

109

Fig. 3. Optimized geometries of (a) Conformation 1 and (b) Conformation 2 of Au3SCH3 obtained at the MP2 level of theory.

determined at the B3LYP and MP2 levels of theory are presented in Table 4. The two conformations of M3SCH3 and M3SeCH3 differ in the number of metal atoms to which the sulfur or selenium atom is directly bonded. In Conformation 1, the sulfur or selenium atom is directly bonded to only one metal atom, while in Conformation 2, the sulfur or selenium atom is equally bonded to two metal atoms. In both conformations, the metal–metal bonds are not all equivalent though two of the bond lengths, M1–M2 and M1–M3 as indicated in Fig. 3, are identical. In almost all cases, the M1–M2 and M1–M3 bonds are longer than the other metal–metal bond, M2–M3. In addition to the two conformations that were located as stable structures, several attempts were made to obtain a conformation in which the sulfur or selenium atom was directly bonded to all three metal atoms; however, no conformation of this type was located using the levels of theory considered in the present work. This finding is consistent with the previous computational studies of Cho et al. [17] and Kruger et al. [18] for the binding of CH3S to small gold and silver clusters. The metal–metal bond lengths of M3SCH3 and M3SeCH3 are nearly independent of sulfur/selenium substitution. The metal–metal bonds of the sulfur-containing ˚ from those of the compounds differ by at most 0.009 A selenium-containing compounds. On the other hand, the metal–metal bond lengths are not invariant with respect to metal atom substitution. The Cu–Cu bonds are signifi˚ than the Ag–Ag bonds, though cantly shorter by 0.3–0.4 A the Ag–Ag and Au–Au bond lengths are more similar, dif˚. fering by at most 0.13 A Other nearly invariant quantities with respect to metal cluster size are the metal–sulfur bond lengths of Conformation 1 of M3SCH3, which are nearly identical to those of the corresponding MSCH3 compounds, differing by at ˚ . However, the invariance depends on the natmost 0.03 A ure of the binding since the metal–sulfur bond lengths of Conformation 1 of M3SCH3 are shorter by about 0.15– ˚ than the corresponding bond lengths of Conforma0.2 A tion 2. This difference is expected since in Conformation

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Table 4 Selected geometrical parameters of metal alkanethiolates and metal alkaneselenates containing three metal atoms, M = Cu, Ag, Au, calculated at the B3LYP and MP2 levels of theory ˚) ˚) ˚) M–S(e) bond length (A M1–M2, M1–M3 bond lengthsa (A M2–M3 bond lengtha (A Cu

Ag

Au

Cu

Ag

Au

0m

Ag

Au

M3SCH3 Conformation 1 B3LYP MP2

2.187 2.175

2.400 2.392

2.306 2.277

2.432 2.475

2.794 2.795

2.750 2.708

2.331 2.373

2.674 2.690

2.655 2.627

Conformation 2 B3LYP MP2

2.358 2.334

2.616 2.583

2.538 2.491

2.438 2.492

2.786 2.793

2.759 2.723

2.383 2.414

2.767 2.764

2.769 2.714

M3SeCH3 Conformation 1 B3LYP MP2

2.288 2.273

2.500 2.483

2.408 2.373

2.433 2.469

2.797 2.790

2.754 2.712

2.330 2.377

2.674 2.690

2.658 2.627

Conformation 2 B3LYP MP2

2.460 2.441

2.712 2.681

2.620 2.568

2.438 2.490

2.788 2.796

2.763 2.724

2.386 2.417

2.771 2.770

2.782 2.730

a

The atom numbering scheme is shown in Fig. 3.

1 the sulfur is bonded to a single metal atom rather than to two. The same trends are observed for the metal–selenium bonds in the metal alkaneselenates. The S–C and Se–C bond distances and the M–S–C and M–Se–C bond angles of Conformations 1 and 2 of the M3SCH3 and M3SeCH3 compounds are not reported in Table 4 because they are very similar to those determined for the MSCH3 and MSeCH3 compounds. Furthermore, as was observed for the compounds containing one metal atom, little change in the S–C/Se–C bond lengths and the M–S–C/M–Se–C bond angles with respect to variation of metal atom is observed. For all levels of theory, the S–C bond lengths of M3SCH3 and the Se–C bond lengths of

