Theoretical Analysis of the Electronic Structure and Optical Properties of DNA-Stabilized Silver Cluster Ag 16 Cl 2 in Aqueous Solvent

. DNA-stabilized silver nanoclusters with 10 to 30 silver atoms are by construction ideal candidates for biocompatible bright fluorescent emitters but their electronic structure is not well understood. Here, using density functional theory (DFT), we analyze the ground-state electronic structure and optical absorption of a bright NIR-emitting cluster Ag 16 Cl 2 which is stabilized by two DNA strands of 9-base sequence 5’-CACCTAGCG-3’ and whose atomic structure was very recently confirmed to have two chlorides bound to the silver core. We are able to (i) unambiguously assign the charge of this cluster in aqueous solvent, (ii) analyze the details of silver–DNA interactions and their effect on the cluster charge, (iii) analyze the character of low-energy optical absorption peaks and the involved electron orbitals and make a first assessment on circular dichroism, and (iv) evaluate the suitability of various DFT exchange-correlation functionals via benchmarking to experimental optical data. This work lays out a baseline for all future theoretical work to understand the electronic, chiroptical and fluorescence properties of these fascinating bio-compatible nanostructures.

ABSTRACT. DNA-stabilized silver nanoclusters with 10 to 30 silver atoms are by construction ideal candidates for biocompatible bright fluorescent emitters but their electronic structure is not well understood. Here, using density functional theory (DFT), we analyze the ground-state electronic structure and optical absorption of a bright NIR-emitting cluster Ag 16 Cl 2 which is stabilized by two DNA strands of 9-base sequence 5'-CACCTAGCG-3' and whose atomic structure was very recently confirmed to have two chlorides bound to the silver core. We are able to (i) unambiguously assign the charge of this cluster in aqueous solvent, (ii) analyze the details of silver-DNA interactions and their effect on the cluster charge, (iii) analyze the character of low-energy optical absorption peaks and the involved electron orbitals and make a first assessment on circular dichroism, and (iv) evaluate the suitability of various DFT exchangecorrelation functionals via benchmarking to experimental optical data. This work lays out a baseline for all future theoretical work to understand the electronic, chiroptical and fluorescence properties of these fascinating bio-compatible nanostructures.

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KEYWORDS density functional theory, silver, DNA, optical absorption, circular dichroism, exchange-correlation functionals Small metal clusters stabilized by ligand molecules confine a discrete number of delocalized valence electrons to their inorganic core, which leads to a quantized electronic structure and distinct optical properties. 1 These properties are highly sensitive to the metal type, ligand type, cluster size, and cluster shape, creating a possibility to tune the optical response such as the intensity and wave length of fluorescence by changing the chemical parameters in the synthesis.
For almost two decades, DNA-templated silver clusters having up to about 30 silver atoms have been demonstrated as bright emitters in the visible to near-infrared (NIR) range of wave lengths controlled by the selected DNA sequence. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] Theoretical studies on this intriguing phenomenon have been limited due to absence of solid experimental evidence on the atomic structures of such clusters, although model studies on small silver -DNA complexes have produced important information of interactions between silver cations and different DNA bases. [16][17][18][19] The field took important steps forward when crystal structures of two DNA-templated silver clusters (Ag 8 and Ag 16 ) were reported in 2019. 5,20 The rod-like and geometrically slightly chiral Ag 16 cluster, 20 templated by two DNA strands (each strands has the 10-base sequence 5'-CACCTAGCGA-3') is particularly interesting since it is fluorescent in the NIR region and has a large Stokes shift. Very recently, re-analysis of this cluster by means of electrospray ionization mass spectrometry, nuclear magnetic spectroscopy (NMR), density functional theory (DFT) calculations, and refined single-crystal X-ray analysis discovered that the 16-atom silver core has two chlorides bound to it. 21 The two Cl sites had been previously assigned as partially occupied silver sites. 20 Our preliminary DFT calculations provided a rather good description of the optical absorption of the (DNA) 2 -Ag 16 Cl 2 cluster and helped to interpret the NMR data.
