TDDFT Study of Charge-Transfer Raman Spectra of 4

Article Cite This: J. Phys. Chem. C 2018, 122, 4908−4927

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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*,†,‡ and John R. Lombardi†,‡ †

Department of Chemistry and Biochemistry, The City College of the City University of New York, New York, New York 10031, United States ‡ Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, United States S Supporting Information *

ABSTRACT: We have used DFT and TDDFT calculations mostly at the B3LYP/631+G(d) level to investigate the optimized geometry and the normal (static) Raman and preresonance 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 nanoclusters 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 related to the type of surface bond formed.

1. INTRODUCTION The phenomenon of surface enhanced Raman scattering1−4 (SERS), first discovered in 19745 and elucidated by Jeanmaire and Van Duyne6,7 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.8−10 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 scattering11−13 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− © 2018 American Chemical Society

nanoparticle−molecule 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 explain single-molecule enhancements of 1014. Furthermore, then there are unique Herzberg−Teller surface selection rules that are not the same as the electromagnetic, EM, surface selection rules derived from the SPR alone.11−13 However, Raman scattering from molecules on semiconductors from a resonant energy-transfer process involving excitons was considered theoretically by Ueba14 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 Received: December 16, 2017 Revised: January 23, 2018 Published: January 25, 2018 4908

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C excitons, as suggested originally by Ueba,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 that generates nearfield 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 NiO.18 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 surfaceenhanced Raman scattering. Several applications of SERS on semiconductors (SC-SERS) have been recently discussed in timely review articles20,21 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 CdS,22 ZnS23 ZnSe,16 ZnO,24−26 CuO,27 CdTe,28 TiO229,30 PbS,31 MoS2,32 and αFe2O3.33 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 solid or solution 4-Mpy, but the relative intensity of these bands varies in two distinct ways. 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 that 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 nanoparticles29,30 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 non-normal SERS where three bands near 685, 778, and 1281 cm−1 distinguish these spectra on PbS (682, 780, 1278 cm−1), ZnSe (685, 778, 1281 cm−1), and MoS2 (685, 778, 1281, 1577 cm−1). In these non-normal 4-Mpy SERS spectra, the two lowest bands at around 685 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 “non-normal” SC-SERS spectra of 4Mpy. 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 2-fold; (i) it had shown the nonnormal SERS spectrum of 4-Mpy experimentally,16 and (ii) for the small 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 greenblue-ultraviolet based photonic devices.36 The structural, electronic, and optical properties of ZnSe QDs have been well investigated both experimentally and theoretically.37,38 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 to 9. 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 four- and six-membered rings. Subsequent theoretical studies with B3LYP for stoichiometric ZnnSen clusters with B3LYP from n = 1− to 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 out37 that ZnSe clusters of 13 and 33 or 34 monomeric units are ultrastable 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 study has been to use DFT 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 that 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 = 1047 and n = 13.48 In the present paper, we also examine both normal Raman scattering (NRS) and preresonance Raman scattering (pre-RRS) from chargetransfer 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 4909

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C

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 frequency-dependent 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 = (45ap′ 2 + 7γp′ 2), where ap′ and γp′ are the mean isotropic and anisotropic polarizability expressions in terms of the derivatives of the dynamic polarizability tensor components

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 photooxidation50 particularly on II/VI quantum dots51,52 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 that couple to form the disulfide.52,53

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 0954 and Gaussian 16 programs55 with linear response time-dependent density Functional, TDDFT, calculations following Casida.56 We used both the hybrid exchange− correlation functional B3LYP57,58 and the long-range corrected hybrid CAM-B3LYP59 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 CAM-B3LYP for comparison. Previously, the effect of different density functionals on various properties of Cd33Se33 was investigated, and it was concluded that B3LYP provide reasonable values.60 Similarly to this paper, we found that CAM-B3LYP overestimated the orbital band gap energies by several electronvolts. 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 potential61 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 4-Mpy (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. Unscaled 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 water solvent using the conductor polarized continuum model (cpcm) in the self-consistent reaction field to check if this effected the surface structure. To describe hole− electron pair excited state transitions, we have used the natural transition orbital (NTO) method of Martin62 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 Wright63 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