˚ from those determined M3SeCH3 differ by at most 0.008 A for MSCH3 and MSeCH3, respectively. For Conformation 1, the M–S–C bond angles of M3SCH3 and the M–Se–C bond angles of M3SeCH3 are at most 1.3 different than the bond angles computed for MSCH3 and MSeCH3, respectively. For Conformation 2, the M–S–C bond angles of M3SCH3 and the M–Se–C bond angles of M3SeCH3 are a maximum of 3.7 different than the bond angles computed for MSCH3 and MSeCH3. 3.3.2. Charge distributions The atomic charges of the M3SCH3 and M3SeCH3 compounds determined using Natural Population Analysis at

Table 5 Selected atomic charges for metal alkanethiolates and metal alkaneselenates containing three metal atoms, M=Cu, Ag, Au, calculated using Natural Population Analysis at the B3LYP and MP2 levels of theory Charge of M1a Cu

Charge of M2a Ag

Cu

Ag

Au

0.229 0.174

0.105 0.154

0.107 0.153

0.057 0.126

0.476 0.552

0.449 0.532

0.254 0.325

0.225 0.248

0.301 0.311

0.434 0.467

0.422 0.469

0.338 0.368

0.548 0.596

0.521 0.585

0.306 0.351

0.334 0.335

0.315 0.329

0.186 0.140

0.103 0.155

0.103 0.154

0.049 0.124

0.402 0.503

0.373 0.484

0.160 0.261

0.237 0.242

0.242 0.249

0.316 0.324

0.403 0.445

0.399 0.449

0.301 0.338

0.456 0.532

0.431 0.522

0.186 0.252

M3SCH3 Conformation 1 B3LYP MP2

0.374 0.365

0.352 0.358

Conformation 2 B3LYP MP2

0.237 0.247

M3SeCH3 Conformation 1 B3LYP MP2 Conformation 2 B3LYP MP2 a

Au

Charge of S(e) Cu

Ag

Au

The atom numbering scheme is shown in Fig. 3. For Conformation 1, M1 is bonded directly to S or Se. For Conformation 2, M1 is bonded to M2 and M3 but not directly to S or Se.

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111

Table 6 HOMO and LUMO energies and HOMO–LUMO gap for metal alkanethiolates and metal alkaneselenates containing three metal atoms, M = Cu, Ag, Au, calculated at the B3LYP and MP2 levels of theory HOMO (eV) Cu

LUMO (eV) Ag

Au

Cu

HOMO–LUMO gap (eV) Ag

Au

Cu

Ag

Au

M3SCH3 Conformation 1 B3LYP MP2

7.115 6.658

7.010 6.460

7.627 7.217

1.498 1.023

1.782 1.291

2.516 2.204

5.617 5.635

5.228 5.169

5.111 5.013

Conformation 2 B3LYP MP2

7.184 6.786

7.065 6.636

7.755 7.567

0.771 0.308

1.076 0.557

1.806 1.297

6.413 6.477

5.988 6.079

5.950 6.270

M3SeCH3 Conformation 1 B3LYP MP2

7.000 6.615

6.890 6.436

7.481 7.090

1.503 1.055

1.783 1.317

2.503 2.221

5.497 5.560

5.108 5.119

4.977 4.869

Conformation 2 B3LYP MP2

7.127 6.777

7.000 6.613

7.674 7.520

0.771 0.330

1.072 0.570

1.773 1.305

6.356 6.447

5.928 6.043

5.901 6.215

the B3LYP and MP2 levels of theory are presented in Table 5. The numbering scheme for the metal atoms is shown in Fig. 3. The only quantity in the charge distributions of M3SCH3 found to be independent of metal cluster size is the carbon atom charge. Because they are so similar to the carbon charges reported in Table 2 for MSCH3, the charges of the carbon atoms of M3SCH3 are not listed in Table 5. In contrast to the carbon charges, the charge of the sulfur atom of M3SCH3 exhibits fairly significant variations as a function of metal cluster size. For example, the charge of the sulfur atom of Conformation 1 of M3SCH3 is more negative than the charge of sulfur in the corresponding MSCH3 compound by 0.03–0.12. In addition, the total metal charge of M3SCH3 is more positive by 0.05–0.12 than the metal charge of the corresponding MSCH3 compound. As was observed for compounds containing one metal atom, the Cu–S and Ag–S bonds of M3SCH3 are significantly more polar than the Au–S bonds. For example, for Conformation 1 at the MP2 level of theory, the charge of the Cu or Ag atom directly attached to sulfur is 0.36– 0.37 and the charge of the S atom is 0.53 to 0.55. In contrast, the charge of the Au atom directly attached to sulfur is only 0.17 while the charge of the S atom is 0.33. Results for the charge distributions of compounds containing selenium are consistent with these findings. 3.3.3. HOMO–LUMO energies The HOMO and LUMO energies and the HOMO– LUMO energy gaps obtained for the two conformations of the M3SCH3 and M3SeCH3 compounds at the B3LYP and MP2 levels of theory are presented in Table 6. The major finding related to the HOMO–LUMO energy gaps is that they show substantial variation with respect to metal cluster size. For example, Conformer 1 of M3SCH3 exhibits

