Comparative study of gold and silver interactions with amino acids and nucleobases

Metal nanoclusters (NCs) have gained much attention in the last decade. In solution, metal nanoclusters can be stabilized by proteins, and, thus, exhibit many advantages in biocatalysis, biosensing, and bioimaging. In spite of much progress in the synthesis of polypeptide-stabilized gold (Au) clusters, their structure, as well as amino acid-cluster and amino acid–Au+ interactions, remain poorly understood. It is not entirely clear which amino acid (AA) residues and sites in the protein are preferred for binding. The understanding of NC-protein interactions and how they evolve in the polypeptide templates is the key to designing Au NCs. In this work, binding of gold ion Au+ and diatomic neutral gold nanocluster Au2 with a full set of α-proteinogenic amino acids is studied using Density Functional Theory (DFT) and the ab initio RI-MP2 method in order to find the preferred sites of gold interaction in proteins. We demonstrated that the interaction of gold cations and clusters with protonated and deprotonated amino acid residues do not differ greatly. The binding affinity of AAs to the Au2 cluster increases in the following order: Cys(−H+) > Asp(−H+) > Tyr(−H+) > Glu(−H+) > Arg > Gln, His, Met ≫ Asn, Pro, Trp > Lys, Tyr, Phe > His(+H+) > Asp > Lys(+H+) > Glu, Leu > Arg(+H+) > Ile, Val, Ala > Thr, Ser > Gly, Cys, which agrees with the available experimental data that gold cluster synthesis occurs in a wide range of pH – amino acid residues with different protonation states are involved in this process. The significant difference in the binding energy of metal atoms with nucleobases and amino acids apparently means that unlike on DNA templates, neutral metal atoms are strongly bound to amino acid residues and can't freely diffuse in a polypeptide globula. This fact allows one to conclude that formation of metal NCs in proteins occurs through the nucleation of reduced Au atoms bound to the neighboring amino acid residues, and the flexibility of the amino acid residue side-chains and protein chain as a whole plays a significant role in this process.


