Article pubs.acs.org/JPCC
How Crucial Are Finite Temperature and Solvent Effects on Structure and Absorption Spectra of Si10? N. Arul Murugan,*,† Indra Dasgupta,‡ Arup Chakraborty,‡ Nirmal Ganguli,‡ Jacob Kongsted,§ and Hans Ågren† †
Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden ‡ Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India § Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark S Supporting Information *
ABSTRACT: We have investigated finite temperature and solvent effects on the structure, and optical absorption properties of the Si10 cluster, as a model for functionalized clusters used in biomedical applications. Among the many isomers possible for Si10 clusters we have studied tetracapped trigonal prism (TCTP) with C3v symmetry, which previously has been reported to be the global minimum structure, using the Car−Parrinello hybrid QM/ MM technique. We observe that Si10 remains to be in the TCTP structure in the gas phase, while in solvents we see dominant population of a distorted TCTP conformer which has a similar structure like TCTP except for one of the surface atoms changing its face center position to the edge. We find that there is frequent conformational transitions between these two structures. In the presence of solvents, the interatomic distances are lowered significantly compared to the case of gas phase. While solvent effects appear not to be very significant for the prediction of the excitation energy in the silicon cluster, we find that temperature effects have a substantial influence on its structure and optical properties. surfaces.9 Basically, the design of nanoparticles for such applications requires understanding of the structure and properties of the clusters and nanoparticles either in solvents or in the vicinity of biostructures or when these are interfaced with surfaces. In addition, finite temperature and pressure effects also play a dominant role in dictating the structure and properties of the cluster. Solvents in particular the capping ligands are found to play a key role in deciding the structure of CdS/CdSe nanocrystals10 during the growth process. There also exist reports on zinc oxide clusters which show dramatic difference in their optical (particularly photoluminescence) properties which are found to be highly sensitive to changes in the vapor pressure, and so these clusters can serve as gas sensors.11 Such small changes in environment have a larger influence on the structure of these clusters and so eventually lead to dramatic difference in their optical and magnetic properties. However, from a computational point of view the study of such systems poses problems due to a number of reasons including the general unavailability of force fields for clusters, the heterogeneous nature of the cluster−interface system, and the relatively large size of such systems. A delicate and accurate method is needed to model the environment induced structural changes and subsequent changes in proper-
1. INTRODUCTION The Si10 cluster is one of the most stable small size silicon clusters and dominates the cluster mass distribution obtained when bulk silicon is evaporated.1−3 It exists in numerous isomeric forms4−7 with at least 26 minimum energy structures being reported.7 There has been a long discussion in the literature concerning the global minimum structure for the Si10 cluster,4,5,7 where mostly structures either with tetracapped octahedron (TCO) (Td symmetry) or tetracapped trigonal prism (TCTP) (C3v symmetry) have been proposed to be the global minimum. Earlier theoretical predictions indicate that the TCTP and TCO structures have comparable energetics, while with more recent application of a highly correlated ab initio MP4(SDQ)/6-31G* method, the TCTP structure has been predicted to be more stable than the TCO structure.7 It is interesting to ask whether this isomer continues to dominate the conformational distribution (or isomer distribution) even at room temperature or if there will be transitions to other isomers as seen for many molecular crystals that show temperature-induced phase transition to other polymorphs with comparable energetics. In addition, it will be of relevance to explore the role of solvents on this cluster geometry given the fact that nanoparticles and clusters are usually prepared in colloidal media.8 The real world applications of atomic clusters and nanoparticles for bioimaging, sensing, and drug delivery require that the clusters are interfaced with organic linkers, proteins, and © 2012 American Chemical Society
Received: September 3, 2012 Revised: November 27, 2012 Published: November 28, 2012 26618