⎛ ∂α ⎞ ij ⎟ (αij′)p = ⎜⎜ ⎟ ∂ Q ⎝ p ⎠eq

(1)

with respect to the pth normal mode coordinate. For 90° scattering angle and incident light that is plane polarized perpendicular to the scattering plane, relative Stokes Raman intensity can be expressed in terms of the differential scattering cross section64 π2 dσ h ⎛S ⎞ 1 = 2 (νL̅ − νp̅ )4 2 ⎜ ⎟ dΩ ε0 8π cνp̅ ⎝ 45 ⎠ 1 − exp( −hcνp̅ /kBT ) (2a)

where νL̅ is the wavenumber of the incident beam and νp̅ is the wavenumber of the vibrational transition of the pth normal mode. In eq 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 eq 2a can be converted to a more convenient numerical form (νL̅ − νp̅ )4 dσ 1 S cm 2/sr = 5.8385 × 10−46 dΩ (1 − exp − (0.00483νp̅ ) νp̅ (2b)

with S in Å4/amu, ν̅ in cm−1, and T = 298 K. This conversion has been made by multiplying eq 2a by 16π2ε02, which converts the square polarizability in S of eq 2a into the square volume polarizability S of eq 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 preresonance Raman spectra at different excitation frequencies, we use the scattering cross-section calculated from eq 2b. In previous work11,12 we extended the ideas of Albrecht65 to surface enhanced Raman spectroscopy. We assumed that the molecule was bound to the metal surface through a weak 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-tosolid transition moment μIM through the Herzberg−Teller coupling term hMK or by the solid-to-molecule transition 4910

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C

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−.

moment μMK through the Herzberg−Teller coupling term hIM. We then obtain analogues of the Albrecht A, B, C terms for the molecule−metal system.

referred to as Franck−Condon (FC) scattering and the B (C) term as Herzberg−Teller (HT) scattering. Our calculation of static and preresonance 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 sumover-states method of Aspuru-Guzik et al.66 in the absence of the excited state line widths. These authors use the frequencydependent electronic Placzek polarizability tensor

ασρ = A + B + C ⎡

S = F,K ≠ I

B=

μSIσ μSIρ

∑ ∑⎢

A=

k

⎣ ℏ(ωSI − ω)

+

⎤ ⎥⟨i|k⟩⟨k|f ⟩ ℏ(ωSI + ω) ⎦

⎡ μ σ hRSμ ρ IR SI

∑ ∑ ∑⎢ R = F,K S = F,K

× +

k

⎣ ℏ(ωRI − ω)

μSIρ μSIσ

+

μIRσ hRSμSIρ ⎤ ⎥ ℏ(ωRI + ω) ⎦

α mn(ω) =

⟨i|k⟩⟨k|Q k|f ⟩

k

ℏωRS

⎡ μ σ hSR μ ρ IS RI

∑ ∑ ∑⎢ R = F,K S = F,K

k

⎣ ℏ(ωRI − ω)

+

μIRσ hSR μRIρ ⎤ ⎥ ℏ(ωRI + ω) ⎦

ℏωRS σ ⎤ μIRρ hISμSR ⎥ ℏ(ωRI + ω) ⎦ R = F,K S = F,K k ⎣ ℏ(ωRI − ω) ⎡ μ σ hISμ ρ ⟨i|k⟩⟨k|Q k|f ⟩ SR × + ∑ ∑ ∑ ⎢ IR ( ω ω) ℏωSI ℏ − ⎣ RI R = F,K S = F,K k ρ σ ⎤ μIR hISμSR ⟨i|Q k|k⟩⟨k|f ⟩ ⎥ + ℏ(ωRI + ω) ⎦ ℏωSI

⎡ μ σ hISμ ρ IR SR

∑ ∑ ∑⎢

μokm μokn Ωk − ω

+

μokm μokn Ωk + ω

] (4)

and indicate that the derivative of αmn(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 eq 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 preresonance 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 chargetransfer 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, ∂Ωk , where Ωk is the

⟨i|Q k|k⟩⟨k|f ⟩

C=

∑[

+

(3)

We should emphasize that in these expressions the sums range over all excited states (R and S), which include both chargetransfer 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

∂Q

kth excited state, whereas the B (C) term is proportional to the derivative of the transition moments with respect to Q, i.e., ∂μ . ∂Q

4911

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C Table 1. Geometric and Binding Properties of ZnnSem Complexes with Edge-On 4-Mpy Binding ZnnSem−SPyr

n = m = 3 cyclic

n = 7, m = 6

n = 13, m = 12

n = 13, m = 13

n = 33, m = 33

RZn−S (Å) ∠Zn−S−C (deg) Eg (eV) bare cluster Ebind (kcal/mol) bond type

2.13 105.676 4.01 −54.07 single

2.23, 2.52 99.288 3.08 −398.94 bridged

2.33, 2.33 107.386 3.90 −216.43 bridged

2.37 95.745 3.83 −52.84 on-top single

2.44, 2.56 107.606 3.16 −73.73 bridged(?)

