TDDFT Study of Charge-Transfer Raman Spectra of 4

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A TDDFT Study of Charge Transfer Raman Spectra of 4Mercaptopyridine on Various ZnSe Nanoclusters as a Model for the SERS of 4-Mpy on Semiconductors Ronald L. Birke, and John R. Lombardi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12392 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on February 1, 2018

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The Journal of Physical Chemistry

A TDDFT Study of Charge Transfer Raman Spectra of 4-Mercaptopyridine on Various ZnSe Nanoclusters as a Model for the SERS of 4-Mpy on Semiconductors Ronald L. Birke a , b* and John R. Lombardi a , b a

Department of Chemistry and Biochemistry, The City College of the City University of New York, New York, NY 10031, USA

b

Ph. D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York, 10016, USA

*[email protected]

ACS Paragon Plus Environment

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ABSTRACT: We have used DFT and TDDFT calculations mostly at the B3LYP/6-31+G(d) level to investigated the optimized geometry and the normal (static) Raman and pre-resonance Raman (RR) spectra of ZnnSem nanoclusters with several forms of 4-mercaptopyridine, 4-Mpy, ligated to Zn surface atoms on the nanocluster. Both symmetrical nanoclusters with n=m, Zn3Se3, Zn13Se13, and Zn33Se33 , and unsymmetrical nanocluster with m=n-1 , Zn7Se6 and Zn13Se12, were studied as the bare cluster and the cluster-ligand complex. The optimized structures show two types of surface bonds are formed for the 4-Mpy anion bound through the thiol end of the molecule. Binding energy calculations and the structures demonstrate that a bridged structure involving a Zn-S-Zn bond forms with 4-Mpy anion on the unsymmetrical clusters and a single Zn-S bonded anion forms on the symmetrical clusters. A pyridine protonated form of 4-Mpy and the disulfide dimer of 4-Mpy were also studied as a Zn13Se13-ligand complex. Normal mode assignments are given for all these molecular forms on the various nanoclusters. Charge transfer (CT) states of the Zn13Se13-ligand complexes were examined with both B3LYP and CAM-B3LYP and it was concluded that B3LYP is adequate to study pre-RR simulations. All the complexes studied showed several CT states in the first 20 or more excited states and excitation near these CT states gave CT enhancements for the strong bands in the spectra as high as 104 comparable to experimental SERS spectra of 4-Mpy on semiconductor nanoparticles. Both Franck-Condon and Herzberg-Teller types of scattering were found depending on surface geometry and the preresonant CT state. The spectra also show features which are related to the type of surface bond formed.


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1.

INTRODUCTION

The phenomenon of surface enhanced Raman scattering 1,2,3,4 (SERS), first discovered in 1974 5

and elucidated by Jeanmaire and Van Duyne 6,7 in 1977 , has become an important tool of

considerable utility in understanding nanotechnology as well as making possible

numerous

practical applications such as chemical analysis of ultratrace quantities of molecules 8,9, 10 The giant enhancement of molecules absorbed on coinage metal surfaces ( Ag and Au) has led to the overwhelming number of SERS studies on these metal surfaces. The fact that Raman intensity can develop from three different resonances - surface plasmon resonance (SPR) , charge transfer resonance (CT), and molecular resonance (MR)- led us to consider a unified approach to SERS based on Herzberg-Teller (HT) resonance Raman scattering11,12, 13 where vibrational intensity can be predicted by Herzberg-Teller selection rules. On metal nanoparticles like Ag and Au, there is a strong contribution of the surface plasmon resonance to the enhancement. However, the theory also predicts a possible CT resonance when the exciting light is on resonance between a filled orbital of the solid and a vacant molecule orbital (or vice-versa) in any solid-nanoparticlemolecule system indicating the possibility of semiconductors as enhancing substrates. The Herzberg-Teller (HT) coupling between electronic states of any solid-molecule system allows intensity borrowing. When the excitation profiles of the possible resonances intersect each other at a given excitation wavelength, as on metal nanoparticles, it is possible to easily predict singlemolecule enhancements of 1014. Furthermore, then there are unique Herzberg-Teller surface selection rules which are not the same as the electromagnetic, EM, surface selection rules derived from the SPR alone.

11,12 ,1312

However, Raman scattering from molecules on semiconductors

from a resonant energy transfer process involving excitons was considered theoretically by


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Ubea14 only a few years after SERS on metals was established. More recently we have extended this Herzberg-Teller (HT) theory for metal nanoparticles to those of semiconductor, SC, nanoparticles. 15 However, on semiconductors a new phenomenon involving the formation of excitons, as suggested originally by Ubea

14

, can provide various new vibronic CT coupling

schemes involving the semiconductor band gap. Thus, SERS on SC surfaces comes mainly from various possible CT resonances between the SC nanoparticle and the molecule; however, there is still a possible plasmon resonance from valence electrons which generates near-field Mie scattering 16 . The first report of observed Raman enhancement on semiconductors, SCs, was in 1982 by Yamada et al.17 in which an enhancement of the pyridine spectrum on NiO was reported. They later expanded the research to TiO2 as well as NiO18. Observation of a large enhancement of Raman intensity from the surface of a GaP semiconductor nanoparticle19 was reported in 1988. Since then, there has been increasing interest in extending the range of substrates available for surface-enhanced Raman scattering. Several applications of SERS on semiconductors (SC-SERS) have been recently discussed in timely review articles 20,21 Furthermore a sizable number of studies of surface enhancement have more recently been observed on semiconductor nanoparticles in colloidal suspensions or on etched surfaces with 4-mercaptopyridine (4-Mpy) as the target molecule such as on CdS22 , ZnS 23 ZnSe 16 , ZnO 24,25,26 , CuO 27, CdTe28, TiO229, 30 PbS 31

, MoS232 and α-Fe2O333. The enhancements on these SC surfaces of 4-Mpy range from 102 to 106; however,

examining the various experimental spectra on the SC surfaces, we find two rather distinct types of spectral profiles. In both types of spectral profiles of 4-Mpy, most of the bands appear in SERS which are of moderate to strong intensity in the normal Raman spectrum, NRS, of the isolated


4

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solid or solution 4-Mpy, but the relative intensity of these bands varies in two distinct way. In one type of spectrum, called the normal type, the relative intensities look very much like that of the NRS of isolated 4-Mpy, whereas in the other type spectra, the non-normal type, bands which are weak in the NRS of the isolated molecule become strong and give a distinctive SERS spectrum on the SC surface. In the normal type, the most intense bands of 4-Mpy in the NRS are found in the SERS spectra, and this occurs on CdS (1023, 1117, 1594 cm-1), ZnS (1023, 1119, 1594 cm-1), CdTe ( 1013, 1113, 1585 cm-1) , ZnO (1021, 1119, 1594 cm-1) , CuO ( 1023, 1106, 1208, 1594 cm-1) and α-Fe2O3 (1002, 1031, 1600 cm-1). The spectra of 4-Mpy on TiO2 are similar to the normal SERS, but in this case Ag nanoparticles have been aggregated on TiO2 nanoparticles

29,30

so that the spectra are considered to include an SPR effect from the Ag nanoaggregates. In contrast to these “normal” SC-SERS spectra, there is a strikingly different pattern for the nonnormal SERS where three bands near 685, 778, and 1281 cm-1 distinguish these spectra on PbS (682, 780, 1278 cm-1), ZnSe ( 685, 778, 1281cm-1) and MoS2 ( 685, 778, 1281, 1577 cm-1). In these non-normal 4-Mpy SERS spectra, the two lowest bands at around 685 cm-1 and 778 cm-1 are relatively much stronger than in the normal SERS type and the band at 1281 cm-1 is the strongest band of all of the bands in the non-normal SERS spectrum. Furthermore, the 1281 cm- 1 band of b2 symmetry is hardly observable in the normal SC-SERS of 4-Mpy. Thus, part of the motivation of this study was to elucidate the source of the spectral difference between “normal” and “nonnormal” SC-SERS spectra of 4-Mpy. We have simulated the Raman spectrum of 4-Mpy bound on several different sizes of ZnSe clusters. Our motivation for choosing to study the wide band gap (Eg=2.8 eV ) ZnSe quantum dots (QDs) from among the II-VI semiconductors for the cluster material was twofold; (i) it had shown the non-normal SERS spectrum of 4-Mpy experimentally 16, and (ii) for the small


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nanocluster calculations, an all electron basis set can be used for the period four elements- Zn and Se. Furthermore, ZnSe QDots are of general interest having been used recently in quantum dot sensitized solar cells 34 , as a biological fluorescent marker 35 , and have been investigated for green-blue-ultraviolet based photonic devices. 36 The structural, electronic, and optical properties of ZnSe QDs have been well investigated both experimentally and theoretically37, 38. One of the first studies of small ZnSe clusters by DFT was that of Matxain et al.39 who used the B3LYP density functional for ZnnSen and ZnnTen pairs from n=1-8. They found geometry optimized structures depended on size, n=3-5 giving optimized ring structures and n=6-9 giving optimized three-dimensional (3D) spheroid structures. The three-dimensional structures were built from 4 and 6 membered rings. Subsequent theoretical studies with B3LYP for stoichiometric ZnnSen clusters with B3LYP from n=1-16 have been undertaken by Sanville et al. 37 , and their optimized structures agree well with those of Matxain et al.39 It was pointed out

37

that ZnSe clusters of 13

and 33 or 34 monomeric units are ultra-stable in experimental ablation studies. Both bare and surface passivated structures have been studied with the density-functional tight-binding (DFTB) method.

38,40

Other investigations have used the pure DFT method with the B86 exchange-

correlation potential for small clusters (up to n=7) and for larger clusters with a Wurzite bulk structure with the experimental bond lengths 41. More recently Nanavati et al. 42 used a plane wave method to study ZnnSen clusters up to n=13 for bare and hydrogen atom passivated surfaces. In addition to structural and electronic properties, the B3LYP density functional has been used to calculate other nanoparticle properties such as polarizabilities and chemical hardness and softness 43

. There have been relatively few DFT Raman simulations of vibrational spectra of organic

molecules on II/VI semiconductor surfaces. One goal of this type of studies has been to use DFT


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frequency calculations to understand capped CdSe qdots.44 However, a recent DFT study by Weiss et al.45 investigated resonant excitation to give resonance Raman for different ligands on a Cd16Se13 nanoparticle in terms of the SERS CT process. They considered the excitation to be to an excitonic state which involves charge transfer Herzberg-Teller coupling schemes in SERS spectra.15 Zayak et al. 46 have used DFT to study the

effect of electric field on nonresonant

Raman scattering on semiconductors, the so-called SERS chemical effect. They examined the trans-1,2-bis(4-pyridyl)ethylene molecule adsorbed on a PdS slab using the DFT SIESTA code. Previously we have used DFT and TDDFT methods to study the Raman spectroscopy of 4-Mpy on small Ag nanoclusters Agn for n=10

47

and n=13. 48 In the present paper, we also

examine both normal Raman scattering (NRS) and pre-resonance Raman scattering (pre-RRS) from charge transfer states of 4-Mpy absorbed on a variety of different ZnSe nanostructures. We used three stoichiometric ZnnSen nanoclusters, where n=3, 13, and 33 and two nonstoichiometric, Zn7Se62+ and Zn13Se122+ , clusters. The largest cluster is about 1.4 nm in diameter and represents the size of a possible nanocluster formed for SERS spectroscopy. Mass spectroscopy on laser ablation of elemental zinc and sulfur show the presence of ultrastable ZnS clusters of 13, 33 or 34 monomer units 49,37. In most cases 4-Mpy ( HS-C5H4N) was considered absorbed to a Zn ion of the cluster as the :SPyr- anion through the thiol S atom, but we also examined an adsorbed state where the pyridine N atom of the molecule was bound to Zn ion. Another possibility considered is that the dimerization of 4-Mpy could take place near the surface by photooxidation

50

particularly on II/VI quantum dots 51, 52 giving 4,4´-dipyridyl (NC5H4-S-S–C5H4N) denoted as Pyr-S-S-Pyr which can be adsorbed on nanoclusters via the N atom of the pyridine. A mechanism was suggested for this process as hole transfer to a thiolate anions forming thyil radicals which couple to form the disulfide. 52, 53


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2. COMPUTATIONAL DETAILS Ground state geometry optimizations, UV-VIS excitation spectra, and static and preresonance Raman spectra in the infinite lifetime approximation were calculated with the Gaussian 09

54

and Gaussian 16 programs

55

with linear response Time-Dependent Density

Functional , TDDFT , calculations following Casida 56. We used both the hybrid exchangecorrelation functional B3LYP

57 , 58

and the long-range corrected hybrid CAM-B3LYP

59

Coulomb–attenuating functional for calculations. In the calculation of excited states, the systems were first optimized with B3LYP and excited states calculated with B3LYP and CAMB3LYP for comparison. Previously, the effect of different density functionals on various properties of Cd33Se33 has been investigated, and it was concluded that B3LYP provide reasonable values. 60 Similar to this paper, we found that CAM-B3LYP overestimated the orbital band gap energies by several eVs. For isolated 4-Mpy molecules and in cluster-4-Mpy complexes up to n=13 in ZnnSen, we used the 6-31+G(d) basis set for all elements in both the cluster and molecule.