HOMO–LUMO energy gaps that are 0.8–2.1 eV smaller than the HOMO–LUMO gaps of the corresponding MSCH3 compounds. Also, the HOMO–LUMO gaps of Conformer 2 of M3SCH3 are smaller than those of MSCH3 by 0.2–1.2 eV. Results for the selenium-containing compounds are consistent with these observations. 4. Conclusions Ab initio and density functional calculations have been completed for metal alkanethiolates and metal alkaneselenates containing copper, silver, and gold and with alkane chains of one, three, or six carbons in length. Metal methylthiolates and methylselenates containing three metal atoms also were investigated. Equilibrium geometries, charge distributions, and HOMO–LUMO energy gaps were determined. Key properties that were invariant to metal atom substitution, sulfur/selenium substitution, or alkane chain length were sought. For the MSCH3 and MSeCH3 compounds, the geometrical properties that exhibited invariance to metal atom substitution included the S–C and Se–C bond distances as well as the M–S–C and M–Se–C bond angles. With respect to other properties, the charge of the carbon atom was determined to be nearly invariant to metal atom substitution. On the other hand, the charges of the metal atom and the sulfur or selenium atom exhibited significant variations with respect to metal atom substitution. Finally, the HUMO–LUMO gaps of MSCH3 and MSeCH3 were determined to be rather insensitive to metal atom or sulfur/selenium atom substitution. Increasing the alkane chain length had little effect on any of the properties. No significant changes were displayed in bond lengths or bond angles as the alkane chain was increased from one to six carbons. The charges of the metal atoms and sulfur or selenium atoms were found to be

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nearly invariant to alkane chain length. A small drop of less than 0.2 eV in the HOMO–LUMO energy gap occurred as the alkane chain lengthened, with the most significant drop as the chain was increased from one to three carbons. Geometrical parameters, including M–S and M–Se bond lengths, S–C and Se–C bond lengths, and M–S–C and M–Se–C bond angles, for metal alkanethiolates and metal alkaneselenates containing three metal atoms were found to be very similar to those containing only one metal atom. The closest comparisons were obtained for Conformation 1 of the M3SCH3 and M3SeCH3 compounds in which the sulfur or selenium is directly bonded to only one metal atom. The charge of the carbon atom also was found to be almost identical in the compounds containing three metal atoms compared to those containing one metal atom. Finally, significant drops of 1–2 eV in the HOMO– LUMO gaps were observed for compounds containing three metal atoms compared to those containing one metal atom. A number of intriguing results suggesting invariant properties with respect to metal atom substitution, sulfur/ selenium substitution, alkane chain length, and metal cluster size have been uncovered in this study. While the present investigation focused only on interactions between individual alkanethiolates and alkaneselenates with one or a few metal atoms, it is likely that some of these properties play a role in the invariance observed in the experimental SEERS spectra [2–6]. Future work will continue to investigate these properties in larger systems in order to more directly probe the origins of the invariance of the experimental SEERS spectra. Acknowledgment Partial support of this work through a grant of supercomputer time from the National Center for Supercomputing Applications, Champaign, Illinois, is acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.theochem.2006.09.029. References [1] G. Chumanov, S. Konstantin, B.W. Gregory, T.M. Cotton, J. Phys. Chem. 99 (1995) 9466. [2] B.K. Clark, B.W. Gregory, A. Avila, T.M. Cotton, J.M. Standard, J. Phys. Chem. B 103 (1999) 8201. [3] B.K. Clark, B.W. Gregory, J.M. Standard, Phys. Rev. B 62 (2000) 17084. [4] B.W. Gregory, B.K. Clark, J.M. Standard, A. Avila, J. Phys. Chem. B 105 (2001) 4684. [5] B.K. Clark, J.M. Standard, B.W. Gregory, A.D. Hall, Surf. Sci. 498 (2002) 285. [6] A. Avila, B.W. Gregory, B.K. Clark, J.M. Standard, T.M. Cotton, Langmuir 18 (2002) 4709.

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