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 2.51 Å 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, because the distance between the Se central atom and three surface Zn atoms is 2.53 Å structure with a fourth Zn at 2.76 Å. 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/6-31+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 (Figure 1e) Zn13Se13−SPyr− where the Zn−S−C bond angle is 95.745 deg 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 away from any atom of any of the clusters. In Table 1 a summary of the calculated properties is given. Table 1 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 1 but has the shortest bond Zn−S bond of 2.169 Å compared to 2.313 Å for the cyclic Zn3Se3−SPyr−. For the Zn7Se6−SPyr+ complex, the cluster has a structure with stacked four- and six-membered rings and shows a bond (Figure 1c) between the S atom in 4Mpy 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+ (Figure 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 a nonstoichiometric cluster when one Se atom is removed, the 4-Mpy geometry is bridging between 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−SPyr− complex now has only an on-top single bonded 4-Mpy anion. In this representative structure, all the 13 Zn atoms are on the surface and there are three Zn ions that 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, 2.535, and 2.577 Å. For the other Zn atoms, there are six Zn atoms trigonally bonded with Se and three Zn atoms that bind to only two Se atoms in the cluster. The largest symmetric cluster complex Zn33Se33−SPyr− complex (Figure 1f) has a much more “glassy” cluster structure and shows eight-

It is thus possible in the infinite lifetime approximation (setting γk = 0) to equate the second term in the SOS approach of Aspru-Guzik et al. (in their eq 3) with, e.g., the B term in eq 3 above for the preresonance 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, eq 4.9.3) that their term in ∂μ is equivalent to our term in ∂Q

(

hRSμIR E R − ES

),

which contains the Herzberg−Teller coupling

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

B terms, the relevant comparison is hRSμIR (E R − ES)(Ωk − ω)

μIS

∂Ωk ∂Ω

( )

(Ωk − ω)2

with

.

Because 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 Ωk − ω ≈ ER − ES, then the determining factor in the relative intensity of the A and B terms is the comparison of ∂Ωk with ∂Q

hRS. The vibronic theory of Albrecht shows that hRS is the expectation value of the derivative of the electronic−nuclear

( )|

potential energy with respect to the normal mode, ⟨S,o|

∂Vne ∂Q

0

R,o⟩ evaluated at the equilibrium position, (o). Thus, both derivative terms are the 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 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 scattering term is active. Because a finite lifetime is not included in our application of linear response theory, the absolute values of the preresonance 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−SPyr−, are shown in Figure 1 for n = 3, 6, 13, 33 and also for the nonstiochiometrric Zn7Se6−SPyr+ 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 clusters.39,42 Indeed, the cluster in the Zn13Se13−SPyr− complex (Figure 1e) is very similar to the bare Zn13Se13 cluster 4912

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C membered rings as well as four- and six-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 and 2.54 Å. In contrast, optimizing the Zn33Se33−SPyr− 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 (Figure 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 1 we also have given the results for cluster−SPyr binding energies and the HOMO−LUMO energy gap, Eg, of the bare clusters in the 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 a vacuum. It is observed that the bridged bonded complex Zn13Se12−SPyr+ with the exact same Zn−S bond distances for each bridge has about 4 times (−216 kcal/mol) the binding energy of the other complexes with a single bond. Here the bond angle Zn−S−Zn is 91.14o. 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 79.48° 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 that 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 (Figure 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 given in Table 1 are for the bare clusters without the adsorbed 4-Mpy. Because 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 the n value (R2 = 0.98). We have also investigated two other possible chemical forms of 4-Mpy. One is where 4-Mpy is protonated at the pyridine N atom and the other is the disulfide dimer Pyr−S−S−Pyr that 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. The Zn−S−C bond angle is 93.173° in the protonated complex, which is similar to its unprotonated form (Figure 1e) where the pyridine ring is directed parallel to cluster surface. In the dimer complex one of its pyridine rings is perpendicular and another parallel to the 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 whereas that of the dimer is

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.