For the case of n=33 clusters, we used the LANL2DZ relativistically

corrected effective core potential

61

basis set with augmented polarization functions, an f

function for Zn and two d functions for Se all from the 6-31G basis set. For other atoms in 4Mpy (C, H, N, S), the 6-31+G(d) basis set was always used. The Zn33Se33 was constructed from the Wurzite lattice and then optimized. The vacuum optimized geometries were calculated to the default convergence criteria of G09 or G16. Vacuum frequency calculations showed zero imaginary frequencies in all cases; however, the Normal Raman simulation of Zn33Se33-SPyr in water had one imaginary frequency. Un-scaled vibrational frequencies are reported throughout. In all cases the calculations were for either bare clusters or a cluster with a single bound molecule. In the case of the cluster-molecule complex Zn33Se33–SPyr we also optimized in


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water solvent using the conductor polarized continuum model (cpcm) in the self-consistent reaction field to check if this effected the surface structure. In order to describe hole-electron pair excited state transitions, we have used the natural transition orbital (NTO) method of Martin

62

as implemented in Gaussian. This method gives a compact representation of the

electronic transition density matrix that is brought to a diagonal form. It allows a simple qualitative description of electronic transitions in terms of a molecular orbital representation of the hole-to-electron transition. Vibrational mode assignments were made using two notations for normal modes (i) that of Gardner and Wright 63 for monosubstituted benzenes and (ii) the familiar Wilson numbers from benzene. GaussView 5.09 was used to visualize and interpret the G09 and G16 results. The dynamic polarizability calculations follow the outline of Neugebauer et al. 64 which is based on the Placzek theory with the double harmonic approximation (harmonic oscillator force field and truncation of the Taylor expansion of the polarizability with respect to a normal mode after the quadratic term). This requires numerical derivatives of the polarizability tensor components with respect to a normal coordinate. The dynamic polarizability is found at each band position by calculating the frequency-dependent polarizability. The derivatives of the frequencydependent polarizability can then be found from single-point calculations of small displacements of Cartesian coordinates from equilibrium along the normal modes. A numerical derivative is used for obtaining the dynamic polarizability derivatives. These derivatives are used to obtain the Raman activity S = (45a’p 2 + 7γ’p 2) where a’p and γ’p are the mean isotropic and anisotropic polarizability expressions in terms of the derivatives of the dynamic polarizability tensor components

(α 'ij ) p = (

∂α ij ) ∂Qp eq


(1) 9


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with respect to the pth normal mode coordinate. For 90o scattering angle and incident light which is plane polarized perpendicular to the scattering plane, relative Stokes Raman intensity can be expressed in terms of the differential scattering cross section 64

dσ π 2 h S 1 = 2 (ν L − ν p )4 2 ( ) 8π cν p 45 1 − exp(−hcν p / k BT ) dΩ ε o

(2a)

where ν L is the wavenumber of the incident beam and ν p is the wavenumber of the vibrational transition of the pth normal mode. In equation 2a, the Raman Activity S has units of (C2 m2/amu V2). Output from the Gaussian software gives S in units of Å4/amu so the equation 2a can be converted to a more convenient numerical form

(ν − ν p )4 dσ 1 = 5.8385x10 −46 L S cm2/sr (1 − exp− (0.00483ν p ) dΩ νp

(2b)

with S in Å4/amu , ν in cm-1 and T=298K. This conversion has been made by multiplying equation 2a by 16π2ε02 which converts the square polarizability in S of equation 2a into the square volume polarizability S of equation 2b and by converting amu to kg and using numerical constants in SI units. The computation of the Raman activity S using the definition of a’p and γ’p requires the calculation of the dynamic polarizability tensor components αxx, αyy, αzz , αxy , αyz , and αzx at optical frequencies as well as their derivatives with respect to normal modes. In most cases, we make relative comparisons of Raman intensities so only the values of the Raman activity S are used. However, in comparing pre-resonance Raman spectra at different excitation frequencies, we use the scattering cross-section calculated from equation 2b. In previous work

11,12

we applied the ideas of Albrecht

65

to surface enhanced Raman

spectroscopy. We assumed that the molecule was bound to the metal surface through a weak


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covalent bond, and that the molecule-metal system may be considered together for purposes of calculations. When the molecule is not coupled to the metal, charge transfer transitions between the molecule and metal are forbidden. On coupling, charge-transfer intensity is borrowed from some allowed molecular or solid transition moment µKI by the molecule-to-solid transition moment µIM through the Herzberg-Teller coupling term hMK or by the solid-to-molecule transition moment µMK through the Herzberg-Teller coupling term hIM. We then obtain analogs of the Albrecht A, B, C terms for the molecule-metal system.

ασρ = A + B + C A=

 µ SIσ µ SIρ µ SIρ µ SIσ  + ∑ ∑  〈i | k 〉〈 k | f 〉 h(ω SI + ω )  S = F , K ≠ I k  h (ω SI − ω )

B=

σ  µ IR µ IRρ hRS µ SIσ  〈i | k 〉〈 k | Qk | f 〉 hRS µ SIρ + + ∑ ∑ ∑  h(ω RI + ω )  hω RS R = F , K S = F , K k  h (ω RI − ω )

(3)

 µ ISσ hSR µ RIρ µ ISρ hSR µ RIσ  〈i | Qk | k 〉〈 k | f 〉 + ∑ ∑ ∑  h(ω RI + ω )  hω RS R = F , K S = F , K k  h (ω RI − ω ) σ ρ σ  µ IR  〈i | k 〉〈 k | Qk | f 〉 hIS µ SR µ IRρ hIS µ SR C = ∑ ∑ ∑ + +  h (ω RI + ω )  hω SI R = F , K S = F , K k  h (ω RI − ω )

σ ρ σ  µ IR  〈i | Qk | k 〉〈 k | f 〉 hIS µ SR µ IRρ hIS µ SR + ∑ ∑ ∑   h(ω RI + ω )  hω SI R = F , K S = F , K k  h (ω RI − ω )

We should emphasize that in these expressions the sums range over all excited states (R and S) which include both charge transfer states (F) and molecular states (K) {but of course exclude terms for which a denominator vanishes (such as S or R = I)}. This constitutes one of the important differences between SERS and normal Raman spectroscopy. The A term is referred to as Franck-Condon (FC) scattering and the B( C) term as Herzberg-Teller (HT) scattering.


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Our calculation of static and pre-resonance Raman spectra from the numerical derivative of the dynamic polarizability uses the linear response TDDFT approach in the Gaussian suite of programs which is a calculation in the infinite lifetime approximation. Such a calculation is analogous to the sum-over-states method of Aspuru-Guzik et al. 66 in the absence of the excited state linewidths. These authors use the frequency-dependent electronic Placzek polarizability tensor

µokm µokn µokm µokn α (ω ) = ∑ [ + ] Ω k − ω Ωk + ω k mn

(4)

and indicate that the derivative of α mn (ω ) with respect to the vibrational normal mode Q yields two terms at each excited state k > 0 corresponding to the Albrecht A and B or A and C terms in equation 3 above. Analytically, the A term results from the derivative of the denominator and the B(C) term from the derivative of the numerator of this Placzek SOS polarizability tensor. It should be noted that the pre-resonance software code uses the same assumption in the Placzek tensor that the excited states in the polarizability tensor do not contain vibrational energy states. The numerical calculation of the derivative of the dynamic polarizability with respect to the normal mode in the linear response TDDFT approach also has embedded in it the same corresponding two derivatives. We claim that for charge transfer excitations, both terms can be important near a resonance with the totally symmetric vibrations resulting from the A term and both totally symmetric and nontotally symmetric vibrations resulting from the B(C) term. AspruGuzik et al. show that the A term is proportional to the gradient of the excitation energy with respect to Q ,

∂Ω k , where Ωk is the kth excited state, while the B(C) term is proportional to the ∂Q


12

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derivative of the transition moments with respect to Q, i.e.,

∂µ . It is thus possible in the infinite ∂Q

lifetime approximation (setting γk =0) to equate the second term in the SOS approach of AspruGuzik et al. ( in their equation 3) with, say, the B term in equation 3 above for the pre-resonance case ( considering only the leading term in the expansion over excited states) where the CT excitation is S←I. With this comparison, it is seen (also see ref. 67, equation 4.9.3) that their term in

∂µ h µ is equivalent to our term in ( RS IR ) which contains the Herzberg-Teller coupling ∂Q E R − ES

coefficient hRS , the electronic transition moment µIR to the borrowing state, and the energy denominator of the coupled states R and S. In order to estimate the relative magnitudes of the A

∂Ω k ) hRS µ IR ∂Q with . 2 (Ωk − ω ) (ER − ES )(Ωk − ω )

µ IS (

and B terms, the relevant comparison is

Since the CT transition moment µIS is only weakly allowed, it should be much smaller than the strongly allowed transition moment µIR from which intensity is borrowed. Thus if Ω k − ω ≈

ER − ES , then the determining factor in the relative intensity of the A and B terms is the comparison of

∂Ω k with hRS. The vibronic theory of Albrecht shows that hRS is the expectation ∂Q

value of the derivative of the electronic-nuclear potential energy with respect to the normal mode, evaluated at the equilibrium position. Thus, both derivative terms are the ∂Q

result of a change in energy with respect to the change in the normal mode. We examine our cluster-molecule complexes with TDDFT close to a CT resonance condition in order to observe the effect on the relative intensity of normal modes of different symmetry in the spectra. A nontotally symmetric mode of comparable intensity to a totally symmetric mode shows the HT


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scattering term is active. Because a finite lifetime is not included in our application of linear response theory, the absolute values of the pre-resonance intensities will be overestimated ; however, as long as none of the intensities go off scale, the relative intensity of the modes in terms of their symmetry type should be valid.