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components where the silicon cluster is described using density functional theory while the remaining solvent subsystem is described using a molecular mechanics force field (as similar to the one used in MD). The QM/MM Hamiltonian describes the coupling between the QM and MM subsystems and include short-range repulsion, long-range attraction, and electrostatic interaction between QM and MM regions. In this way the QM/MM framework accounts for polarization of the QM system by the partial charges of the MM atoms. The QM subsystem is described using density functional theory with the BLYP gradient corrected functional23,24 and the Troullier− Martins norm conserving pseudopotentials.25 Here, the electronic wave function is expanded in a plane wave basis set with an energy cutoff of 80 Ry. We have used 5 atomic unit as the time step for the integration of the Lagrange’s equation of motion and 600 amu as the fictitious electronic mass. The CP-QM/MM calculations are initiated with a quenching run that relaxes the initial structure to the Born−Oppenheimer surface of QM/MM system. A temperature scaling run is then subsequently carried out for 0.5 ps to bring the system temperature to 300 K. Finally, the system is allowed to sample the isothermal ensemble by connecting to the Nose−Hoover thermostat. The total time scale for the production run was ∼30 ps in the case of all cluster−solvent systems. The cluster gas-phase calculations were carried out using the CPMD software,26 while for the silicon cluster in solvents, the CPMD/ GROMOS software26,27,22 has been employed. 2.2. Property Modeling Using Hybrid QM/MM Response Technique. The effect of solvents or media on general molecular properties are usually discussed in terms of two contributions: (i) direct solvent effect and (ii) indirect solvent effect. The indirect solvent effect refers to geometrical changes in the solute induced by the solvent while the direct solvent effect arises due to a differential stabilization or destabilization of the excited/ground states of the solute molecule, thereby resulting in either a blue or red shift in the absorption spectra.28 The stabilization is usually dominated by the dipole−dipole interaction between the solute and solvent and is due to the difference in the dipole moments of the excited and ground states of the molecule. Obviously, the structural changes in the solute caused by the solvent (the indirect solvent effect) is also reflected in the solute molecular properties. The direct and indirect solvent effect on the optical properties have been reported to be dramatically large in the case of solvatochromic molecules.28 There are no detailed investigations to analyze such individual contributions to the optical properties in case of the clusters and nanoparticles. So, we have carried out the three sets of calculations to look into the temperature effect and solvent effect on the optical property of silicon cluster. The first set of calculations refer to the isolated Si10 cluster sampled from the Car−Parrinello molecular dynamics simulation in the gas phase. The two remaining sets of calculations refer to the structures obtained from the hybrid QM/MM Car−Parrinello molecular dynamics simulations and are described in detail below. In all these cases, the excitation energy calculations were carried out using time-dependent density functional theory. In particular, we have used B3LYP and PBE0 levels of theory along with Turbomole-TZVP basis set. These two functionals were adopted to check the reliability of the excitation energies computed for silicon cluster. The calculations were performed using a development version of Dalton2.0.29 The implementation of excitation energy calcu-
ties in these clusters. In this respect the use of the hybrid quantum mechanics/molecular mechanics framework (QM/ MM) would represent a good balance for such studies.12 While such studies have been performed to a large extent for organic systems, it has hardly been explored for inorganic systems. In the present work we have used methods rooted in QM and QM/MM to study the structure and absorption spectra of Si10 cluster in gas phase and in solvents. We are not aware of many other investigations that deal with finite temperature and solvent effects on silicon clusters. However, we mention a recent study based on Car−Parrinello molecular dynamics which contributes to the subject of solvent and finite temperature effect on the structure and band gap of passivated Si 5 clusters.13 A recent study using isokinetic Born− Oppenheimer molecular dynamics has investigated in detail the finite temperature behavior of Si10.14 In view of the above, our study using QM/MM method will provide further insight into the influence of such effects for a representative case, the Si10 cluster, which may be of relevance to cluster functionalization for various applications such as biomedical imaging, drug delivery, and photodynamic therapy. We employ an integrated approach and model the structure and property sequentially. For the structure modeling we use ab initio molecular dynamics. In particular, we have carried out Car−Parrinello molecular dynamics calculation for the Si10 cluster in the gas phase. We have also studied the Si10 cluster in chloroform and water solvents using the Car−Parrinello hybrid quantum mechanics/molecular mechanics approach.12 Finally, for calculating the absorption spectra, we use the polarizable embedding response approach which accounts for electrostatic and mutual polarization interaction between the cluster−solvent subsystems during the property calculations.15 The remainder of the paper is organized as follows. In section 2 we present our computational details. Section 3 is devoted to the results and discussion. Finally, we conclude the main results of the report in section 4.