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 Figure 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 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 the Raman activity in parentheses. In terms of Wilson numbers, these modes are the symmetrical ring breathing 1a1 mode, the ν(S−C) and in̅ 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 12a1 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 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) spectra 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 bands for 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 (Figure S2) for this surface adsorption structure, which is weakly bridging. It is seen that all the bands above 400 cm−1 are unshifted 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 Figure 3 and Figure 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. The frequencies and assignments of the static or normal Raman spectra for all the ZnnSem−4Mpy complexes in Figure 1 with n ≥ 7 are given in Table 2. We use Wilson numbers and also the Gardner and Wright M notation63 for the normal mode assignments in the table. The Gardner and Wright 4913

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

Article

The Journal of Physical Chemistry C

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

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 (Figure 2a) and the disulfide dimer (Figure 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. In the low frequency region, the cluster vibrational bands are very similar and of equal intensity for the two spectra. However, the 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 nonprotonated 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 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

notation is based on the normal mode diagrams for fluorobenzene in Figure 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 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 8b2 ring stretching modes both near 1600 cm−1 are switched so that the higher frequency mode is the 8b2 mode. Vibrations involving Zn−S stretching are observed at around 4914

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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Table 2. Vibrational Frequencies and Normal Mode Assignments of the Normal (or Static) Raman Spectra of ZnnSem−SPyr Complexes Zn7Se6−SPyr 6-31+G(d) static (cm−1)

Zn13Se12−SPyr 6-31+G(d) static (cm−1)

Zn13Se13−SPyr 6-31+G(d) static (cm−1)

Zn33Se33−SPyr Lanl2dz(d,f)/6-31+G(d)

316.6 379.4

331.9

330.8

392.7

390.0

389.8

388.9 421.5

415.0

423.6

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

1081.6

1086.0

1092.6

1091.9

1117.4

1116.7

1108.4

1116.6

1122.2

1121.3

1120.0

1125.9

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

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

400.7 426.1 ν(Zn−S) ̅

a

Wilson no. and M no.a

16a2 M14(a2) 17a1 & 6a1 M11(a1) 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) 12a1 M8(a1) 15b2 M27(b2 18a1 M5(a1) 9a1 M7(a1) 3b2 M25(b2) 14b2 M26(b2) 19b2 M24(b2) 19a1 M5(a1) 8b2 M23(b2) 8a1

assignment description (this paper) ν̅s(Zn−S−Zn) ν̅ (Zn−S) ν̅as(Zn−S−Zn) 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. C−H ̅ deform. i.p. C−H deform. i.p. C−H deform. i.p. C−H deform. ring stretch ring stretch ring stretch ring stretch

Based on ref 63.

spectrum of 4-Mpy on 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 cases, 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

simulated bands is given in parentheses as well as the estimated intensities from the experimental spectrum (given in Figure 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 is for the band at 683 cm−1, which was originally assigned to b1 symmetry (Figure S4) but should be 6b2. Although, the vibrations of the experimental 4915

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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of the transitions for B3LYP with those from CAM-B3LYP. The hole−electron pair natural transition orbitals (NTOs) show 11 CT transitions, 10 mixed transitions, and 12 intercluster transitions (IC) in the first 33 singlet excitations (3−4 eV) for B3LYP compared to 9 CT transitions, 6 mixed transition, 2 molecular resonance (MR) transition (solely within the bound 4-Mpy anion), and 16 IC transitions (4−5 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 transitions 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 natures of the transitions are 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 preresonance Raman spectra of CT excitations, we have used the B3LYP functional for all our TDDFT preresonance 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 molecule-to-cluster CT transition calculated by TDDFT at 2.785 eV with a wave function 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 does not show up on the UV−vis plot in Figure 5. The second TDDFT excitation with 0.0348 oscillator strength at 3.13 eV is a mixed CT state and is the onset of the UV−vis spectrum (Figure 5, blue curve). The HOMO−1 is a mixed molecule−cluster MO while the HOMO−2 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 3.77 eV 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 midgap 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 (Figure 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

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 cutoff to better display the lower intensity bands.)