3. RESULTS AND DISCUSSION 3.1 Structures of the monoligated Clusters. The optimized structures of the singlet complexes formed from bare ZnSe clusters with one 4-Mpy anion bound to Zn on the surface, ZnnSen-SPyr1- , are shown in Fig 1 for n=3, 6, 13, 33 and also for the nonstiochiometrric Zn7Se6SPyr+ and Zn13Se12-SPyr+ complexes. The first structure (a) is a linear chain Zn3Se3H-SPyr+ complex and is interesting because if the proton on the end Se atom is removed as a starting point for the optimization it gives ring structure (b). This is the cluster found in a previous computational studies of II/VI stoichiometric clusters39, 42. Indeed, the

cluster in the Zn13Se13-

SPyr1- complex (Fig 1e.) is very similar to the bare Zn13Se13 cluster found using the projector augmented wave method with a GGA exchange correlation energy. This closed shell bare cluster has buckled four- and six-membered rings with a central Se bound to three Zn ions on the surface at a distance of 2.51Å with a fourth surface Zn bound to the central Se at 2.64 Å. Our B3LYP calculation of the bare cluster without 4-Mpy is very similar, since the distance between the Se atoms and three surface Zn atoms is 2.53 Å structure with a fourth Zn at 2.76 Å.


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(c)

(b) (a)

(f)

(e) (d)

Figure 1: Optimized Geometry of ZnSe-4Mpy Complexes. (a) HSe3Zn3-SPyr , (b) Zn3Se3SPyr- , (c) Zn7Se6-SPyr+ , (d) Zn13Se12-SPyr+ , (e) ) Zn13Se13-SPyr- (f) Zn33Se33-SPyr- . With the 4-Mpy anion bound to the cluster, the optimized bond distance for the three Zn-Se bonds is 2.56 Å with the fourth at 2.77 Å. Thus, the full electron DFT calculation at the B3LYP/631+G(d) level for either a bare cluster or 4-Mpy-cluster complex reproduced almost exactly the same optimized structure as found with the plane-wave method. We can characterize all the structures in Figure 1 as edge-on complexes except for (Fig. 1e) Zn13Se13-SPyr1- where the Zn-SC bond angle is 95.745 degrees and pyridine ring is effectively parallel to the cluster surface (Table 1). However, in all complexes the nitrogen atom end of the pyridine ring is at least 5 Å


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away from any atom of any of the clusters. In Table I a summary of the calculated properties is given. Table 1: Geometric and Binding Properties of ZnnSem Complexes with Edge-On 4-Mpy Binding ZnnSem-SPyr

n=m=3

n=7, m=6

n=13, m=12

n=13, m=13

n=33, m=33

cyclic RZn-S (Å)

2.13

2.23, 2.52

2.33, 2.33

2.37

2.44, 2.56

>Zn-S-C (deg)

105.676

99.288

107.386

95.745

107.606

3.08

3.90

3.83

3.16

-54.07

-398.94

-216.43

-52.84

-73.73

single

bridged

bridged

On-top single bridged(?)

Eg (eV) bare 4.01 cluster Ebind (kcal/mol) Bond Type

Table I shows the bond distances for the S atom bound to surface Zn atoms and the bond type. The simple straight chain Zn3Se3H-SPyr complex is not included in Table I but has the shortest bond Zn-S bond of 2.169 Å compared to 2.313 Å for the cyclic Zn3Se3-SPyr1-. For the Zn7Se6SPyr1+ complex, the cluster has a structure with stacked four and six membered rings and shows a bond ( Fig 1c) between the S atom in 4-Mpy and a surface Zn with a bond distance of 2.23 Å . However, there is another Zn-S bond distance (which GaussView does indicate) at a slightly larger distance of 2.52 Å. This is an unsymmetrical bridging bond between the S atom and two surface Zn atoms. The Zn13Se12-SPyr+ ( Fig. 1d) clearly shows the bridging bonding, but now it is a symmetrical bridge with the same bridging bond distance of 2.332 Å for each Zn-S. Thus, in nonstoichiometric cluster when one Se atom is removed, the 4-Mpy geometry is bridging between


16

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two Zn atoms. These two Zn atoms are coordinated to other Se atoms on the cluster surface. It appears that metal rich II/VI semiconductors prefer bridged binding with thiols. 68 When the cluster is made symmetrical by adding a Se atom, the optimized geometry for the Zn13Se13-SPyr1complex now has only an on-top single bonded 4-Mpy anion. In this representative structure, all the thirteen Zn atoms are on the surface and there are three Zn ions which are tetrahedrally bonded to Se and one Zn ion bonded to three Se and the S atom of 4-Mpy. In this tetrahedral bonding of the Zn atom involving 4-Mpy, the bond distances of the three other Zn-Se bonds are 2.516 Å, 2.535 and 2.577 Å. For the other Zn atoms, there are six Zn atoms trigonally bonded with Se and three Zn atoms which bind to only two Se atoms in the cluster. The largest symmetric cluster complex Zn33Se33-SPyr1- complex (Fig. 1f) has a much more ” glassy “ cluster structure and shows 8-membered rings as-well-as 4- and 6-membered rings. This complex also shows the unsymmetrical bridging type bond between the S atom and two surface Zn atoms, with Zn-S bond distances of 2.33 Å and 2.54 Å . In contrast, optimizing the Zn33Se33-SPyr1- complex in a water environment with the cpcm reaction field gave an on-top geometry with only

one

single Zn-S bond at 2.54 Å ( Fig. S1). However, the water environment was anticipated to improve the glassy nature of the bare cluster structure in the complex but this was not found to be the case. In Table I we also have given the results for cluster-SPyr binding energies and the HOMO-LUMO energy gap , Eg, of the bare clusters in absence of 4-MPy. The energies are calculated as the reaction between the optimized cluster and the optimized 4-Mpy anion ligand _

( :SPyr ) going to the optimized cluster-SPyr complex all in vacuum. It is observed that the bridged bonded complex Zn13Se12-SPyr+ with the exact same Zn-S bond distances for each bridge has about four times (-216 kcal/mol) the binding energy of the other complexes with a single


17


Page 18 of 61

bond. Here the bond angle Zn-S-Zn is 91.14 o. This indicates 3px and 3py S orbitals binding to 4s Zn orbitals. The Zn7Se6-SPyr+ bridged bonded complex has an even higher binding energy ( 399 kcal/mol) and a significantly smaller Zn-S-Zn bond angle of 79.48o due to the asymmetry in the Zn-S bonds. The single bonded complexes have a binding energy around 53 kcal/mol for the n=3 and n=13. The binding energy for the n=33 symmetrical cluster which has a longer Zn-S bond distance is only slightly higher at around -74 kcal/mol. When this complex is optimized in a water environment only the on-top linear bonding is observed (Fig. S1); however, the type of bond may depend on the surface site from which the optimization was started. In view of the bond energy, we can conclude that the symmetrical (n=m) clusters give close to the on-top single bond. Also, for comparison, the Zn-S-C bond angle is also given in Table 1. The bang gaps which are given in Table I are for the bare clusters without the adsorbed 4Mpy. Since all the complexes are well below the ZnSe exciton Bohr radius of 3.8 nm, they are in the strong-confinement region and the HOMO-LUMO band gap is larger than the bulk value of around 2.8 eV and decreases as the nanoclusters are made larger as expected except for the Zn7Se6 nanocluster which has a bandgap around the bulk value. Considering only the symmetrical nanoclusters, there is a linear decrease with n value ( R2=0.98). We have also investigated two other possible chemical forms of 4-Mpy. One is where 4Mpy is protonated at the pyridine N atom and the other is the disulfide dimer Pyr-S-S-Pyr which can be formed by photo-oxidation. 50 Figure 2 shows the optimized structures of the two species on a Zn13Se13 cluster. The bond distance for Zn-S in the protonated form is 2.43 Å compared with the Zn-N bond distance of 2.08 Å for the dimer.


18

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(a)

(b)

Figure 2. Optimized structure of (a) Zn13Se13-SPyrH and (b) Zn13Se13-Pyr-S-SPyr both at B3LYP/6-31+G(d). Image with van der Waals radii.

The Zn-S-C bond angle is 93.173 degrees in the protonated complex which is similar to its unprotonated form ( Fig.1e) where the pyridine ring is directed parallel to cluster surface. In the dimer complex one of its pyridine rings is perpendicular and other parallel to cluster surface. The binding energy for the protonated form of complexes is -26.475 kcal/mol and that for the disulfide dimer is -30.942 kcal/mol. Both values are about one-half the single bond binding energy of the SPyr anion to a single surface Zn atom. The lower binding energy of the protonated form is most likely a consequence of charge withdrawal from the pyridine ring while the that of the dimer is mostly likely due to the lack of binding interaction of either pyridine ring with the cluster surface , in spite of the short Zn-N bond distance.

3.2 Normal (Static) Raman Spectra. We have calculated either the normal Raman spectra with DFT or the static Raman spectrum with TDDFT for all the ZnnSem-SPyr complexes in Fig.1. Figure 3 shows a comparison of static spectra for the bridged, Zn13Se12-SPyr+, complex and the on-top (single bond) , Zn13Se13-SPyr-, complex for both the phonon modes and molecular


19


Page 20 of 61

modes except for the C-H stretching vibrations above 2000 cm-1. The three strongest bands in the spectrum with the symmetrical cluster ( n=13) are at 1009 (72), 1120 (70) , and 1619 (57) cm-1 , with Raman Activity

in parentheses. In terms of Wilson numbers, these modes are the

symmetrical ring breathing 1a1 mode, the ν (S-C) and in-plane C-H deformation 18a1 , and the 8a1 ring stretch, respectively, all very typical of strong mercaptopyridine ring vibrations. In contrast, the static spectrum of Zn13Se12-SPyr- shows four strong modes at 1007 (61) , 1086 (53), 1121 (54) , and 1610 (39) cm-1. The mode at 1086 cm-1 is the 12 a1 trigonal ring breathing mode which is now relatively stronger and shifted down from its 1093 (13) cm-1 value in the spectrum of the Zn13Se13-SPyr- complex. A similar trend is observed for Zn7Se6-SPyr+ unsymmetrical complex where, however, the four strongest bands are 1009 (34), 1081(83), 1117 (23), and 1285 (23) cm-1. Here both the bands at around 1090 cm-1 and 1120 cm-1 have shifted to even lower frequencies and the band at around 1282 cm-1 has increased in relative intensity. Figure S2 compares the Normal Raman ( Static Raman) of Zn3Se3-SPyr- , Zn13Se12-SPyr+, Zn13Se13-SPyr- , and Zn33Se33-SPyr- and shows that that 1085 cm-1 band is greatly enhanced for Zn13Se12-SPyr+ compared to the other complexes. However, the Raman Activity of the 1092 cm-1 (48) band has also grown with respect to the 1125 cm-1 (110) band in Zn33Se33-SPyr- spectrum ( Fig. S2) for this surface adsorption structure which is weakly bridging. It is seen that all the bands above 400 cm-1 are un-shifted with respect to the band at 1086 cm-1 which gets slightly shifted to higher wavenumbers. In Zn3Se3-SPyr- , it is a shoulder band of the 1108 cm-1 band . In Fig.3 and Fig. S2 , the bands at 1086 and 1117 cm-1 stand out as a doublet of nearly equal intensity in the unsymmetrical cluster Zn13Se12-SPyr complex in the normal Raman Spectrum.


20

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Figure 3. Static Raman Spectra of Zn13Se12-SPyr+(blue) and Zn13Se13-SPyr-(red) at the B3LYP/6-31+G(d) level.