The firm knowledge of the crystal structure of the (DNA) 2 -Ag 16 Cl 2 allows now for more detailed theoretical DFT analysis, paving ways to better understanding of the structure-property relations of these materials. Here, we expand our previous theoretical investigations 21 based on the A10-variant 22 of the (DNA) 2 -Ag 16 Cl 2 cluster (Figure 1). Our DFT calculations are able to unambiguously determine the natural charge state of the complex in the solvent, derived from the electronic stability of the silver core having a six-free-electron configuration. We highlight an important role of a specific guanine-silver interaction contributing to the total charge. We show an excellent agreement between computed and measured optical absorption data allowing us to interpret the character of the low-energy absorption peaks in detail in terms of electron-hole excitations and contributions from the silver core and DNA strands also determining the origin of circular dichroism. We explore the electronic structure with a variety of electronic exchangecorrelation functionals and are able to benchmark the most reliable functional against experimental data, laying groundwork for further theoretical investigations of electronic, optical, chiral, and fluorescence properties of these materials. The necessary next steps are discussed.
Our preliminary DFT calculations employed the PBE exchange-correlation functional 23 treating (DNA) 2 -Ag 16 Cl 2 as an isolated complex in gas phase with total charge matching the expected configuration of six "free" electrons in the silver core. 21 This amounts to a charge of -8 |e| based on 16 negatively charged phosphate groups, 16 donated Ag(s) electrons, and two electronwithdrawing chlorides, i.e., the net count of electrons is (8 -16 + 16 -2 = 6). This model gave an optical absorption spectrum that qualitatively agreed with the measured data, specifically, a clear lowest-energy peak at 694 nm and two weak higher-energy signals around 400-500 nm ( Figure   2a) although all these peaks were significantly red-shifted with respect to the experiment. 21 The character of the lowest-energy peak was analyzed in terms of single electron-hole transitions and induced dipole density that showed clear longitudinal excitations along the silver core. Minor contributions from the phosphate groups were also observed in the induced dipole density. This was assigned tentatively due to the missing dielectric environment as no solvent was modeled.
The potential solvent effects were not investigated further as our efforts concentrated on interpreting the 35 Cl NMR spectra, being an important part of producing evidence for the existence of the chlorides in the silver core. 21 Optimal charge state in the solvent. Our new work concentrated first on detailed analysis of the character of electronic states of (DNA) 2 -Ag 16 Cl 2 with -8 |e| charge without the solvent using the PBE functional. As Figure 2b shows, the phosphate contributions show up strongly also in the density of electron states when they are projected (PDOS) onto the natural components of the system (silver, chloride, base, sugar, phosphate), creating partially occupied states close to the energy of the highest occupied molecular orbital (HOMO). This explains their activity also in the low-lying optical absorption. We then repeated the calculation with the implicit water solvent model and observed that the phosphate states moved down to more negative energies, (i.e., were stabilized by the solvent) as expected, however, the degenerate HOMO/LUMO state remained displaying a two-electron hole (not shown here). This fact indicated to us that the used -8 |e| total charge was not optimal, but there would be added electronic stability of the compound for -10 |e| charge due to opening of a large HOMO-LUMO energy gap at that charge in the PDOS (Figure   2c). With that charge and using the solvent model, the shape of the optical absorption spectrum remained similar as compared to [(DNA) 2 -Ag 16 Cl 2 ] 8without solvent, but the lowest-energy absorption peak of [(DNA) 2 -Ag 16 Cl 2 ] 10blue-shifted by 65 nm, giving a better agreement with the experimental data (Figure 2a).
The chemical argument to add two additional electrons in the model (increasing the charge of the complex to -10 |e|) is found by examining the silver-DNA interface in the crystal structure data of the A10-variant. 22 As Figure 1 and S1 show, there are two guanines, G 7 and G 9 , interacting with silver on both sides of the Ag 16 Cl 2 core. Remarkably, whereas G 7 is found in the neutral form, G 9 is deprotonated at the N1 position (G 9 -), but both N7(G 7 )-Ag and N1(G 9 -)-Ag distances are the same (about 2.3 Å) (Figures 1b,c). The N1(G 9 -)-Ag interactions form the grounds for the added electronic charge. The interaction between neutral guanine and silver cations through the N7 atom and the neighboring carbonyl group (C6 position) has been documented in literature to be the most stable position for the metallobase pair. 24,25 However, different protonation states of the same nucleobase can coexist within the same metal-DNA complex. This interesting phenomenon is not yet fully understood but it has been reported that it could be due to a perturbation of silver on the charge distribution (shifting of pK a values) of the nucleobases. 26 Similar to how metal cations induce deprotonation of guanine at N1 position in ribozymes, 27 silver could cause acidification of the NH groups of G 9 , suggesting that there are different microenvironments inside [(DNA) 2 -Ag 16 Cl 2 ] 10-. Bader charges for silver atoms interacting with N7(G 7 ) and N1(G 9 -) are similar (0.393 and 0.383 |e| vs. 0.377 and 0.369 |e|, respectively; Figure   S1) but the environment of G 7 and G 9is different in terms of hydrogen bonds contribution and pi-stacking interactions established with their neighboring bases. In both strands, G 7 forms hydrogen bonds with T 5 and pi-stacking interactions with A 6 and C 8 , while G 9forms hydrogen bonds with C 4 , and pi-stacking interactions only with C 1, being more exposed to the solvent. In fact, it is observed in the crystal structure (PDB ID: 6M2P) that G 9form multiple hydrogen bonds with three or even six water molecules, while only one water molecule is found near G 7 , which indicates that a synergy of hydration and base stacking dictates the metal-mediated deprotonation of specific nucleobases. Overall, atomic Bader charges summed up to the natural components of the system follow an expected pattern where the silver atoms and sugar groups are positively charged and chlorides, bases and phosphates are negatively charged (Table S1).