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 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 the disulfide bond, S− S, at 528.5 cm−1 is 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-Gordon71 makes it clear that hybrid functionals like B3LYP (which has 20% HF exchange) should do better for CT excitations than pure density functionals 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 because 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 results for an optimized long-range corrected LC-BLYP functional!74 We can compare the natures 4916

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

4917

rB: M9(a1)

rA: M12(a2) rA: M8(a1) M8(a1) M7(a1)

M6(a1) rA: M8(a1) rB: M24(b2)

rA: rB: rA: rB:

1006.7 (42.2)

1013.6 (1.8) 1036.7 (169) 1090.2* (30.8) 1092.6* (119)

1106.3* (43.9) 1114.8* (60.2) 1121.2 (6.3)

1142.3 1256.2 1259.3 1289.1

M24(b2) M7(a1) M7(a1) M25(b2)

rA: M10(a1) rA: M11(a1) M17(b1) rB: M19(b1) rA: M19(b1) rB: M13(a2) rA: M13(a2) rB: M15(b1) rA: M15(b1) rB: M12(a2)

717.2 (1.1) 729.1* (2.3) 732.9* (0.1) 813.6 (0.1) 831.7 (1.4) 866.9 (0.2) 875.6 (0.2) 973.6 (0.06) 984.4 (2.2) 998.0 (0.1)

(4.4) (7.4) (9.7) (20.5)

rB: M10(a1)

697.1 (6.2)

rB: M14(a2) rA: M14(a2) rB:ν(SSC) rA: M14(a2) rA: ν(CSS)

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

(0.4) (5) (3.7) (0.3) (3.6)

assignments Zn13Se13Pyr−S−S−Pyr

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

383.2 391.5 416.5 438.2 438.3

Zn13Se13Pyr−S−S−Pyrb 6-31+G(d) static

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

1121 (18a1) (1)

1022 (12a) (18)

1011 (1a1) (2)

777 (4b1) (12)

685 (6b2) (16)

ZnSec 514 nm (cm−1)

1284.0 (4.6)

1228.5 (1.0)

1133.4 (14.9)

1105.0 (0.1)

1064.3 (25.4)

1008.8 (86.7)

959.63 (3.2)

949.8 (8.4)

838.5 (6.5)

832.1 (8.1)

735.43 (23.5)

691.42 (24.1)

612.85 (5.7) 648.85 (2.7)

468.2 (0.2)

416.2 (1.3) 428.2 (12.2)

304

Zn13Se13−SPyrH 6-31+G(d) (cm−1)

M5(a1) 9a1 M7(a1) 19b2

15b2 M27(b2) 18a1 & ν̅(S−C)

M18(b1) 6a1 M10(a1) 11b1 M17(b1) 10a2 M13(a2) 5b1 M15(b1) 17a2 M12(a2) 1a1 M9(a1) 12a1 M6(a1)

N−H wag 6b2 M29(b2) 4b1

16a2 M14(a2) 6a1 M11(a1) 16b1 M19(b1)

S−C wag

assignments Zn13Se13−SPyrH

1282.7 (7.5)

1249.9 (6.8)

1120.0 (70.4)

1108.4 (3.7)

1092.6 (13)

1008.5 (72.4)

979.8 (0.9)

963.1 (0.1)

865.2 (0.4)

809.3 (0.9)

734.5 (1.6)

711.7 (8.31)

680.8 (4.7)

514.3 (0.7)

415.0 (3.3)

331.9 (7.1) 390.0 (0.2)

Zn13Se13−SPyr 6-31+G(d)

M5(a1) 9a1 M7(a1) 3b2

15b2 M27(b2) 18a1

M10(a1) 4b1 M18(b1) 11b1 M17(b1) 10a2 M13(a2) 5b1 M15(b1) 17a2 M12(a2) 1a1 M9(a1) 12a1 M6(a1)

6a1

6b2 M29(b2)

16b1 M19(b1)

ν(Zn−S) ̅ 16a2 M14(a2) 17a1 & 6a1 M11(a1)

assignments Zn13Se13−SPyr

i.p. C−H deform.

i.p. C−H deform.

ν̅(S−C) i.p. C−H deform.

sym ring & C−H deform. i.p. C−H deform.

trigonal ring breathing

sym ring breathing

o.p. C−H deform.

o.p. C−H deform.

o.p. C−H deform.

o.p. C−H deform.

o.p. ring deform.

i.p. ring deform. & ν̅(C−S)

i.p. ring deform.

o.p. ring deform.

ν(Zn−S) & ν̅(C−S) ̅ i.p. ring deform.