Table 2. Vibrational Frequencies and Normal Mode Assignments of the Normal (or Static) Raman Spectra of ZnnSem-SPyr Complexes . a) Based on ref.63

Zn7Se6-SPyr 6-31+G(d) Static (cm-1)

Zn13Se12SPyr 631+G(d) Static (cm-1) 316.6

Zn13Se13SPyr 6-31+G(d) Static (cm-1)

Zn33Se33SPyr Lanl2dz( d,f)/631+G(d)

331.9

330.8

Wilson no. and M no. a


Assignment Description This paper

ν s(Zn-S-Zn) ν (Zn-S)

21


ν as(Zn-S-Zn)

379.4 392.7

388.9

390.0

389.8

16a2 M14(a2)

421.5

415.0

423.6

17a1& 6 a1 M11(a1)

522.9

505.7

514.3

503.1

676.0

676.4

680.8

679.6

696.3

700.6

711.7

708.5

756.3

733.5

734.5

736.2

824.0

816.0

809.3

821.4

870.0

856.4

865.2

878.6

985.0

978.1

963.1

974.3

1003.2

1001.1

979.8

994.9

1009.2

1007.1

1008.5

1009.0

16b1 M19(b1) 6b2 M29(b2) 6a1 M10(a1) 4b1 M18(b1) 11b1 M17(b1) 10a2 M13(a2) 5b1 M15(b1) 17a2 M12(a2) 1a1 M9(a1)

1081.6

1086.0

1092.6

1091.9

1117.4

1116.7

1108.4

1116.6

1122.2

1121.3

1120.0

1125.9

400.7 426.1 ν (Zn-S)

Page 22 of 61

1256.4

1254.8

1249.9

1254.7

1285.9

1286.1

1282.7

1286.3

1368.8

1357.6

1353.2

1359.0

1445.2

1445.7

1446

1446.4

12a1 M8(a1) 15b2 M27(b2

18a1 M5(a1) 9a1 M7(a1) 3b2 M25(b2) 14b2 M26(b2) 19b2 M24(b2)


o.p. ring deform. wag(Zn-S-C ) ν (Zn-S) & ν (C-S) i.p. ring deform. o.p. ring deform. i.p. ring deform. i.p. ring deform. o.p. ring deform. o.p. C-H deform. o.p. C-H deform. o.p. C-H deform. o.p. C-H deform. Sym. ring breathing Trigonal ring breathing i.p. C-H deform.

ν (S-C) i.p. CH deform. i.p. C-H deform. i.p. C-H deform. i.p. C-H deform. Ring stretch

22

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1520.1

1519.5

1514.8

1521.2

1605.1(8a1)

1606.7

1576.7

1592.8

1607.6.1(8b2)

1609.9

1618.7

1619.4

19a1 M5(a1) 8b2 M23(b2 8a1 M4(a1)

Ring stretch Ring stretch Ring stretch

The frequencies and assignments of the Static or Normal Raman spectra for all the ZnnSem-4Mpy complexes in Fig 1. with n≥7 are given in Table 2. We use Wilson numbers and also the Gardner and Wright M notation

63

for the normal mode assignments in the table. The

Gardner and Wright notation is based on the normal mode diagrams for fluorobenzene in Fig 5 of ref. 63 and are given under a corresponding Wilson number. The Wilson number assignments are very close to those assigned to an experimental SERS of 4-Mpy on Ag.69 For all vibrational bands above 500 cm-1, assignments are exactly the same for all the molecular modes of the four complexes, although the bands frequencies all show slight shifts. As pointed out above, both of the complexes with an unsymmetrical cluster and bridged bonding show the shift of the trigonal ring breathing from 1092 cm-1 to lower frequencies ( by 6-10 cm-1), which might be used to identify this bridging structure. The Zn33Se33-SPyr- complex does not show this shift which is consistent with its unsymmetrical weakly Zn-S-Zn bonding motif and with its binding energy which is close to the other complexes with a single bond to the surface. Looking at frequencies of the lowest molecular modes, new bands are found for the bridging bonded species. Thus, there is a very low intensity Zn-S-Zn stretching mode for the Zn33Se33-SPyr- at 330.8 cm-1. For Zn13Se12-SPyr+ , both symmetric (316.6 cm-1) and asymmetric ( 379.4 cm-1) Zn-S-Zn stretching vibrational modes are found but they are also of low intensity. A new band at 400.7 cm-1 is observed for Zn7Se6-SPyr+ which is Zn-S-C wag and is not observed in


23


the other complexes. Also, a Zn-S stretching vibration is observed at 426.1 cm-1. This complex is also unusual in that the 8a1 and 81 ring stretching modes both near 1600 cm-1 are switched so that the higher frequency mode is the 8b1 mode. Vibrations involving Zn-S stretching are observed at around 331 cm-1 for both the Zn13Se13-SPyr- and Zn33Se33-SPyr- complexes. The NRS spectrum of

molecular structures related to the parent 4-Mpy were also

considered such as the protonated species ( Fig. 2a) and the disulfide dimer ( Fig. 2b). Upon protonation or disulfide dimerization of 4-Mpy , there are significant shifts in the normal Raman spectra (Figure 4 ) for the two species adsorbed on the symmetrical Zn13Se13 cluster.

10 9 8 7 Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 61

6 5 4 3 2 1 0 0

200

400

600

800 1000 1200 Raman Shift cm-1


1400

1600

1800

24

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Figure 4. Normal Raman Spectra of Zn13Se13-SPyrH (red) and Zn13Se13-Pyr-S-SPyr (blue) both at the B3LYP/6-31+G(d) level. (The three most intense bands in dimer spectrum were cut-off to better display the lower intensity bands.)

In the low frequency region, the cluster vibrational bands are very similar and of equal intensity for the two spectra. However, Zn13Se13-Pyr-S-SPyr dimer complex has over twice the intensity of the protonated species and has a more unique molecular spectrum of the two in that there are several very strong bands between 1000 and 1200 cm-1. In contrast, the protonated complex has about the same intensity for its strongest bands as its non-protonated form Zn13Se13-SPyr- . The protonated complex is very typical of protonated 4-Mpy spectra in that the ring breathing mode 8a1 is shifted to higher wavenumber at 1662 cm-1 and the two other strong bands are the 1a1 ring breathing mode at 1008 cm-1 and the 19a1 ring stretch at 1499 cm-1 . In comparison, the three strongest bands in the dimer complex spectrum are at 1036 cm-1, near 1100 cm-1, and 1648 cm-1. The band around 1100 cm-1 is composed of two bands at 1090 cm-1 and 1093 cm-1 and two other slightly higher bands at 1108 and 1115 cm-1. We display the assignment of all the molecular normal modes of these two complexes in Table 3. For comparison, we have included in the table the Zn13Se13-SPyr- complex and the experimental spectrum of 4-Mpy obtained from a chemically etched ZnSe surface. 16 The DFT calculated Raman Activity of all the simulated bands is given in parentheses as-well-as estimated intensities from the experimental spectrum (given in Fig. S4). It is seen that almost all the bands in the experimental spectrum have their counterpart in the calculated spectra of the complexes. Some of the Wilson number assignments originally given for this spectrum 16 which were based on the Wang and Rothberg assignments 70 do not agree with our present assignments which we now believe are more accurate. The only important difference in Table 3 are for the band at 683 cm-1 which was originally assigned to b1 symmetry ( Fig. S4) but should be 6b2. Although, the vibrations of the experimental spectrum of 4-Mpy on


25


Page 26 of 61

etched ZnSe are all found in the calculated spectra, their relative intensities are not simulated by any of the NRS spectra. The normal mode assignments for the dimer absorbed on the Zn13Se13 cluster are complicated by the two pyridine rings in the structure. We label the ring bound to the Zn atom of the cluster as rA and the other ring as rB. Modes where both rings are vibrating are noted by an asterisk. In most cases the ring motions are decoupled and then each ring shows the same normal mode separated by a few wavenumbers. In some case, the separation is larger, for example the pyridine ring mode M9(a1) or Wilson mode 1 is at 1006.7 cm-1 for the B ring and at 1036.7 cm-1 for the A ring with the latter being much stronger. Surveying table 3, it is readily seen that the b1 and a2 vibrational modes are the weakest across all the three simulated spectra. An interesting feature of the dimer

Table 3. Normal Mode Assignments and Raman Activity ( in parentheses ) from DFT simulations of three forms of 4-Mpy adsorbed a Zn13Se13 Cluster: PyrSSPyr, SPyrH, and SPyr- anion. Wilson numbers and Gardner and Wright M notations are both used except for the dimer where only the M notation is given. (a) rA is the dimer pyridine ring bound to the cluster and rB is the ring further away. An asterisk labels the modes where both rings vibrate. (b) Based on experimental spectrum Fig. S4.

Zn13Se13PyrS-S-Pyr (a) 6-31+G(d) Static

AssignZnSe (b) ments 514 nm Zn13Se13Py (cm-1) r-S-S-Pyr

Zn13Se13SPyrH 631+G(d) (cm-1)

Assignments Zn13Se13SPyrH

304

S-C wag

Zn13Se13- Assign- AssignSPyr ments ment 6Zn13Se1 Description 31+G(d) 3-SPyr This paper

331.9 (7.1) 383.2 (0.4)

391.5(5)

rB: M14(a2)

390.0 (0.2)

ν (Zn-

S)

16a2 M14(a2)

ν(SC) o.p. ring deform.

rA:


26

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M14(a2) 416.5 (3.7) 438.2 (0.3)

416.2 (1.3)

16a2 M14(a2) 6 a1 M11(a1)

415.0 (3.3)

468.2 (0.2)

16b1 M19(b1)

514.3 (0.7)

16b1 M19(b1)

o.p. ring deform.

612.85 (5.7)

N-H wag 6b2 M29(b2)

680.8 (4.7)

6b2 M29(b2)

i.p. ring deform.

648.85 (2.7) 691.42 (24.1)

4b1 M18(b1)

711.7 (8.31)

6a1 M10(a1)

i.p. ring deform.& ν (C-S)

735.43 (23.5)

6a1 M10(a1)

734.5 (1.6)

4b1 M18(b1)

o.p. ring deform.

832.1 (8.1)

11b1 M17(b1)

809.3 (0.9)

11b1 M17(b1)

o.p. C-H deform.

838.5 (6.5)

10a2 M13(a2)

865.2 (0.4)

10a2 M13(a2)

o.p. C-H deform.

949.8 (8.4)

5b1 M15(b1)

963.1 (0.1)

5b1 M15(b1)

o.p. C-H deform.

959.63 (3.2) 1011(1a1) 1008.8 (2) (86.7)

17a2 M12(a2) 1a1 M9(a1)

979.8 (0.9) 1008.5 (72.4)

17a2 M12(a2) 1a1 M9(a1)

o.p. C-H deform. Sym. ring breathing

1022(12a ) (18)

12a1 M6(a1)

1092.6 (13.)

12a1 M6(a1)

rB:ν(SSC) rA: M14(a2)

428.2 (12.2)

438.3 (3.6) 498.5* (0.2) 510.2* (1.2) 528.5 (6.3) 677.0 (3.0) 677.8 (5.3)

rA: ν(CSS) M19(b1) M18(b1) ν(S-S) rA: M29(b2) rB: M29(b2)

685(6b2) (16)

697.1 (6.2) 717.2 (1.1)

rB: M10(a1) rA: M10(a1)

729.1* (2.3) 732.9* (0.1)

998.0 (0.1)

rA: 777(4b1) M11(a1) (12) M17(b1) rB: M19(b1) rA: M19(b1) rB: M13(a2) rA: M13(a2) rB: M15(b1) rA: M15(b1) rB: M12(a2)

1006.7(42.2)

rB: M9(a1)

813.6 (0.1) 831.7 (1.4)

866.9 (0.2) 875.6 (0.2) 973.6 (.06) 984.4 (2.2)

1013.6 (1.8)

rA: M12(a2) 1036.7 (169) rA:M8 1090.2* (30.8) (a1) M8 (a1) 1092.6* (119)

1064.3 (25.4)


17a1& 6 a1 M11(a1)

ν (Zn-S) & ν (C-S)

i.p. ring deform.

Trigonal ring breathing Sym ring & C-H deform.