2. COMPUTATIONAL DETAILS 2.1. Structure Modeling Using Hybrid QM/MM Molecular Dynamics. Si10 in its tetracapped trigonal prism geometry was optimized using B3LYP/aug-cc-pvtz16 as implemented in the Gaussian09 software.17 The optimized structure was used as the input geometry for Car−Parrinello molecular dynamics simulation in the gas phase as well as for the hybrid QM/MM Car−Parrinello molecular dynamics calculations in chloroform or in water solvents. The initial configuration for hybrid QM/MM simulations were taken from a pre-equilibrated molecular dynamics (MD) run carried out for the silicon cluster−solvent structure prepared by solvating a single Si10 cluster in chloroform or water solvents. The MD calculations were carried out using the SANDER module of the Amber8 software.18 The MD calculations for the cluster− solvent systems were carried out in the isothermal−isobaric ensemble. During the MD run, the GAFF19 and TIP3P20 force fields were used for chloroform and water solvents, respectively. The atomic partial charges for Si10 have been obtained from the CHELPG21 procedure while the nonbonded interaction parameters were taken from the GROMOS force field.22 The MD simulations were continued until the structure and energetics were converged in the case of both cluster−solvent systems. The total time scale of these equilibration runs were a few hundreds of picoseconds. The hybrid QM/MM approach employs two different descriptions for the cluster−solvent 26619
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lation for molecules in solvents using the polarizable embedding scheme has been described in detail in ref 15. 2.2.1. Calculations on the Isolated Si10. In order to elucidate indirect solvent contributions to the optical property of the silicon cluster, we have calculated the excitation energy for the configurations obtained from CPMD-QM/MM calculations but without including the solvent molecules explicitly. The results from this set of calculations will be referred to as MM-0. 2.2.2. Calculations on the Silicon Cluster with a Discrete Solvent Description. The excitation energy calculations for Si10 in solution are based on the polarizable embedding response function technique which retain the discrete description of the solvent and also includes the cluster−solvent interaction through different coupling terms in the QM effective Hamiltonian. In the present work the solvents are described using partial charges plus distributed isotropic polarizabilities. The use of charges alone in the solvent model only accounts for the polarization of the solute due to the solvent and the solvent polarization is neglected. On the other hand, when both atomic charges and polarizabilities are used in the description of the solvent molecules, both the solute polarization and the explicit back-polarization effects are included. In the present study we have used a modified Ahlström water model30 to describe the water solvent. The original Ahlström water model describes polarization by assigning to each water molecule a molecular polarizability to the oxygen interaction site. However, in this work this molecular polarizability is replaced by the use of a distributed polarizability with expansion points assigned to the atomic nuclei. These atomic polarizabilities have been calculated at the B3LYP/aug-cc-pVTZ level using the LoProp approach.31 The spectral results obtained using the modified Ahlström potential will be referred to as MM-2. For chloroform solvent also we have used a solvent model at the same level that includes partial charges on each atomic sites of chloroform and a distributed isotropic polarizability. The charges for chloroform solvent were obtained from the CHELPG procedure carried out at B3LYP/aug-cc-pVTZ level, and the polarizabilities were obtained using the same computational level as for water (described above). 2.3. Calculation of Band Gap. We have studied the energetics of the frontier orbitals and HOMO−LUMO gap for the optimized geometry of the Si10 cluster. We have also studied temperature and solvent effects on these quantities. Particularly, we have studied the energetics of the 10 frontier Kohn−Sham orbitals calculated for the instantaneous geometries obtained during the Car−Parrinello MD, and these calculations have been carried out for 60 configurations.
Figure 1. Molecular structure of Si10.
between 2.25 and 3.1 Å. The average Si−Si bond lengths are 2.53 and 2.56 Å at 0 and 300 K, respectively. In chloroform and water solvents the average bond length slightly reducedas compared to the gas-phase value at 300 Kto 2.54 Å. On the basis of these values, we suggest that the cluster size is smaller for the zero temperature case while it is maximum for the finite temperature case in the gas phase while in solvents it has intermediate values. As it has been discussed in detail, in the literature the cluster size is the most important parameter for the cluster and dictates its various properties.32 We will discuss in following sections how these structural changes influence the band gap and optical properties of the silicon cluster. The distance distribution function for all four cases are shown in Figure 2. Three different peaks are seen in the distance
Figure 2. Distance distribution in the bare silicon cluster and in water and chloroform solvents.