ν(SC) o.p. ring deform.

assignment description (this paper)

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− Aniona

The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

Article

Wilson numbers and Gardner and Wright M notations are both used except for the dimer where only the M notation is given. brA 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. cBased on experimental spectrum Figure S4.

1661.9 (69.0) 1615 (8a1) (7) 1635 (3)

1624.3 (26.4) 1580 (8b2) (7)

M23(b2) M23(b2) M4(a1) M4(a1) (7.3) (3.3) (36.1) (329) 1594.1 1602.7 1615.1 1648.8

rA: rB: rB: rA:

1499.4 (40.0) 1522.1 (6.0) 1494 (19a1) (10)

1428.0 (15.2) 1455 (19b2) (11)

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

Table 4. Comparison of MO Energy Gaps (eV) with the TDDFT Transitions for Band Edges in the Nanocluster and for the First CT Transition in the Complexa

a

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.

on the unsymmetrical cluster. Comparing the UV−vis spectra (Figure 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 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

a

ring stretch

ring stretch

8b2 M26(b2) 8a1 M4(a1) 1618.7 (57.8)

1514.8 (3.9)

1446 (8,1)

1576.7 (1.0)

ring stretch

ring stretch

i.p. C−H deform.

M25(b2) 14b2 M26(b2) 19b2 M24(b2) 19a1 M5(a1) 1353.2 (10.6)

M24(b2) 15b2 M25(b2) 19b2 M24(b2) 19a1 M5(a1) 3b2 M25(b2) 8b2 N−H wag M26(b2) 8a1 M4(a1) 1312.0 (2.4)

rA: M25(b2) rB: M26(b2) rA:M26(b2) rB:M24(b2) rA: M24(b2) rB: M5(a1) rA: M5(a1) (24.9) (3.6) (8.6) (5.2) (2.9) (0.8) (2.7) 1303.6 1359.4 1363.0 1445.4 1464.6 1519.3 1524.0

Zn13Se13Pyr−S−S−Pyrb 6-31+G(d) static

Table 3. continued

assignments Zn13Se13Pyr−S−S−Pyr

ZnSec 514 nm (cm−1)

Zn13Se13−SPyrH 6-31+G(d) (cm−1)

assignments Zn13Se13−SPyrH

Zn13Se13−SPyr 6-31+G(d)

assignments Zn13Se13−SPyr

assignment description (this paper)

The Journal of Physical Chemistry C

4918

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C

We will also investigate the preresonance Raman of the dimer species Pyr−S−S−Pyr adsorbed on the Zn13 Se 13 nanocluster giving the neutral Zn13Se13−Pyr−S−S−Pyr complex (Figure 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 and 3.8 eV on the UV−vis spectrum (Figure 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 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 nanoclusterto-dimer molecule excitations (Figure 8) in contrast to the above previous cases where they were molecule-to-nanocluster excitations. Figure 6. Natural transitions orbital (NTO) hole-to-electron excitations for Zn13Se13−SPyr− for the first three CT states: state 1 (2.785 eV or 445.06 nm, f = 0.0016), 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).

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 intercluster character (Figure 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

Figure 8. Natural transitions orbital (NTO) hole-to-electron excitations for the Zn13Se13Pyr−S−SPyr CT state 6 (3.481 eV or 356.67 nm) calculated with B3LYP/6-31+G(d).

For Zn13Se13−Pyr−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 HOMO− LUMO 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 CAM-B3LYP in the first 25 excited states, there are five pure or almost pure CT states with four mixed CT states, 14 intercluster transitions, and two molecular resonance excitations; so with this complex, CAM-B3LYP again shows less CT

Figure 7. Natural transitions orbital (NTO) hole-to-electron excitations for 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). 4919

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C states than B3LYP. Here state 5 is the first pure CT state. The difference in excited state energies between B3LYP and CAMB3LYP is again about 1.0 eV over the first 30 excitations. Figure 6S shows a comparison of the UV−vis spectra of the nanocluster−dimer complex calculated with the two density functionals. 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, which is a cationic complex with bridged bonding to the ligand. 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 CAMB3LYP than with B3LYP; however, empirical results show that the accuracy of the hybrid functionals is system dependent.75 Because 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 preresonance 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 nanoparticle−molecule 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 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 wave function