27


M7 (a1) 1106.3* (43.9) M6 (a1) rA:M8 1114.8* (60.2) (a1) 1121.2 (6.3)

1259.3 (9.7) 1289.1 (20.5)

1105.0 (0.1)

15b2 M27(b2)

1108.4 (3.7)

15b2 M27(b2)

i.p. C-H deform.

rB:M24(b2) rA:M24(b2)

1121(18a 1) (1)

1133.4 (14.9)

18a1 & ν (S-C) M5(a1)

1120.0 (70.4)

18a1 M5(a1)

ν (S-C) i.p. C-H deform.

rB: M7 (a1) rA: M7 (a1) rB:M25(b2) rA:M25(b2)

1211 1235(9a1) (8) 1280 (3b2) (21)

1228.5 (1.0)

9a1 M7 (a1)

1249.9 (6.8)

9a1 M7 (a1)

i.p. C-H deform.

1284.0 (4.6)

19b2 M24(b2)

1282.7 (7.5)

3b2 M25(b2)

i.p. C-H deform.

1312.0 (2.4)

15b2 M25(b2)

1353.2 (10.6)

14b2 M26(b2)

i.p. C-H deform.

1142.3 (4.4) 1256.2 (7.4)

Page 28 of 61

1303.6 (24.9) 1359.4 (3.6) 1363.0 (8.6)

rB:M26(b2) rA:M26(b2)

1445.4 (5.2) 1464.6 (2.9)

rB:M24(b2) rA:M24(b2)

1455(19b 2) (11)

1428.0 (15.2)

19b2 M24(b2)

1446 (8,1)

19b2 M24(b2)

Ring stretch

1519.3 (0.8) 1524.0 (2.7)

rB: M5(a1) rA: M5(a1)

1494(19a 1) (10)

1499.4 (40.0)

19a1 M5(a1) 3b2 M25(b2)

1514.8 (3.9)

19a1 M5(a1)

Ring stretch

8b2 N-H wag M26(b2) 8a1 M4(a1)

1576.7 (1.0)

8b2 M26(b2)

Ring stretch

1618.7 (57.8)

8a1 M4(a1)

Ring stretch

1594.1 (7.3) 1602.7 (3.3)

rA:M23(b2) rB:M23(b2)

1615.1 (36.1) 1648.8 (329)

rB: M4(a1) rA: M4(a1)

1580(8b2 ) (7) 1615 (8a1) (7) 1635 ( 3)

1522.1 (6.0) 1624.3 (26.4) 1661.9 (69.0)

and protonated cluster-complexes is that they both have two bands above 1610 cm-1 but for the dimer both bands are 8a1 symmetry, one vibrational mode from each pyridine ring, and for the protonated species the lower mode is the 8b2 mode with an N-H wag and the higher and more intense mode is 8a1, M4(a1) . Also, the stretching vibration of disulfide bond, S-S, at 528.5 cm-1 is


28

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rather weak in the static spectrum, but becomes the strongest band in the pre-RR spectrum near some excited states.

3.3 Electronic Spectra and Charge Transfer, CT, States. For the investigation of preresonance Raman spectra of various forms of 4-Mpy absorbed on a ZnSe QD cluster, we have limited our simulations to the molecules absorbed on a symmetrical Zn13Se13 and unsymmetrical Zn13Se12 clusters. For these size clusters, we can use the full electron 6-31+G(d) basis set for the entire QD cluster-molecule system. Because of the concern for the self-interaction error in charge transfer processes, excited states and TDDFT UV-Vis spectra were calculated both with B3LYP and with the long-range corrected CAM-B3LYP for comparison. The review article of Dreuw and Head-Gordon 71 makes it clear that hybrid functionals like B3LYP (which has 20% HF exchange) should do better for CT excitations than pure density functions due the partial cancelation of the electron self-interaction effect in the TDDFT A matrix term of the linear response equations of TDDFT. Indeed, several previous studies have indicated that B3LYP provides reasonable values for energy gaps and transition energies with capped quantum dots.60, 72, 73

Figure 5 shows the broadened optical spectra of Zn13Se13-SPyr- calculated with both B3LYP and CAM-B3LYP. The transition states in the B3LYP spectrum are about 1.0 eV lower than for the CAM-B3LYP spectra. Unfortunately, it is not known how accurate the CAM-B3LYP calculation is with respect to optimized long-range corrected functionals since experimental data for such a small cluster is not available. In a very recent article, it was found that optical gaps of Cd33Se33 ligated with mercaptoproprionic acid are about 0.3 eV larger with B3LYP compared with an optimized long-range corrected LC-BLYP functional!74 We can compare the nature of


29


the transitions for B3LYP with those from CAM-B3LYP. The hole-electron pair

Page 30 of 61

natural

transition orbitals ( NTOs) show 11 CT transitions, 10 mixed transitions , and 12 intercluster transitions ( IC) in the first 33 singlet excitations ( 3 eV to 4 eV) for B3LYP compared to 9 CT transitions, 6 mixed transition, 2 molecular resonance (MR) transition (solely within the bound 4Mpy anion), and 16 IC transitions ( 4 eV to 5 eV) with CAM-B3LYP. In the mixed transition both the hole and electron NTO have both cluster and molecule contributions, whereas in the IC transitions the hole and the electron NTO are nearly completely within the nanocluster. The molecular resonance transition are deep in the UV and are probably found for excited states above the first 33 states in the B3LYP excitation spectrum. In general, the nature of the transitions is similar for the two functionals. On the basis of the above cited literature for ligated QDs and because we are mainly interested in the spectral nature of pre-resonance Raman spectra of CT excitations, we have used the B3LYP functional for all our TDDFT pre-resonance Raman Studies. The molecular orbitals for the energy level diagram of Zn13Se13-SPyr- , calculated at B3LYL/6-31+G(d), shows that the HOMO level isosurface belongs to the molecule and the LUMO level belongs to the Zn13Se13 cluster. Thus, the first excited state transition is a moleculeto-cluster CT transition calculated by TDDFT at 2.785 eV with a wavefunction coefficient of 0.69877 or 97.7 %. This TDDFT optical excitation is represented by a single orbital transition and should be close to the ground state HOMO-LUMO MO energy gap. The MO energy gap is higher with a value of 3.18 eV so that the difference of about 0.4 eV represents corrections for the coulombic self-interaction and hole-electron excitonic attraction in the TDDFT treatment ( Table 4). The first CT excitation state at 2.785 eV has an oscillator strength f=0.0016 which is so weak that it doesn’t show up on the UV-VIS plot in Fig 5. The second TDDFT excitation with 0.0348 oscillator strength at 3.13 eV is a mixed CT state and is the on-set of the UV-VIS


30

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spectrum ( Fig. 5 , blue curve). The HOMO-1 is a mixed molecule-cluster MO while the HOMO2 shows a pure SC cluster isosurface with Se p atomic orbitals. Thus, we find with one 4-Mpy anion ligated on the cluster, the H-2 → L transition at

3.77eV

represents

the ligated

nanocluster ground state orbital band gap compared with the ground state HOMO-LUMO orbital gap of 3.83 eV for the bare nanocluster ( Table 4). In this case ligation lowers the orbital energy gap corresponding to the band edges. For this Zn13Se13-SPyr- complex, the HOMO of the complex is also the HOMO of the bound molecular anion and the H-1 is also from 4-Mpy anion so both these two levels are in the band gap of the ligated nanocluster orbitals ( H-2→L). Thus, these mid-gap states are hole trap states and have the proper energies for a photooxidation dimerization mechanism53 for this ZnSe nanocluster. All the unoccupied orbitals of the complex from the LUMO to the LUMO+7 are from the nanocluster alone so that the first 20 excited state transitions all involve excitation to these unoccupied orbitals of the nanocluster representing excitonic transitions. The first three CT excitations of the Zn13Se13-SPyr- complex are excited states 1, 5, and 6 (see Fig.6) . For the unsymmetrical Zn13Se12-SPyr+, the orbital energies are quite different with the first nine optical transition being mainly intercluster transitions with the HOMO level being shifted 6.3 eV down with respect to the symmetrical ligated nanocluster. This shift, off course, is due to the positive charge on the unsymmetrical cluster. Comparing the UV-VIS spectra ( Fig. S5) of the symmetrical and unsymmetrical complexes shows that Zn13Se12-SPyr+ complex is shifted to higher energy values

and has a different excitation structure. Its ground state ligated HOMO-

LUMO gap is solely due to the nanocluster with a gap of 4.145 eV. For the bare Zn13Se12 nanocluster, this MO gap is 3.90 eV which in this case is lower than the ligated nanocluster (Table 4). For the ligated cluster, the HOMO is made of atomic Se p orbitals and the LUMO is


31


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made of antibonding atomic Zn s orbitals. Because the filled levels for MOs of the 4-Mpy anion in the complex are below the HOMO-LUMO gap of the complex, a photooxidation dimerization process would not be possible for Zn13Se12-SPyr+. The first IC optical transition from TDDFT calculations is at 3.55 eV and involves mixed states with a transition from two degenerate orbitals below the HOMO ( HOMO-1 and HOMO-2) to the LUMO and LUMO+1. The second IC TDDFT optical excited state transition is a transition from the pure HOMO to pure LUMO with a 3.58 eV energy, again lower than the ground state DFT cluster orbital gap energy of 4.145 eV by about 0.5 eV. Similar results were found for capped Cd33Se33 where the lowest TDDFT transitions were 0.3-0.4 eV lower than the uncorrelated ground state HOMO-LUMO gap.60 For the unsymmetrical nanocluster, the lowest energy CT state is state 10 at 3.99 eV with f=0.0002 followed by another CT state 11 at 4.04 eV with a much higher oscillator strength (f=0.0105) ; both of these transition are of mixed CT and inter-cluster character ( see Fig.7 ). Because the overlap between the ground state and the CT states are small or in other words the overlap of the hole and electron natural transition orbitals (NTOs) are small , the oscillator strengths states are expected to be quite small for pure CT transitions. 75


32

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90000 80000 70000 60000 Epsilon

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50000 B3LYP

40000

Cam-B3LYP 30000 20000 10000 0 3

3.5

4 4.5 Photon Energy , eV

5

5.5

Figure 5. Optical Spectra of Zn13Se13-SPyr- calculated at B3LYP/6-31+G(d) level (blue) and CAM-B3LYP/6-31+G(d) level (red). Plotted with hwhm broadening of 0.030 eV.