3. RESULTS AND DISCUSSION 3.1. Finite Temperature and Solvent Effect on the Structure of the Si10 Cluster. Si10 in the TCTP structure as shown in Figure 1 has Si6 as the core and four of the five faces are capped with Si atoms.7 Previous calculations based on the full potential linearized muffin tin orbital (FP-LMTO) molecular dynamics method revealed Si−Si bond lengths of the silicon cluster in the range 2.32−2.66 Å depending on the position of the atoms in the trigonal prism or at the edge.7 We have also looked into the average structure of the silicon cluster at 0 and 300 K and also in the presence of polar and nonpolar solvents. The bond lengths corresponding to zero temperature structure varied between 2.35 and 2.78 Å while for the structure at ambient temperature (at 300 K) the bond lengths varied
distribution function (DDF), which shows that each silicon atom is associated with three different neighboring atoms. The peaks appearing at smaller r value should be attributed to core atom−core atom contact and core atom−surface atom contacts. The peaks appearing at larger value of r should be attributed to surface atom−surface atom contact. Here, the atoms that are occupying the corners of the trigonal prism are referred as core atoms while those occupy the face centers of the trigonal prism are referred to surface atoms. The DDFs corresponding to pristine cluster and in solvents show slightly different features explaining that the solvent effect on the silicon cluster geometry is significant. Theoretical modeling of clusters 26620
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are usually carried out in vacuum, and our present calculations show that in fact there are significant changes in the cluster geometry due to solvent. However, the DDFs for the silicon cluster in two different solvents appear similar, suggesting that the solvent polarity effect on the cluster geometry is not very significant. Particularly, a significant difference is seen in the third peak in the DDFs corresponding to pristine and the solvated cluster. The disappearance of peak-like feature at a distance 4.5 Å for the solvated clusters suggest that the edge atoms are more mobile in solvent than in the case of pristine cluster. The mobility has its origin in the availability of a vacancy in the TCTP structure. Among the five faces available for the trigonal biprism, only four are capped in TCTP structure. So, there is always a flipping of edge atoms to the empty site and which has to be attributed to the mobility of the edge atoms. Such flipping involves the passage of the silicon atom from one face center to another empty face center through the edge center and is associated with a kinetic barrier. We have observed such flippings only in the presence of solvents which suggests that solvents also play an important role in the dynamics (conformational transition dynamics) by altering the barrier heights between different conformers. 3.2. Solvent Effect on the Charge Distribution and the Dipole Moment. In the previous section we discussed the finite temperature and solvent effects on the structure and conformational dynamics of the silicon cluster. In this section we will discuss the solvent effect on the charge distribution and cluster dipole moment. We have computed the site charges for each atom of the optimized Si10 cluster at the level of B3LYP/ aug-cc-pvtz theory using the Gaussian09 software.17 These charges are obtained by fitting the electrostatic potential at number of points around the Si10 cluster. Interestingly, the charges for the core and surface atoms follow a specific pattern. The six core atoms have a positive charge while the remaining four surface atoms possesses negative charges. The negative charges for the surface silicon atoms may be attributed to the presence of dangling bonds. See Figure S1a of the Supporting Information where the positive and negatively charged atoms are shown using cyan and yellow colors, respectively. The core atoms have charges between 0.039 and 0.131 while the surface atoms have charges of −0.146 and −0.070. The values presented here correspond to the zero temperature case. To understand the finite temperature and solvent effect on the charge distribution, we have computed the same parameters for the Si10 cluster in chloroform and water solvents, and the results are shown in Figure 3. The charges used for this analysis are the D-RESP charges27 obtained from the hybrid QM/MM molecular dynamics simulations. These are again charges similar to electrostatic potential fitted charges and are obtained from a fitting in order to reproduce the molecular electrostatic potential and depend on the dynamic solvent environment. In other words, here the charges are dynamical quantities and depend on the conformational or chemical nature of the QM system and also depends on the instantaneous potential generated by the solvent environment. The magnitude of charges of silicon atoms varies in the range of −0.2 to 0.2 in the case of water solvent while in chloroform solvent it varies in the range of −0.1 to 0.1. This clearly explains that the water solvent polarizes the cluster to a higher degree than the chloroform solvent. It is interesting to note that even though the solvent polarity does not change the cluster geometry (as seen from similar DDFs for cluster in both solvents) it alters the charge distribution in the cluster significantly. However, the average
Figure 3. Charge distribution and dipole moment distribution of Si10 cluster in chloroform and water solvents.