Performance of exchange-correlation functionals.
We then employed three other exchangecorrelation functionals to calculate the electronic ground state of [Ag 16 Cl 2 -DNA] 10in solvent: GLLB-SC, 28 LB94, 29 and CAMH-B3LYP, 30 and recalculated the optical spectra by using the PBE functional in the exchange-correlation kernel (see Methods and Figures S2 and S3). We found that the character of the frontier orbitals remains largely the same independent of the functional except in the case for CAMH-B3LYP where the LUMO state having weight on silver is next to a continuous band of empty states ( Figure S2d). However, the functional by which the ground state was calculated has a clear effect on the optical spectrum ( Figure S3). The HOMO-LUMO energy gap depends somewhat on the functional as follows: 1.70 eV (PBE), 1.68 eV (LB94), 1.88 eV (GLLB-SC), and 1.53 eV (CAMH-B3LYP). The largest energy gap produced by GLLB-SC gave a reason to expect a further blue-shift of the lowest-energy absorption peak which indeed turned out to be the case (Figure S3 and Figure 3a). Figure 3a compares the computed results with PBE and GLLB-SC in reference to the experimental data. Remarkably, the spectrum computed by using the GLLB-SC functional for the ground state shows an excellent agreement with the experiment as the lowest-energy peak is clearly the most intensive one in the region of 350 -550 nm and its position at 530 nm is very close to the experimental value at 522 nm. The peaks at 375 nm and 407 nm are close to ones regularly seen in the experimental data, 21 and a very recent study 31 also reported a weak signal close to our computed peak at 449 nm.
Analysis of the optical spectrum and frontier orbitals. We then analyzed the character of all four peaks mentioned above by creating the corresponding dipole transition contribution maps 32 (Figure 3b and Figure S4). The lowest-energy peak at 530 nm is clearly a single orbital transition of HOMO à LUMO (silver à silver) character, without any collective contributions from other states (Figure 3b). This unambiguously clarifies the nature of this intense transition which is sometimes hypothesized as being of collective or "plasmonic" character. The three weaker peaks at 449 nm, 407 nm, and 375 nm are more collective (Figure S4), having contributions both from the HOMO à LUMO transition and from silver à base and base à silver transitions.
We visualize the frontier orbitals from HOMO-7 to LUMO+3 in Figure 4. Most of these orbitals have a major weight in the inorganic silver-chloride core except HOMO-(3,2,1). HOMO-1 and HOMO-2 are localized on the deprotonated G 9on each DNA strand (second and first strand, respectively), while HOMO-3 is localized on A 2 '. Orbitals that are localized in the inorganic core follow systematic particle-in-a-box symmetries, with HOMO-(7,6) having one node plane in the "silver box" perpendicular to the longitudinal direction, HOMO having two node planes, LUMO having three node planes, and LUMO+(1,2,3) having node planes in the transverse direction. The symmetry analysis reinforces the picture of a strong dipole-allowed HOMO à LUMO longitudinal transition which indeed is seen in Figure 3b.