We will also investigate the pre-resonance Raman of the dimer species Pry-S-S-Pyr adsorbed on the Zn13Se13 nanocluster giving the neutral Zn13Se13-Pry-S-S-Pyr complex ( Fig. 2b). In the previous complexes, the CT states typically have low oscillator strengths and the same is true for the dimer complex. However, in this case most of the low lying optical transitions have CT character with B3LYP/6-31+G(d). Thus, of the first 14 optical transitions between 3.1 eV to 3.8 eV on the UV-VIS spectrum ( Fig. S5) nine have mostly pure or nearly pure CT character (excited states 1, 3, 5, 6, 8, 11, 12, 13, and 14) and only one (state 10) has pure intercluster ( IC) character. The other four excitations ( 2, 4, 7, 9) are of mixed IC and CT transitions where the hole is all on the Zn13Se13 nanocluster and the electron state contains both nanocluster and dimer natural transition orbitals. Some of these mixed transitions such as states 7 through 10 are very


33


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close together, spanning only 0.06 eV. It should be pointed out that all of the hole states for these 14 states are entirely on the nanocluster part of the complex. For the pre-RR spectra, we have excited close to states 1, 5, 6, 11, 12, and 13 which are pure CT states. It is noteworthy that these CT excitations are now nanocluster-to-dimer molecule excitations ( see Fig.8) in contrast to the above previous cases where they were molecule-to-nanocluster excitations. For Zn13Se13-Pry-S-S-Pyr , the ground state HOMO isosurface is contained entirely within the nanocluster and the LUMO isosurface is all on the dimer molecule. This HOMOLUMO gap corresponds to the lowest CT transition of the complex at 3.622 eV . This is also the lowest TDDFT excited state which is a CT transition at 3.239 eV with f= 0.0015 and the NTO analysis shows this involves 98.6% CT transitions from to HOMO and HOMO-1 to the LUMO. In contrast, the LUMO+1 is a MO entirely of the nanocluster made up of Zn s orbitals. Thus, we can take the H→L+1 to represent the uncorrelated band edges with gap energy of 3.86 eV also almost exactly equal to bare nanocluster ground state gap of 3.83 eV. The corresponding TDDFT intercluster transition is state 2 at 3.26 eV with contributions of the intercluster H→L+1 and H-1→L+1 transitions. It should be pointed out that with CAM-B3LYP, the HOMO-LUMO gap is all in the nanocluster for the Zn13Se13-Pyr-S-S-Pyr complex and has a large band gap of 6.17 eV. The TDDFT calculations brings this excitation energy to 4.13 eV which again is consistent with coulombic and excitonic corrections in the linear response equations. With CAMB3LYP in the first 25 excited states , there are five pure or almost pure CT states with four mixed CT states , fourteen intercluster transitions and two molecular resonance excitations; so with this complex , CAM-B3LYP again shows less CT states compared to B3LYP. Here state 5 is the first pure CT state. The difference in excited state energies between B3LYP and CAM-


34

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B3LYP is again about 1.0 eV over the first 30 excitations. Fig. 6S shows a comparison of the UV-VIS spectra of the nanocluster-dimer complex calculated with the two density functionals. Table 4. Comparison of MO Energy Gaps with the TDDFT Transitions for Band Edges in the Nanocluster and for the First CT Transition in the Complex. The TDDFT energy in the grayed boxes is for transitions between the lowest UMO and the highest OMO of the nanocluster in the ligated complex. Complex

MO gap bare Cluster MO gap ligated Cluster 3.77 eV

TDDFT Excitation Energy ligated Cluster 3.229 eV

Zn13Se13-SPyr-

3.83 eV

3.18 eV

2.79 eV

4.15 eV

3.58 eV

Zn13Se12-SPyr+ 1st CT transition

4.55 eV

3.99 eV

Zn13Se13-Pry-S-S-Pyr 3.83 eV

3.86 eV

3.26 eV

Zn13Se13-Pry-S-S-Pyr 1st CT transition

3.62 eV

3.24 eV

Zn13Se13-SPyr1st CT transition Zn13Se12-SPyr+

3.90 eV

A summary of the difference between ground state MO gaps from the

optimized

geometry and from the TDDFT transition energies is given in Table 4. The MO energies that represents the “ band edges” ( grayed boxes in Table 4) are elucidated from MO isosurfaces of the geometry optimized energies and corresponding TDDFT transitions are elucidated from the NTO hole → NTO electron isosurfaces of the excitation spectrum.

The electron particle

isosurfaces correspond to those that are almost entirely nanocluster isosurfaces in the ligated complex. The effect of the monoligated complex on the “ band edges” compared to the bare cluster is to lower it on Zn13Se13 when the complex is an anion and to increases it on Zn13Se12 ,


35


which is a cationic complex with bridged bonding to the ligand.

Page 36 of 61

With the weakly bound

neutral dimer ligand, there is very little effect of the ligand on the “band edge” energy gap. The lowering of the CT excitation orbital gap

energies which on average is about 0.51 eV in the

TDDFT excitation calculations indicates that linear response with B3LYP (20% Hartree-Fock exchange energy) reduces the electron self-interaction problem and should include some of the attractive hole-electron stabilization of the excitonic interaction. However, this hybrid functional most likely does not give the fundamental optical gap for charge transfer , I–A-(1/R) , which is the difference between the ionization potential (I) and the electron affinity (A) with a -1/R electrostatic correction after charge-transfer. This is because B3LYP includes only a fraction of the coulombic correction which does not allow correct approximation of the -1/R potential. 76,77 This fundamental gap is most likely closer to results with CAM-B3LYP than with B3LYP; however, empirical results show that the accuracy of the hybrid functionals is system dependent.75 Since we are more interested in the effect of CT resonances on relative intensities of the calculated spectra, we use B3LYP results for selecting excitation energies and for calculation of pre-resonance Raman simulations with TDDFT. We have selected several CT excited states to excite close to by investigating the hole to electron transition with Martin’s natural transition orbitals. 62 We illustrate some of these hole-electron particle transitions in Figures 6, 7 and 8 for the three different nanoparticlemolecule complexes we used to calculate pre-RR spectra for CT states. In figure 6 we show the NTO hole-to-electron isosurfaces, calculated with B3LYP/6-31+G(d), for the first three CT excitations of Zn13Se13-SPyr-: excited state 1 , excited state 5 and excited state 6. In fact, for the 4-Mpy anion, all of the CT transitions are of the molecule-to-cluster type for

all the various

nanoclusters we have investigated. The first CT excitation for Zn13Se13-SPyr- is at 2.785 eV or


36

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445.06 nm with f=0.0016 as already mentioned and is 97.68 % accounted for by a single ground state HOMO to LUMO transition. The second CT excitation is for excited state 5 at 3.363 eV or 368.7 nm with f= 0.0219 and is 85.51 % accounted for by a single HOMO-4 to LUMO transition. The third CT state is excited state 6 and is very close to State 5 at 3.418 eV or 362.76 nm with f=0.0038. One observes from these NTOs that there is only a very small contribution from two or three Se p orbitals in the hole. In these three CT states a major contribution to the wavefunction in the hole state comes from the S py orbital of 4-Mpy. All three optical transitions are very close to pure CT transitions. The isosurface in the electron-state is made up of mainly contributions from Zn s orbitals. For the unsymmetrical nanocluster complex Zn13Se12-SPyr+, the NTOs for the first two CT states 10 and 11 are illustrated in Figure 7. Here CT state 10 at 3.893 eV is almost a pure charge transfer with a very small amount Se p orbital in the hole-state and a very weak oscillator strength of f=0.0002. In contrast to CT state 10, CT state 11 at 4.04 eV is of a mixed nature with f= 0.0105 where the hole-state has major contributions from both the molecule and the nanocluster Se p atomic orbitals. In state 10 the electron-state is pure nanocluster; whereas, in electron state 11, there is a tiny amount of density on the N atom. Finally, in Fig.8, we examine the hole-electron pair NTOs of excited CT state 6 for the Zn13Se13-Pyr-S-SPyr complex which is one of the states we probe in the pre-resonance Raman for this complex. As previously noted this transition is a nanocluster-to-molecule excitation unlike all of the cases where the thiol end of 4-Mpy is bound to the nanocluster. In this respect, it is similar to CT transitions for pyridine on Ag. This CT excited state is at 3.4805 eV with f=0.0046. It is 71.3 % a HOMO-4 →LUMO orbital transition. The electron isoform density is on ring A of the dimer and has a contribution from the S-S disulfide bond p orbitals (Fig. 8) which is


37


Page 38 of 61

the case for almost all the CT transitions we studied with pre-RR for this complex. A holeelectron NTO pair CT state with almost the exact same features is found with the rangeseparated CAM-B3LYP/6-31+G(d) as shown in S7. However, in this case it is at 4.91 eV or 1.33eV higher than with B3LYP/6-31+G(d) .

Hole State 1

Electron State 1

Hole State 5 Electron State 5

Hole State 6

Electron State 6


38

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Figure 6. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se13SPyr- for the first three CT States. State1 (2.785 eV or 445.06 nm, f=0.0016 ) and State 5 (3.363 eV or 368.70 nm, f= 0.0219) and State 6 (3.418 eV or 362.70 nm, f=0.0038)

Hole State 10

Electron State 10

Hole State 11

Electron State 11

Figure 7. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se12SPyr+ with pure CT State 10 (3.990 eV or 310.79 nm, f=0.0002 ) and mixed CT State 11 (4.038 eV or 307.02 nm, f= 0.0105) .


39


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Electron State 6

Hole State 6

Figure 8. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se13Pyr-S-SPyr CT State 6 (3.481 eV or 356.6723 nm ) Calculated with B3LYP/631+G(d).

3.4 Pre-Resonance Raman scattering Spectra.

We first investigate the pre-resonance

Raman of the Zn13Se13-SPyr- for CT states 1 and 5. The pre-RR spectra for CT state 1 at 445 nm was excited at 500 nm , 447 nm, 446 nm , 444 nm, and 443 nm. At 500 nm the excitation frequency is 2472 cm-1 below the resonance and the Raman spectrum is identical to the static spectrum but about twice as intense. At 447 nm it is 98 cm-1 below the resonance at 445 nm or 22,469 cm-1 ( 2.785 eV). This is quite close to the resonance energy but with the small oscillator strength f= 0.0016 the spectrum is far from being off-scale having a maximum Raman Activity of 2.83 x105 Å4/amu.

Figure 9 shows this spectrum and we have labeled most of the peaks.

Compared to the static spectrum ( Fig. 3 red spectrum), there is a completely different set


40

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18000

1619 16000 14000 Relative intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12000

415

10000 8000

332 274

6000

1092 4000 2000

514

1514 712 865 1120 1009 1250

0 -200

300

800 Raman Shift cm-1

1300

1800

Figure 9. Pre-resonance Raman Spectrum of Zn13Se13-SPyr- Excited at 477 nm ( 22,371.3 cm-1) of relative Raman intensities in the spectrum. First of all, the low frequency molecular bands at 332 cm-1 and 415 cm-1 which involve a Zn-S stretching vibration ( Table 3) are greatly enhanced by over 104. Also, a band at 273.5 cm-1 which was not assigned previously is greatly enhanced and is a Zn-S-C stretching vibration with an associated

wag of the entire pyridine ring and

concurrent stretching of a Se-Zn bond in the cluster attached to the Zn which binds the ligand. Furthermore, the strongest band in the static spectra at 1009 cm-1, the 1a1 symmetrical ring stretch, has been greatly reduced. Now the symmetrical ring stretch 8a1 at 1619 cm-1 is the strongest band in the spectrum. Most interestingly, the forbidden a2 modes at 390 cm-1 (16a2) and 865 cm-1 (10 a2) have considerable relative intensity and are the most enhanced bands in the spectrum. This enhancement of forbidden modes shows that a Herzberg-Teller intensity borrowing mechanism is involved for these bands. A very similar spectrum is found on exciting with light of 446 nm which is 47 cm-1 below the resonance at 445 nm. We can compare the differential cross-sections


41


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of the intense 8a1 mode at 1619 cm for the NRS (2.83 x10-30 cm2/sr ) with those excited at 500 nm, 447 nm, 446nm, 444 nm and 443 nm which are, 6.53 x10-30, 1.90 x10-26, 3.56 x10-25 , 2.21 x10-25, 1.64 x10-26 cm2/sr, respectively. The resonance is at 445 nm and the pre-resonance crosssection on either side at 444 nm and 446 nm is enhanced by about 105 over the static Raman intensity for this mode in the infinite-life time approximation. We can quantify the enhancements by analyzing what we have called

47, 48

the CT

integrated enhancement factor EFm which is the sum of the Raman Activity , Si , of the preresonance spectrum of the complex over all the bands from i to n of a given symmetry type m

∑in S ZnSeSpyr(447) i EFm = ∑in S ZnSeSpyr(static) i

(5)

divided by the analogous sum for the static spectrum of the complex. Here m= a2, a1, b1, b2 for C2v symmetry of the 4-Mpy anion. From the data in Table 5 we calculate EFa2 = 2.8 x104, EFb1 = 3.9 x103, EFa1 = 3.3 x103, EFb2 = 0.9 x102 for excitation of