value has a peak corresponding to zero in both the cases. We have also computed the dipole moment of the silicon cluster in these solvents (see Figure 3), and the average values are 1 and 2 Debye for chloroform and water, respectively. Thus, the dipole moment of the Si10 cluster in water solvent is twice as large compared to that in chloroform solvent. This again shows that the solvent polarity effect on the cluster charge distribution is not negligible and probably important to be accounted for. As discussed previously, we have observed that the Si10 cluster undergoes rapid conformational transition in solvents. The trigonal biprism structure has five faces, and in the Si10 cluster only four of them are occupied. So, the surface atoms have larger mobility to occupy the empty site which we believe is responsible for such conformational jumps. We also notice that when there is conformational transition the ratio of number of atoms having positive and negative charges change, and we have used this as an indicator to study the population of different conformers and the transition between them. As we have mentioned above, the charge distribution depends on the chemical and conformational nature of a molecule or cluster, and so the characterization of different conformers can be followed from the charge distribution analysis. We have plotted the population of different conformers based on the number of atoms having negative charges. The results are shown in Figure 4. Surprisingly, the population of conformers having four negative charges (which correspond to the TCTP global minimum structure) is not the largely populated one rather the conformer with five positive charges is the most populated one. We have analyzed the structure that correspond to such charge distribution. We find that this structure is rather closer in geometry to the TCTP structure except that one of the surface atom moves from its face centered position to edge (refer to Figure S1b of the Supporting Information). When we optimize this structure it basically goes to a TCTP structure, suggesting that there is no significant kinetic barrier between this conformer and TCTP conformer. As can be seen from Figure 4, the population of conformers with six positively charged silicon is also significant. Interestingly, the population of different conformers of Si 10 appears to be the same 26621
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Figure 4. Charge magnitude distribution curve for silicon cluster in chloroform and in water solvents.
independent of the change in the solvent polarity. However, no such conformational transition has been seen for pristine silicon cluster in the gas phase, and the charge magnitude distribution curve has a single peak at value 4. 3.3. Solvation Shell Structure. We now discuss the solvation shell structure of silicon cluster in polar and nonpolar solvents. For this we have computed cluster and solvent center of mass radial distribution functions (rdf), and the results are shown in Figure 5. In the case of water solvent, the first
Figure 6. Solvation shell structure of Si10 cluster in chloroform and water solvents.
been compared to its zero temperature result. The energetics (in electronvolts) of the HOMO and LUMO orbitals and the HOMO−LUMO gap are presented for all these cases in Table 1. A larger HOMO−LUMO gap is seen for the silicon cluster at
Figure 5. Radial distribution function for silicon cluster in chloroform and in water solvents.
solvation shell appears at lower r value when compared to chloroform solvent. In the case of water solvent, peak-like feature in the rdf are seen only up to a distance of 11.5 Å while such features are seen up to 15.5 Å in the case of chloroform solvent. The presence of silicon cluster is seen only up to second solvation shell in water, and beyond this the structure of water is similar to that of bulk water. But in the case of chloroform solvent, the presence of the cluster is realized over a longer distance. The stronger hydrogen-bonding network in water should be responsible for this observation. The average number of water molecules in the first and second solvation shells are respectively 112 and 266. Similarly, the number of chloroform solvent molecules in first and second solvation shells are 38 and 125, respectively. A snapshot of silicon cluster and its first solvation shell structure in chloroform and water solvents are shown in Figures 6a and 6b, respectively. 3.4. Temperature and Solvent Dependence on Band Gap. We have calculated the variation in the HOMO−LUMO gap as a function of time step for the Si10 cluster in gas phase and for its chloroform and water solvated forms. The value has
Table 1. Average HOMO and LUMO Orbital Energies and Band Gap (in eV) of Si10 in Gas Phase or in Solution system Si10 Si10 Si10 Si10
at 0 K at 300 K in CHCl3 in water
HOMO
LUMO
gap
−5.61 −5.16 −5.72 −5.22
−3.59 −4.07 −3.83 −3.22
2.02 1.09 1.89 2.00
zero temperature while a smaller one has been observed for the silicon cluster at 300 K. The results corresponding to the solvated silicon cluster appear intermediate to these values. The reduction of the band gap for the finite temperature silicon cluster and for its solvated forms will manifest itself as a red shift in the optical spectra. A similar temperature effect has been observed in the case of passivated Si5 cluster where the band gap reduces by 1.2 eV for the finite temperature case.13 The size dependency of the HOMO−LUMO gap and the optical properties have been discussed in detail in the 26622