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 Figure 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 preresonance 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 (Figure 8), which is the case for almost all the CT transitions we studied with pre-RR for this complex. A hole−electron NTO pair CT state with almost the exact same features is found with the range-separated CAM-B3LYP/6-31+G(d) as shown in S7. However, in this case it is at 4.91 or 1.33 eV higher than with B3LYP/6-31+G(d). 3.4. Pre-Resonance Raman Scattering Spectra. We first investigate the preresonance 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, 447, 446, 444, 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 × 105 Å4/amu. Figure 9 shows this spectrum and we have labeled most of the peaks. Compared to the static spectrum (Figure 3 red spectrum), there is a completely different set of relative Raman intensities in the spectrum. First of all, the low frequency molecular bands at 332 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 that 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 4920

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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Table 5. CT Enhancement Factors for Zn13Se13−SPyr− from Raman Activities for the Pre-resonance Spectrum Excited at 447 nm

Figure 9. Preresonance Raman spectrum of Zn13Se13−SPyr− excited at 477 nm (22 371.3 cm−1).

446 nm that is 47 cm−1 below the resonance at 445 nm. We can compare the differential cross sections of the intense 8a1 mode at 1619 cm for the NRS (2.83 × 10−30 cm2/sr) with those excited at 500, 447, 446, 444, and 443 nm, which are 6.53 × 10−30, 1.90 × 10−26, 3.56 × 10−25, 2.21 × 10−25, and 1.64 × 10−26 cm2/sr, respectively. The resonance is at 445 nm and the preresonance cross-section on either side at 444 and 446 nm is enhanced by about 105 over the static Raman intensity for this mode in the infinite-lifetime approximation. We can quantify the enhancements by analyzing what we have called47,48 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 divided by the analogous sum for the static spectrum of the complex. ∑i SiZnSeSpyr(447) n

∑i SiZnSepyr(static)

Raman activity, static

Raman activity, excited 447 nm

Wilson no. & symmetry

331.9 390.0 415.0 514.3 680.8 711.7 734.5 809.3 865.2 963.1 979.8 1008.5 1092.6 1108.4 1120.0 1249.9 1282.7 1353.2 1446 1514.8 1576.7 1618.7

7.13 0.175 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

121 600 20 710 142 631 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

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

CT enhancement factor 1.70 1.18 4.36 1.33 18.1 2.75 863 425 4.83 2.63 616 1.99 4.62 92 218 834 48 21 37 5.11 1.36 4.91

× × × ×

104 105 104 104

× 104

× 104 × 104 × 103 × 103

× 103 × 103 × 104

0.0105); see NTOs in Figure 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 306 nm is 108.3 cm−1, on the high side of state 11; and the excitation at 305 nm is 215.7 cm−1, on the high side of this state. 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 Figure 10A) to compare with the spectra excited at 306 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 Figure 10A, is almost gone with the 18a mode at 1121.3 cm−1 predominating. We observed that in the static spectrum (Figure 3 blue), a similar mode at 1086 cm−1 was relatively strong as it is in the spectra at 309 nm (blue) and 305 nm (green) in Figure 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+

n

EFm =

Zn13Se13−SPyr 6-31+G(d) (cm−1)

(5)

Here m = a2, a1, b1, and b2 for C2v symmetry of the 4-Mpy anion. From the data in Table 5 we calculate EFa2 = 2.8 × 104, EFb1 = 3.9 × 103, EFa1 = 3.3 × 103, and EFb2 = 0.9 × 102 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. A spectrum with very similar features is also calculated on exciting at 364 nm, which is between the two CT resonance states 5 (368.7 nm) and 362.7 nm shown in Figure 6. Because 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 state 1 (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 Zn13Se13−SPyr− with the pre- resonance Raman spectrum of Zn13Se12−SPyr+. For the unsymmetrical Zn13Se12−SPyr+ complex, we excited at three frequencies at 309, 306 and 305 nm around state 10 at 310.79 nm (f = 0.0002) and state 11 at 307.02 nm (f = 4921

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Figure 10. (A) Preresonance Raman spectra of Zn13Se12−SPyr+ excited at 309 nm (32 362.5 cm−1) (blue) (×10), at 306 nm (32 679.5 cm−1) (red), and at 305 nm (32 786.9 cm−1) (green). (B) Comparison of preresonance Raman spectra of Zn13Se12−SPyr+ excited at 306 nm (red) and Zn13Se13− SPyr− excited at 364 nm (blue).