It is interesting to note that the LUMO orbital that is localized mostly in the silver core is active in all the analyzed absorption peaks, but in some peaks also higher lying empty orbitals are involved. This implies that the details of the electronic relaxation processes should depend on the excitation energy. Although we do not intend to study the fluorescence in this work, one can assume that in the first approximation, similar orbitals (HOMO, LUMO) that are responsible for the lowest-energy absorption also play role in the fluorescence after electronic relaxation. This gives a rather simple framework to understand the size-dependence of the absorption and fluorescence on DNA -Ag cluster materials having the elongated shape of the inorganic core, well documented experimentally. 11,12,33,34 If the absorption and fluorescence are realistically described by one-electron transition, the physics can be drawn from simple electron-in-a-box model, where the energy of the lowest transition should follow 1 / L behavior (L is the box length). In fact, we have documented this physics previously in another cluster model where we built linear chains of thiolate-protected gold nanoclusters up to aspect ratio of 1:6 and showed a strong red-shift and intensity increase (due to increased transition dipole) in the VIS-NIR absorption as the length of the system increased. 35 Silver nanowires also show this behavior as the energetic separation of Ag(4d) and Ag(5s) electrons is large and the low-energy optical absorption can be understood well from a monovalent "jellium rod model" . 36 Circular dichroism. The excellent agreement between the measured data and the computed linear absorption of the [DNA 2 -Ag 16 Cl 2 ] 10cluster with the GLLB-SC functional in solvent model encouraged us to calculate the circular dichroism (CD) spectrum which shows the differences in linear absorption due to different handedness of circular polarized light. Figure 5 compares the CD spectrum with the linear absorption spectrum. Several positive (+) and negative (-) peaks can be identified, forming a "fingerprint" of this structure in our model. The first -and + features in 450 -550 nm range are weak, complying with the facts that in this range the silversilver transitions dominate, and the silver core has only very weak chiral distortion (Figure   1b,c). The signals get stronger towards higher absorption energies, where the DNA bases first start to be active and indirectly also affect the metal transitions. Currently our results serve as a first theoretical prediction since the experimental CD data is not available for comparisons.

Outlook.
Our results clearly point out that any realistic DFT calculations of DNA -silver cluster complexes must consider the proper intrinsic charge in solvent and the solvent environment is needed to be described at least in a minimal (implicit) model like the one used here. Among the electronic exchange-correlation functionals tested in this work, the GLLB-SC functional seems to work best to characterize the ground state electronic structure as judged from the optical absorption spectrum. Although we have been able to use, for the first time, high-resolution crystal structure data to draw realistic atom-scale models of DNA -silver clusters for DFT investigations of their electronic structure, optical properties and circular dichroism, several issues are worth investigating further. Among them is the question how sensitive these properties are to small deviations from the crystal structure, induced by computationally optimized models (different exchange-correlation functionals lead to slightly different optimized atomic bonds) or by temperature-dependent dynamical effects. Long time-scale dynamic studies of these systems will pose a numerical challenge at any DFT level, consequently, reliable classical force fields for the silver -chloride core and its interactions with DNA are needed but are not currently available. This may prove to be especially important for successful attempts to understand the chiroptical response of these materails. 10,37 Long time-scale classical molecular dynamics simulations in water may reveal the fluxionality of the inorganic core and core -DNA interactions that are likely to affect many details of the computed CD spectrum. Other cluster sizes and different cluster shapes will undoubtedly change the characteristics of the electronic structure and (chir)optical response, which will form an interesting challenge for atom-scale theory of these intriguing materials.
Computational methods. The DFT calculations were done with the GPAW software which uses real-space grids for solving for the ground-state electronic structure. 38  showing the distribution of the nucleobases around the inorganic core (grey, Ag; green, Cl). b) Side and top view of the interaction between the deprotonated guanine G 9and the silver atoms. c) Side and top view of the interaction between the neutral guanine G 7 and the silver atoms. Cl, base, sugar, and phosphate groups for the same systems, respectively. Coloring denotes the total weights on the specified atom groups. "Out" denotes weights from spatial distribution of electrons that is not captured by the analysis. In b), the HOMO state at zero energy is partially occupied (degeneracy of states) and the first fully empty orbital lies at 1.19 eV. In c), the HOMO-LUMO energy gap (1.70 eV) is centered around zero and the HOMO state is fully occupied.   The following file is available free of charge. Additional analysis of the electronic structure, optical spectrum, and the silver -DNA interface of the [DNA 2 -Ag 16 Cl 2 ] 10cluster (PDF).

AUTHOR INFORMATION
The authors declare no competing financial interests.