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literature.32 With increasing size of the clusters, the gap reduces. When compared to the gap of 4.5 eV computed for passivated Si5 cluster in vacuum, we report a gap which amounts to 2.03 eV for the Si10 cluster.13 The reduction in the band gap is due to quantum confinement. In the present case, we observe that the finite temperature effect contributes to a 0.93 eV reduction in HOMO−LUMO gap. Similar to that observed in the case of passivated Si5 cluster, the HOMO−LUMO gap for the solvated Si10 cluster appears between those of pristine silicon cluster at zero temperature and at 300 K. As we discussed in the earlier section, the size of the cluster increases in the order Si10 at 0 K < solvated Si10 < Si10 at 300 K. Because of the size dependency, the band gap should go in the order Si10 at 0 K > solvated Si10 > Si10 at 300 K that we eventually see in our calculations. Based on these results, the finite temperature and solvent alter the cluster size, and this is responsible for the change in the properties of the cluster. 3.5. Finite Temperature and Solvent Effect on Absorption Spectra of the Si10 Cluster. Only very little is known for the solvent effect on the absorption spectra for small silicon clusters. However, a recent study on passivated Si5 cluster provides some information in this regard.13 It would be useful to understand how the structure, band gap, and absorption spectra vary with increase in cluster size and the solvent effect on these clusters. In the present study, we have studied the Si10 cluster, and by comparing with the previous results reported for Si5, we wish to shed some light into the above-discussed issues. We have computed the finite temperature absorption spectra as an average over 150 configurations. The average absorption maxima (λmax) for Si10 at 300 K and in solvents were obtained using B3LYP and PBE0 functionals and are given in Table 2. To evaluate the shifts in λmax due to
pristine silicon cluster at 300 K corresponds to 604 nm. So, the finite temperature effect contributes to a red shift of ∼53 nm. Now let us discuss about the solvent effect on the absorption spectra of the cluster. There are two different values presented with labels MM-0 and MM-2. As we discussed earlier, the former one includes only the indirect solvent effect while the latter one includes both direct and indirect solvent effects. As can be seen from Table 2, the results from both the sets of calculations yield comparable λmax values, suggesting that the direct solvent effect is not very significant. It suggests that in the case of solvents the contribution to the absorption spectra merely come from the solvent-induced structural changes. Overall, when compared to the absorption spectra of pristine silicon cluster at 0 K, the spectra at 300 K and in different solvents are red-shifted. It is worth mentioning that a similar red shift was also reported in the case of passivated Si5 cluster.13 This study also reports that finite temperature effect plays the dominant role in the optical property of silicon cluster compared to the solvent effect.13 The PBE0 functional based shifts in absorption maximum due to thermal and solvent effects when compared to zero temperature value also follow the same trend as in B3LYP functional. The thermochromic shifts for silicon cluster as obtained from B3LYP and PBE0 functionals are respectively 53 and 48 nm. The shifts in absorption maximum due to chloroform and water solvents as obtained from these two functionals also agree well. These results clearly show the reliability of the thermochromic and solvatochromic shifts obtained for silicon cluster even though, the PBE0 functional consistently underestimate the absorption maximum by ∼20 nm in all the cases. A similar trend in the excitation energy calculations using these two functionals for a number of organic molecules has been reported in the literature.33
Table 2. Average Absorption Maximum (in nm) Corresponding to the Lowest Energy Excitation of Si10 in Gas Phase or in Solution As Computed from B3LYP and PBE0 Functionalsa system Si10 Si10 Si10 Si10 Si10 Si10
at 0 K at 300 K in CHCl3 at 300 K (MM-0) in CHCl3 at 300 K (MM-2) in water at 300 K (MM-0) in water at 300 K (MM-2)
B3LYP 551 604 590 589 600 597
(53) (37) (38) (49) (46)
4. CONCLUSIONS We have studied finite temperature and solvent effects on structure, conformational dynamics, charge distribution, and optical property of Si10 cluster as a representative cluster for unraveling temperature and solvent effects on properties of clusters used in applied research. We have identified “charge magnitude” distribution as a parameter to characterize different conformational states of the silicon cluster. Particularly, a distorted tetracapped trigonal prism TCTP structure dominates the population in the case of solvents while a perfect TCTP structure is the most probable one in pristine silicon clusters. Even though the solvent polarity is not found to play any essential role for the geometry of the cluster, it has a significant impact on the charge distribution of the cluster. A larger dipole moment and increased values for the atomic charges are seen for the cluster in the case of water solvent. The solvent effect is modest for the optical absorption energy, while a significant finite temperature effect on the structure contributes to this property.