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 × 10−24 cm2/sr compared with 2.01 × 10−25 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 because 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 preresonance Raman of the Zn13Se13−SPyr− complex is closer 4922

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C to the typical experimental Raman spectra of 4-Mpy on semiconductor surfaces such as ZnS, ZnO, CdTe, and ZnS where modes around 1600 and 1120 cm−1 are particularly strong. This may indicate that these surfaces are chalcogen rich. Finally, we consider the preresonance Raman spectra for the dimer Pyr−S−S−Pyr (Figure 2b), which is a putative species that could be formed by photo-oxidation of 4-Mpy on semiconductor surfaces.51,52 On Au78 and Ag79 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 Table 6. Excited State Energy and Excitation Energy for Preresonance Raman Spectra of Zn13Se13Pyr-S-SPyr excited state

oscillator strength

CT S13 CT S12

0.0003 0.0004

CT S11 IC S10 CT S6

0.0003 0.0325 0.0046

CT S5 CT S1

0.0054 0.0015

state energy (cm−1)

excitation energies (cm−1)

difference energy (cm−1) [col 3 − col 4]

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

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

Figure 11. Preresonance Raman spectra of Zn13Se13Pyr−S−SPyr excited at different energies. (A) The red spectrum is excited at 25 926 or 200 cm−1 below S1 (26 126.0 cm−1) and the light blue spectrum is excited at 27 932.5 or 139 cm−1 below S6 (28 071.8 cm−1). (B) The dark blue spectrum is excited at 29 453 or 200 cm−1 above S11.

pure CT state S1 at 3.239 eV or 26 126.0 cm−1 with the next pure CT state S5 at 3.3602 eV or 27 101.7 cm−1, and this is separated by 970 cm−1 from a third pure CT state S6 at 3.4805 eV or 28 071.8 cm−1. The NTO hole-to-electron molecular orbital isoform for this transition is shown in Figure 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 preresonance 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 × 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 4 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 preresonance 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 preresonance Raman spectrum is found if we excite close to CT state 11. This excitation at 29 453.1 cm−1 is 100 cm−1 above S11 and 501 cm−1 below S12. A very similar spectrum is found if we excite at 30 440.0 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 × 106 near S11 and 2.94 × 106 near S13. This band has a Raman Aactivity of 6.6 in the static spectrum of the dimer giving a SERS enhancement factor of 5 × 105 for this band on the Zn13Se13 nanocluster. For clarity we only illustrate the spectrum at 100 cm−1 above S11 in Figure 11B. The next strongest mode in this spectrum is still the 1648.7 M4(a1) with Raman activity 5.2 × 105. 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 nontotally symmetric modes at 1594 cm−1 rA: M23(b2) and several other weaker nontotally 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 intercluster (IC) transition at state 10 with oscillator strength f = 0.0325, from which intensity borrowing can occur. 4923

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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The Journal of Physical Chemistry C

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 a 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 that 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 that depend on the surface binding geometry of 4Mpy. 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 mode compared to the mode at 1121 cm−1. In the preresonance 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 that are characteristic of Franck− Condon scattering. For the 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 nontotally symmetric normal modes and are 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 nonradiant 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, ∂Ωk .

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 moleculeto-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−Condon scattering mechanism. However, exciting into several higher CT excited states yields a unique spectrum that is dominated by the S−S vibration but that also displays large enhancements of the nontotally 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 that 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 fewer CT states with CAM-B3LYP and they are about 1 eV 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 complex (pre-RR complex intensity/static Raman complex intensity) are of the order of 1 × 104 to 5 × 104 for the strongest individual bands in the spectra, which are commensurate with experimentally determined enhancement factors. However, a theoretical treatment that 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.

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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 toward the vacuum by 2−4 eV. In the case of the dimer 4924

DOI: 10.1021/acs.jpcc.7b12392 J. Phys. Chem. C 2018, 122, 4908−4927

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b12392. 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 powder and 4Mpy 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−S−S−Py calculated with B3LYP and CAM-B3LY, and natural transition orbital (NTO) hole-to-electron excitation for the Zn13Se13Pyr− S−SPyr calculated with CAM-B3LYP (PDF)

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AUTHOR INFORMATION

Corresponding Author

*R. L. Birke. E-mail: [email protected]. ORCID

Ronald L. Birke: 0000-0001-8162-9254 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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. 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)

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REFERENCES

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