Zn13Se13-SPyr- at 447 nm. This

gives the order of the CT EFs as a2>>b1≈a1>>b2. The enhancement factors for individual modes are given in Table 5 and we see that the a1 at 1619 cm-1 is enhanced by a factor of around 10 over the a1 mode at 1009 cm-1. Also, the a2 mode at 390 cm-1 has the highest enhancement in the spectrum. Table 5. CT Enhancement Factors for Zn13Se13-SPyr- from Raman Activities for Pre-resonance Spectrum excited at 447 nm. Zn13Se13-SPyr 6-31+G(d) (cm-1)

Raman Activity, S Static

Raman Activity, S Excited 447 nm

Wilson no. & Symmetry

CT Enhancement Factor

331.9 390.0

7.13 0.175

121,600 20,710

ν (Zn-S)

1.70x104 1.18 x105

(16a2)


42

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415.0 514.3 680.8 711.7 734.5 809.3 865.2 963.1 979.8 1008.5 1092.6 1108.4 1120.0 1249.9 1282.7 1353.2 1446 1514.8 1576.7 1618.7

3.27 0.73 4.66 8.30 1.63 0.890 0.390 0.058 0.855 72.4 13.2 3.65 70.4 6.79 7.49 10.6 8.10 3.92 0.99 57.83

142,631 9731 84.5 22,822 1406 378 18,965 1529 526 14,290 61,005 336 15330 5664 361 227 303 20,031 1349 283,291

(6a1) (16b1) (6b2) (6a1) (4b1) (11b1) (10a2) (5b1) (17a2) (1a1) (12a1) (15b2) (18a1) (9a1) (3b2) (14b2) (19b2) (19a1) (8b2) (8a1)

4.36x104 1.33x 104 18.1 2.75x 104 863 425 4.83x 104 2.63x 104 616 1.99x103 4.62x 103 92 218 834 48 21 37 5.11x103 1.36x 103 4.91x 104

A spectrum with very similar features is also calculated on exciting at 364 nm which is in between the two CT resonance states 5 ( 368.7 nm) and 362.7 nm shown in Figure 6. Since the hole NTOs are very similar for states 1, 5, and 6, it might be expected that relative intensities are similar. However, in contrast to the very low oscillator strength of CT state1( f=0.0002) , CT state 5 has a much larger value of oscillator strength (f=0.0219); thus, this pre-RR spectrum of Zn13Se13-SPyr- is much more intense. Below, we compare the spectrum at 364 nm for Zn13Se13SPyr- with the pre- resonance Raman spectrum of Zn13Se12-SPyr+ . For the unsymmetrical Zn13Se12-SPyr+ complex, we excited at three frequencies at 309 nm, 306 nm and 305 nm around state 10 at 310.79 nm (f=0.0002) and state 11 at 307.02 nm f=0.0105), see NTOs in Fig. 7. Figure 10 A shows the spectra excited at these three frequencies. The excitation at 309 nm is 186.4 cm-1 on the high energy side of state 10, the excitation at 306nm


43


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is 108.3 cm-1 on the high side of state 11, and the excitation at 305nm is 215.7 cm-1 on the high side of this state.

A


44

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400000 350000

B 300000 Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


250000 200000 150000 100000 50000 0 0

500

1000

1500

2000

Raman Shift cm-1

Figure 10. A. Pre-resonance Raman Spectra of Zn13Se12-SPyr+ excited at 309 nm ( 32,362.5 cm-1) blue (x10), at 306 nm ( 32,679.5 cm-1) red, and at 305 nm (32,786.9 cm-1) green. B. Comparison of pre-resonance Raman Spectra of Zn13Se12-SPyr+ excited at 306 nm (red) and Zn13Se13-SPyr- excited at 364 nm (blue). Because of the very low oscillator strength of state 10 the intensities have been multiplied by a factor of 10 for the excitation at 309 nm ( blue spectrum Fig. 10 A) to compare with the spectra excited at 306 nm and 305 nm. The spectrum ( red) at 306 nm which is closest to state 11 has the highest relative intensity and has some distinguishing features. Here the strongest band in the spectrum is the 6a mode at 700.6 cm-1 an in-plane pyridine stretch with a strong component of the C-S stretching vibration in the bridging bond. Also, the band at 1086 cm-1 which appears in the other spectra in Fig. 10A is almost gone with the 18a mode at 1121.3 cm-1 predominating. We observed that in the static spectrum ( Fig. 3 blue), a similar mode at 1086 cm-1 was relatively


45


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strong as it is in the spectra at 309 nm ( blue) and 305 nm ( green) in Fig. 10A. In these two spectra the 1007 cm-1 is the strongest band in the spectrum. In contrast, in the red spectrum excited at 306 nm, the order of the five strongest bands are 700.6, 1609.9 , 1121.3, 1007.1 and 421.4 cm-1 , respectively. These are all a1 vibrations and three of them, with the exception of the 1007 cm-1, contain a sizable component of the C-S stretch in the bridged bonding site. In Figure 10B , we compare Zn13Se12-SPyr+ excited at 306 nm ( red spectrum ) with Zn13Se13-SPyr- excited at 364 nm ( blue spectrum). The spectrum excited at 364 nm is 299.7 cm-1 from state 5 (f=0.0219) and 94.8 cm-1 from state 6 ( f=0.0038) for the Zn13Se13-SPyr- complex. As expected, this spectrum is relatively weak with respect to the Zn13Se12-SPyr+ spectrum excited at 306 nm which is 108.3 8 cm-1 from its closest state with f= 0.0105. Comparison of their differential Raman cross-sections shows that excitation at 306 nm (32679.5 cm-1) has a cross-section of 1.39 x10-24 cm2/sr compared with 2.01 x10-25 cm2/sr for excitation of the other complex at 364 nm (27471.6 cm-1). The Zn13Se13-SPyr- complex is easily distinguished from the

Zn13Se12-SPyr+

complex since the order of relative intensities for the Zn13Se13-SPyr- complex for the four strongest molecular bands are 1648.7, 415.0, 331.8, and 1092.6 cm-1 , respectively. Again, three of these bands at 1648.7, 415.0 and 1092.6 cm-1 contain a sizable component of the C-S stretching vibration while the other band at 331.8 cm-1 is mainly a S-Zn stretching vibration. From figure 10 spectra it is observed as expected that relative intensities between spectra depend on how close the excitations are to resonance, the oscillator strength of the excited states, as-well-as the nature of the surface bonding. It would appear that the pre-resonance Raman of the Zn13Se13-SPyr- complex is closer to the typical experimental Raman spectra of 4-Mpy on semiconductor surfaces such as ZnS, ZnO, CdTe and ZnS where modes around 1600 cm-1 and 1120 cm-1 are particularly strong. This may indicate that these surfaces are chalcogen rich.


46

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Finally, we consider the pre-resonance Raman spectra for the dimer Pyr-S-S-Pry ( Fig. 2b) which is a putative species which could be

formed by photo-oxidation of

4-Mpy on

semiconductor surfaces.51, 52 On Au 78 and Ag 79 surfaces the disulfide bond of the dimer appears to be broken and only the SERS spectrum of 4-Mpy is observed. However, under certain conditions, STM shows that the dimer adsorbs on Au(III) with a trans-CSSC skeleton with the pyridine rings parallel to the surface. 80 On our Zn13Se13 nanocluster, we assume the molecule binds on-top through the N atom of one pyridine ring. We have used excitations near seven pure CT states all with low oscillator strengths, Table 6. The first excited state is a pure CT state S1 at 3.239 eV or 26126.0 cm-1 with the next pure CT state S5 at 3.3602 eV or 27101.7 cm-1 and this is separated by 970 cm-1 from a third pure CT state S6 at 3.4805 eV or 28071.8 cm-1 The NTO hole-to-electron molecular orbital isoform for this transition is

shown in Fig. 8. We also

examined other pure CT states S11, S12, and S13 which span 987 cm-1, Table 6. We first compare exciting at 200 cm-1 below S1, f=0.0015, ( red spectrum) with exciting at 139 cm-1 below S6, f=0.0046, (blue spectrum) in Figure 11A. The exact same bands in the pre-resonance Raman spectra are found in both spectra. Figure 11A shows there are

four

strong bands in the spectra which are all of a1 symmetry and are calculated with the following order of relative intensity at 1648.8 M4(a1) , 1259.3 M7 (a1), 1036.7 M8 (a1), and 1092.6 cm-1 M7 (a1) with the Gardner and Wright symmetry assignments ( Table 3). The Raman activity of the blue spectrum at 139 cm-1 below S6 is about 3.5 x 103 times more intense than the static spectrum of the Zn13Se13Pyr-S-SPyr complex and about 8 times more intense than the spectra at 295 cm-1 below S6 which has identical bands. The spectrum at 139 cm-1 below S6 is about four times more intense than the spectra at 200 cm-1 below S1. These differences in the latter are reflected in the oscillator strengths of State 1 ( f=0.0015) and state 6 (f=0.0046). These pre-resonance


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Raman spectra are typical of Franck-Condon resonance Raman scattering with totally symmetric modes dominating. Nevertheless, an important feature of the spectra is that the normal mode M7 (a1) 1259.3 cm-1 is the second strongest band in these spectra in comparison with the static spectrum where it is a very weak band. The band at 1648.7 cm-1 is the strongest band in both the static and pre-RR spectra. A completely different pre-resonance Raman spectrum is found if we excite close to CT state 11. This excitation at 29453.1 cm-1 is 100 cm-1 above S11 and 501 cm-1 below S12. A very similar spectrum is found if we excite at 30440.0 cm-1 which is 49.9 cm-1 below CT state 13. The strongest band by far in these spectra is the stretching mode ν(S-S) at 528.5 cm-1 which has a Raman Activity of 2.84 x 106 near S11 and 2.94 x 106 near S13. This band has a Raman Activity of 6.6 in the static spectrum of the dimer giving a SERS enhancement factor of 5 x105 for this band on the Zn13Se13 nanocluster. For clarity we only illustrate the spectrum at 100 cm-1 above S11 in Fig.11B. The next strongest mode in this spectrum is still the 1648.7 M4(a1) with Raman Activity 5.2 x105. Other strong totally symmetric modes are 1092.6 cm-1 M17(a1) and 1036.7 cm-1 rA: M9(a1); however, there is also one strong non-totally symmetric modes at 1594 cm-1 rA:M23(b2) and several other weaker non-totally symmetric modes at 1603 cm-1 rB:M23(b2), 1446 rB:M24(b2), 1142 rA:M24(b2), and 876 rA: M13(a2), as-well-as the rA: ν(C-S-S) stretching mode at 438.3 cm-1. These results indicate that very close to resonance at S11 the B type Albrecht term becomes significant. This is reasonable because there is strong inter-cluster (IC) transition at state 10 with oscillator strength f=0.0325 from which intensity borrowing can occur. Table 6. Excited State Energy and Excitation Energy for Pre-resonance Raman Spectra of Zn13Se13Pyr-S-SPyr


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Excited State

Oscillator Strength

State Energy (cm-1)

Excitation Energies (cm-1)

CT S13 CT S12 “ CT S11 IC S10 CT S6 “ “ “ “ CT S5 CT S1

0.0003 0.0004 “ 0.0003 0.0325 0.0046 “ “ “ “ 0.0054 0.0015

30489.9 29954.5 29954.5 29353.1 28567.3 28071.8 28071.8 28071.8 28071.8 28071.8 27101.7 26126.0

30440.0 29845.9 29453.1 29453.1

Difference Energy(cm-1) Col. 3 –Col. 4 49.9 109 501 -100

28121.8 28021.4 28011.2 27932.8 27776.7 27202.0 25926.0

-50.0 50.4 60.6 139 295 -100 200


49


80000

A

70000

Relative Raman Intensity

60000

50000

40000 27932.5 25926

30000

20000

10000

0 -200

300

800 1300 Raman Shift cm-1

1800

50000

528

45000 Relative Raman Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 50 of 61

B

40000 35000

1648 1093

30000 25000

1603 1594

20000

29453

1036

15000 10000

438 876

5000

1142

1464

0 0

200

400

600 800 1000 1200 1400 1600 1800 Raman Shift cm-1

Figure 11. Pre-resonance Raman Spectra of Zn13Se13Pyr-S-SPyr excited at different energies. A. The red spectrum is excited at 25926 cm-1 or 200 cm-1 below S1 (26126.0 cm-1 ) and Light Blue spectrum is excited at 27932.5 cm-1 or 139 cm-1 below S6 (28071.8 cm-1) B. Dark blue spectrum excited at 29453 cm-1 or 200 cm-1 above S11.