PBE0 532 580 570 569 583 580
(48) (38) (37) (51) (48)
The shifts in λmax when compared to 0 K value are given in the parentheses.
a
finite temperature (is referred as thermochromic shift) and solvent effect (referred as solvatochromic shift), we have also computed the λmax for the optimized geometry of pristine silicon cluster. The optimized geometry (at B3LYP/aug-cc-pvtz level of theory) of silicon cluster used for calculating 0 K absorption spectra is given in the Supporting Information. The thermochromic and solvatochromic shifts are also presented in Table 2 in parentheses. The convergence of the computed absorption maximum has been checked by plotting the evolution of λmax with number of configurations and its Npoint average (results are not shown). This clearly show that the absorption spectra have converged with number of configurations. First, we will discuss about the results obtained using the B3LYP functional. The λmax for optimized geometry of silicon cluster corresponds to 551 nm. The average λmax of
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ASSOCIATED CONTENT
S Supporting Information *
Optimized coordinates of silicon cluster using the B3LYP/augcc-pvtz level of theory along with the structures of most probable conformer in vacuum and in solvents; complete list of authors for refs 17, 18, and 26. This material is available free of charge via the Internet at http://pubs.acs.org. 26623
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(21) Breneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361−373. (22) van Gunsteren, W. F.; Billeter, S. R.; Eising, A. A.; Hüenberger, P. H.; Krüer, P.; Mark, A. E.; Scott, W. R. P.; Tironi, I. G. Biomolecular Simulation: The GROMOS96 Manual and User Guide; Hochschulverlag AG an der ETH Zürich: Zürich, Switzerland, 1996. (23) Becke, A. D. Phys. Rev. A 1988, 38, 3098−3100. (24) Lee, C.; Yang, W.; Parr, R. C. Phys. Rev. B 1988, 37, 785−789. (25) Trouiller, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993−2006. (26) Hutter, J.; Parrinello, M.; Marx, D.; Focher, P.; Tuckerman, M.; Andreoni, W.; Curioni, A.; Fois, E.; Röthlisberger, U.; Giannozzi, P.; et al. Computer code CPMD, version 3.11; Copyright IBM Corp. and MPI-FKF: Stuttgart, 1990−2002. (27) (a) Laio, A.; VandeVondele, J.; Röthlisberger, U. J. Phys. Chem. B 2002, 106, 7300−7307. (b) Laio, A.; VandeVondele, J.; Röthlisberger, U. J. Chem. Phys. 2002, 116, 6941. (28) (a) Murugan, N. A.; Ågren, H. J. Phys. Chem. A 2009, 113, 2572−2577. (b) Murugan, N. A.; Kongsted, J.; Rinkevicius, Z.; Ågren, H. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 16453−16458. (c) Murugan, N. A.; Aidas, K.; Kongsted, J.; Rinkevicius, Z.; Ågren, H. Chem.Eur. J. 2012, 18, 11677−11684. (29) DALTON, a molecular electronic structure program, Release 2.0, 2005; see http://www.kjemi.uio.no/software/dalton/dalton.html. (30) Ahlström, P.; Wallqvist, A.; Engström, S.; Jönsson, B. Mol. Phys. 1989, 68, 563−581. (31) Gagliardi, L.; Lindh, R.; Karlström, G. J. Chem. Phys. 2004, 121, 4494. (32) Roduner, E. Chem. Soc. Rev. 2006, 35, 583−592. (33) (a) Jacquemin, D.; Planchat, A.; Adamo, C.; Mennucci, B. J. Chem. Theory Comput. 2012, 8, 2359−2372. (b) Day, P. N.; Nguyen, K. A.; Pachter, R. J. Phys. Chem. B 2005, 109, 1803−1814.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by MONAMI, INDO-EU network, funded by DST India and EC. This work was supported by a grant from the Swedish Infrastructure Committee (SNIC) for the project “Multiphysics Modeling of Molecular Materials”, SNIC020-11-23. J.K. thanks the Danish Center for Scientific Computing (DCSC), The Danish Councils for Independent Research (STENO and Sapere Aude programmes), the Lundbeck Foundation, and the Villum foundation for financial support.
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REFERENCES
(1) (a) Bloomfield, L. A.; Freeman, R. R.; Brown, W. L. Phys. Rev. Lett. 1985, 54, 2246−2249. (b) Fuke, K.; Tsukamoto, K.; Misaizu, F.; Sanekata, M. J. Chem. Phys. 1993, 99, 7807. (2) Qin, W.; Lu, W.-C.; Zhao, L.-Z.; Zang, Q.-J.; Wang, C. Z.; Ho, K. M. J. Phys.: Condens. Matter 2009, 21, 455501. (3) Yoo, S.; Zeng, X. C. J. Chem. Phys. 2006, 124, 054304. (4) Ballone, P.; Andreoni, W.; Car, R.; Parrinello, M. Phys. Rev. Lett. 1988, 60, 271−274. (5) Raghavachari, K.; Rohlfing, C. M. J. Chem. Phys. 1988, 89, 2219. (6) Grossman, J. C.; Mitas, L. Phys. Rev. Lett. 1995, 74, 1323−1326. (7) Li, B.-X.; Cao, P.-L.; Jiang, M. Phys. Status Solidi B 2000, 218, 399−409. (8) Wilcoxon, J. P.; Abrams, B. L. Chem. Soc. Rev. 2006, 35, 1162− 1194. (9) (a) Medintz, I. L.; Uyeda, H. T.; Goldman, E. R.; Mattoussi, H. Nat. Mater. 2005, 4, 435−446. (b) Aubin-Tam, M.-E.; HamadSchifferli, K. Biomed. Mater. 2008, 3, 034001. (c) Mrinmoy De, Ghosh, P. S.; Rotello, V. M. Adv. Mater. 2008, 20, 4225−4241. (10) Shanavas, K. V.; Sharma, S. M.; Dasgupta, I.; Nag, A.; Hazarika, A.; Sarma, D. D. J. Phys. Chem. C 2012, 116, 6507−6511. (11) Ghosh, M.; Raychaudhuri, A. K. Nanotechnology 2008, 19, 445704. (12) (a) Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227−249. (b) Senn, H. M.; Thiel, W. Angew. Chem., Int. Ed. 2009, 48, 1198− 1229. (c) Gao, J. L.; Truhlar, D. G. Annu. Rev. Phys. Chem. 2002, 53, 467−505. (13) (a) Prendergast, D.; Grossman, J. C.; Williamson, A. J.; Fattebert, J.-L.; Galli, G. J. Am. Chem. Soc. 2004, 126, 13827−13837. (b) Draegar, E. W.; Grossman, J. C.; Williamson, A. J.; Galli, G. J. Chem. Phys. 2004, 120, 10807. (14) Sailaja, K.; Kavita, J.; Kanhere, D. G.; Blundell, S. A. Phys. Rev. B 2006, 73, 045419. (15) (a) Olsen, J. M. H.; Aidas, K.; Kongsted, J. J. Chem. Theory Comput. 2010, 6, 3721−3734. (b) Olsen, J. M. H.; Kongsted, J. Adv. Quantum Chem. 2011, 61, 107−143. (16) (a) Schafer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829. (b) Silva Junior, M. R.; Schreiber, M.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 129, 104103. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Rev. A.02; Gaussian, Inc.: Pittsburgh, PA, 2009. (18) Case, D. A.; Darden, T. A.; Cheatham, T. E.; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Wang, B.; Pearlman, D. A.; et al. AMBER8, University of California, San Francisco, CA, 2004. (19) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. J. Comput. Chem. 2004, 25, 1157−1174. (20) Jørgensen, W. L. J. Am. Chem. Soc. 1981, 103, 335−340. 26624
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