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4. CONCLUSIONS Our study with DFT and TDDFT calculations of several ZnnSem nanocluster structures ligated with a single molecule of 4-Mpy on the surface has shown that the optimized geometries show variable surface structure and correspondingly different Raman spectra depending on whether the nanocluster is symmetrical or unsymmetrical. This fact is the result of two types of ligand binding geometries- (i) a Zn-S single bond between the thiol end of the 4-Mpy molecule and one Zn surface atom and (ii) a bridging bond between the thiol end of the molecule and two Zn surface atoms. For the unsymmetrical ZnnSem nanoclusters with n=7 or 13 and m=n-1, the bridge type bond is formed. In contrast, with the symmetrical cluster with n=m=13, a single Zn-S bond is found, and for the symmetrical cluster with n=m=33, a similar Zn-S single bond is also observed for the calculation with a cpcm reaction field in water. In vacuum the Zn33Se33 cluster shows a bridging second Zn-S bond with a longer bond distance ; however, its binding energy is about one-fourth lower than that of the symmetrical bridging bond in Zn13Se12-4Mpy. These results suggest that the symmetrical ZnSe nanoclusters will show single bonds with thiolates; whereas, the nonsymmetrical ZnSe nanoclusters which are metal rich (Se vacancies) will lead to bridging bonds with thiols. Similar stable surface geometries with either a single-bond or a bridging bond have also been recently found with DFT calculations for a variety of thiols bound to a Cd16Se13 cluster 81. Our results also show that the single surface bond geometry with the 4-Mpy anion lowers the nanocluster band gap with respect to the bare cluster . The simulated Raman spectra display characteristic band intensities which depend on the surface binding geometry of 4-Mpy. For the bridging ligand binding to the Zn13Se12 cluster, the static Raman spectrum shows a strong 12a1 band shifted to lower wavenumbers at 1085 cm-1 compared to this band at 1092 cm-1 with symmetrical clusters and an increased intensity of this


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mode compared to the mode at 1121 cm-1 . In the pre-resonance CT Raman spectra of this complex, this band also appears in some excitations energies but a much more characteristic band is the 6a1 band at 701 cm-1 which is now the strongest band in the spectrum. These spectra all show strong a1 normal modes which are characteristic of Franck-Condon scattering. For 4-Mpy ligated with a single Zn-S bond in the symmetrical Zn13Se13 nanocluster, the pre-RR spectra of the lowest CT excited state show the highest enhancements for the non-totally symmetric normal modes and is characteristic of Herzberg-Teller scattering. We ascribe this change from Franck-Condon to Herzberg-Teller scattering mechanism to increased vibronic coupling in the single Zn-S bond structure compared to the bridging structure. A similar change in surface bonding with thiols results in higher nonadiabatic non-radiant relaxation rates.

81

As discussed in the Computational

Details section, this shift in scattering mechanism can be attributed to a larger Herzberg-Teller vibronic coupling constant , hRS , compared to the excited state potential energy derivative with respect to normal mode,

∂Ω k . ∂Q

For the weakly bonded dimer on the Zn13Se13 nanocluster which binds through its pyridine N atom, the band gap of the neutral complex corresponding to the band edges of the cluster is very close to that of the bare Zn13Se13 nanocluster. For the strongly bound thiolate end of 4-Mpy in either the single bond or bridged bond, the MO energy values are all shifted up towards the vacuum by 2 to 4 eV. In the case of the dimer complex, the HOMO of the complex is very close to the HOMO of the bare nanocluster and the LUMO of the complex is the LUMO of the dimer molecule. Here the CT excitations are from the

nanocluster-to-molecule as opposed to

molecule-to-

nanocluster transitions for the complexes with the sulfur bonding to the surface. For the preresonance Raman spectrum of the dimer complex excited near the first CT state, the scattering mechanism is dominated by totally symmetric modes which again is characteristic of a Franck-


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Condon scattering mechanism. However exciting into several higher CT excited states yields a unique spectrum dominated by the S-S vibration but which also displays large enhancements of the non-totally symmetric modes again indicating a Herzberg-Teller scattering mechanism. These TDDFT results for the three complexes show that the excited state manifolds contain many charge transfer states which give very different pre-RR spectral signatures depending on the surface geometry and on which of the CT states is probed in the pre-RR simulation. Both B3LYP and CAM-B3LYP show many excited CT states for each of the cluster-thiol systems; however, there are less CT states with CAM-B3LYP and they are about 1eV higher in energy. Also, comparison of the Natural Transition Orbital Hole-Electron pair isoforms shows similar NTOs for CT particle pairs for both the B3LYP and CAM-B3LYP functionals suggesting that for pre-RR studies the B3LYP functional is adequate. Then again, the true fundamental energy level values for CT states may be not be correctly simulated for these model nanocluster-molecule systems by either functional, and it would be beneficial if newer optimized range-separated hybrid functionals were used to obtain the CT excited states.82 In terms of the comparison of simulated Raman spectra with experimental spectra of 4-Mpy on II/VI chalcogens, the simulated spectra of single bonded Zn-S for the symmetrical clusters best fits the experimental spectra of 4-Mpy on CdS, ZnS, CdTe, ZnO, and CuO. None of our simulations were at all similar to the SERS spectra of 4-Mpy on PbS, ZnSe, and MoS2. The reason for this fact is still not obvious. There seems to be little disagreement in the literature that the large experimental enhancement factors for 4-Mpy on nanoparticles semiconductor surfaces comes from the chemical type enhancement of CT resonance Raman. For these systems the CT excited states will involve either molecule-to-conductance band or valence band-to-molecule transitions as we have observed with our model ZnSe-4-Mpy complexes. The CT enhancement factors for the Zn13Se13-4-Mpy


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complex (pre-RR complex intensity/static Raman complex intensity) are of the order of 1x104 to 5x104 for the strongest individual bands in the spectra which are commensurate with experimentally determined enhancement factors. However, a theoretical treatment which includes a finite lifetime would tend to lower these values. In contrast, experimental enhancement factors are calculated using the nonadsorbed molecule which will make them larger than the ratios we have calculated. Also, the experimental SERS spectra on semiconductor surfaces could have other enhancement mechanisms such as a plasmon resonance effect from bound electrons in the valence band which would give an additional factor to the enhancement.16 In conclusion, our results indicate that it is possible to account for the intense SERS spectra observed for 4-Mpy on semiconductor nanoparticles by a resonance Raman scattering process involving charge-transfer excitations.

Associated Content Supporting Information Optimized geometry for Zn33Se33-4-Mpy calculated with cpcm reaction field in water. Normal Raman spectra of 4-Mpy on four different ZnnSem nanoclusters. Normal Raman spectra of Zn33Se33-4-Mpy in vacuum and in water. Experimental spectrum of 4-Mpy power and 4-Mpy adsorbed on an etched ZnSe surface. Comparison of the UV-VIS spectrum of Zn13Se13SPyr, Zn13Se12SPyr+, and Zn13Se13Pyr-S-S-Py. Comparison of the UV-VIS spectrum of Zn13Se13Pyr-SS-Py calculated with B3LYP and CAM-B3LYP. Natural Transitions Orbital (NTO) hole-toelectron Excitation for the Zn13Se13Pyr-S-SPyr calculated with CAM-B3LYP.

Acknowledgement The authors thank Prof. Edward Hohenstein of our Department for many helpful discussions. This work was supported by National Science Foundation, grant No. CHE-1402750, and by a grant from the City University of New York PSC-CUNY Faculty Research Award Program Grant No.


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42205. Computer facilities for this research was supported by a XSEDE Grant CHE090043 and by

the CUNY High Performance Computer Center. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. This work was also partially supported by NSF grant HRD-1547830 (IDEALS CREST)

Figure Captions Figure 1. Optimized Geometry of ZnSe-4Mpy Complexes. (a) HSe3Zn3-SPyr , (b) Zn3Se3-SPyr- , (c) Zn7Se6-SPyr+ , (d) Zn13Se12-SPyr+ , (e) ) Zn13Se13-SPyr- (f) Zn33Se33-SPyr- . Figure 2. Optimized structure of (a) Zn13Se13-SPyrH and (b) Zn13Se13-Pyr-S-SPyr both at B3LYP/6-31+G(d). Image with van der Waals radii. Figure 3. Static Raman Spectra of Zn13Se12-SPyr+(blue) and Zn13Se13-SPyr-(red) at the B3LYP/6-31+G(d) level. Figure 4. Normal Raman Spectra of Zn13Se13-SPyrH (red) and Zn13Se13-Pyr-S-SPyr (blue) both at the B3LYP/6-31+G(d) level. (The three most intense bands in dimer spectrum were cut-off to better display the lower intensity bands.) Figure 5. Optical Spectra of Zn13Se13-SPyr- calculated at B3LYP/6-31+G(d) level (blue) and CAM-B3LYP/6-31+G(d) level (red). Plotted with hwhm broadening of 0.030 eV. Figure 6. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se13-SPyrfor the first three CT States. State1 (2.785 eV or 445.06 nm, f=0.0016 ) and State 5 (3.363 eV or 368.70 nm, f= 0.0219) and State 6 (3.418 eV or 362.70 nm, f=0.0038) Figure 7. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se12-SPyr+ with pure CT State 10 (3.990 eV or 310.79 nm, f=0.0002 ) and mixed CT State 11 (4.038 eV or 307.02 nm, f= 0.0105) . Figure 8. Natural Transitions Orbital (NTO) Hole to Electron Excitations for the Zn13Se13Pyr-SSPyr CT State 6 (3.481 eV or 356.6723 nm ) Calculated with B3LYP/6-31+G(d). Figure 9. Pre-resonance Raman Spectrum of Zn13Se13-SPyr- Excited at 477 nm ( 22,371.3 cm-1)


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Figure 10. A. Pre-resonance Raman Spectra of Zn13Se12-SPyr+ excited at 309 nm ( 32,362.5 cm-1) blue (x10), at 306 nm ( 32,679.5 cm-1) red, and at 305 nm (32,786.9 cm-1) green. B. Comparison of pre-resonance Raman Spectra of Zn13Se12-SPyr+ excited at 306 nm (red) and Zn13Se13-SPyrexcited at 364 nm (blue). Figure 11. Pre-resonance Raman Spectra of Zn13Se13Pyr-S-SPyr excited at different energies. A. The red spectrum is excited at 25926 cm-1 or 200 cm-1 below S1 (26126.0 cm-1 ) and Light Blue spectrum is excited at 27932.5 cm-1 or 139 cm-1 below S6 (28071.8 cm-1) B. Dark blue spectrum excited at 29453 cm-1 or 200 cm-1 above S11.


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TDDFT Study of Charge-Transfer Raman Spectra of 4

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