Introduction
5][6][7] In solution, NCs can be stabilized by various polymer templates.In particular, DNA-stabilized 8,9 and protein-protected 6,7 NCs exhibit many advantages for biosensing and bioimaging: ultrasmall size, photostability, biocompatibility, and brightness.Noble metal NCs, in particular, silver (Ag) and gold (Au) clusters, in comparison with other NCs, exhibit excellent stability, facile synthesis, and low toxicity. 10Metal clusters emitting in the visible range have been synthesized using DNA, 8,9 amino acids, 11,12 peptides, 13,14 and proteins such as bovine serum albumin, [15][16][17][18][19] human serum albumin, egg albumin, 20,21 lysozyme, 22 and immunoglobulin. 5n spite of much progress in the synthesis of a wide variety of NCs, their structure, as well as ligand-cluster interactions, remains poorly understood.For protein-stabilized NCs, it is not entirely clear which amino acid residues and sites in the polypeptide are preferred for binding.The understanding of NCspolypeptide interactions and how they evolve in the polypeptide matrices is the key to design the functional uorescent biolabels.We have investigated earlier the interactions of amino acids with silver ions and clusters. 23We showed that deprotonated amino acid residues are preferable for binding with silver clusters, which is in line with experimental data: the formation of silver clusters on protein templates occurs predominantly at alkaline pH.On the contrary, gold clusters are synthesized in a wide range of pH. 24Several factors may inuence this process: the ability of different amino acid functional groups to reduce gold, charge, and binding energy with gold.
This paper focuses on the Au 2 cluster/amino acid (AA) interactions and on the Au + /AA interactions as a precursor of the cluster.In a typical synthesis, hydrogen tetrachloroaurate is usually taken as a source of gold Au 3+ ions.At the rst stage, proteins reduce most of the Au 3+ to Au 1+ . 257][28] In proteins, Au ions may bind to various AAs able to interact with gold.][31][32][33] It is known that Au can interact with O, N and S atoms.At the same time, it is believed that gold in protein templates interacts most effectively with sulfur, especially with cysteine.Indeed, cysteine is considered as the preferential binding site for gold in proteins, which is conrmed by theoretical calculations. 34[32][33][35][36][37] It was shown experimentally that low temperature and acidic pH favors the growth of gold nanoparticles on protein template. 352][43][44] The synthesis of gold nanostructures through the photo-reduction of amino acids in water is also possible: the most stable structures are produced by arginine, cysteine, threonine, methionine, tryptophan, and phenylalanine. 366][47] Using molecular dynamics, it was shown that negatively charged atoms play a signicant role in adsorption of amino acids on the gold nanoparticles. 37It was shown that the interaction energy with neutral Au 3 cluster is higher for the glycine bearing a negative charge than for glycine with charge 0 or +1, the same is true for cysteine. 45In the case of neutral and negatively charged glycine, the interaction occurs with the nitrogen atom, while in the case of protonated glycine interaction with Au 3 cluster proceeds through the carboxyl.In the case of cysteine, neutral amino acid interacts with the cluster through the nitrogen, negatively charged amino acid forms a bond between Au and sulfur, while for positively charged Gly interaction with Au occurs through both sulfur and hydroxyl of the carboxyl group.They also showed that two major bonding factors are: (1) Au-N, Au-O, and Au-S anchoring bonding; and (2) nonconventional OH/Au and NH/Au hydrogen bonding. 45Rai and co-authors performed theoretical calculations for proline and Au 3 cluster.The interaction of gold cluster with proline occurred predominantly through amide terminal. 46Investigation of the interactions of Au 8 and Au 20 clusters with alanine and tryptophan showed that these clusters prefer single-site interactions through the aminogroup for the amino acids. 47In these works, the authors regarded only alanine, cysteine, glycine, proline, and tryptophan interaction with gold nanoclusters and how the interplay of gold with the remaining 15 amino acids occurs was still unknown.
In our quantum-chemical investigation we focused on the interactions of the neutral Au 2 cluster and Au + cation with a full set of proteinogenic a-amino acids.We tried to identify favorable sites of clusters formation on protein templates.Also, we took into account the effect of amino acid side chain protonation/deprotonation on the effectiveness of these interactions.The Au 2 cluster was chosen as a model object since it is a minimal singlet cluster with a neutral charge.Au 2 diatomic cluster protected by organic ligands is a classical object of nanocluster research. 48,49We calculated the binding Gibbs free energies between Au 2 and amino acids in the neutral, protonated, and deprotonated forms of the side chain.We established the amino acids, which are more preferable for the interaction with Au 2 and Au + .Next, we compared gold-amino acid binding energies with silver binding energies.Also, we examined the interactions in the complexes using Bader's quantum theory "Atoms-in-molecules" approach and natural bond orbital (NBO) analysis.
There is a certain interest to compare the binding energies of gold and silver clusters with protein and DNA matrices.][52] We performed the calculations for gold and silver ions and clusters with cytosine and adenine, the preferred binding residues for Ag and Au clusters in DNA, 53,54 and compared them with the literature data on Au and Ag interactions with DNA.

Methods
Equilibrium geometry optimizations and corresponding hessian calculations of complexes were done with usage of density functional theory (DFT) at the PBE 55 level, and resolution-of-the-identity second order Moller-Plesset perturbation theory (RI-MP2) realized in Orca 3.0 program package. 56ince DFT does not include dispersion forces, the atom-pair wise dispersion correction with Becke-Johnson damping was used. 57Karlsruhe basis set def2-TZVP was used in all the calculations, gold atoms were treated with def2-TZVP effective core potential (ECP). 58The initial geometries of amino acid-Au 2 complexes for optimization were constructed by placing gold atoms near the active sites of amino acids.The active sites of the amino acids are the amino group, the carboxyl group, and sulfur.These groups possess electron-rich nitrogen, oxygen, and sulfur, which may donate electron density to Au from their lone electron pairs.Binding Gibbs free energies (DG) were calculated for the reactions: The NBO analysis 59 was performed for the amino acid-Au 2 complexes using NBO.5 program at the RI-MP2/def2-TZVP level of theory.The NBO analysis was done in order to obtain natural charges and Wiberg bond indices.The NBO orbitals of several complexes were plotted using the Chemcra program.The atoms-in-molecules (AIM) analysis was performed with the Multiwfn program package 60 to calculate the properties of bond critical points (BCPs).

Results and discussion
In our previous study, we showed that RI-MP2 method in combination with def2-TZVP basis set gives reasonable results predicting Gibbs free energy of interaction between simple organic molecules and silver. 61In our next study, we showed that PBE-D3 method along with RI-MP2 give fruitful results when calculating Gibbs free energy of interaction between silver and amino acid residues. 23Thus, in this study we used both PBE-D3 and RI-MP2 method with def2-TZVP basis set and def2-TZVP ECP for another noble metal-gold.

Amino acid interaction with gold cation Au +
We started with the analysis of amino acid interactions with gold cation Au + .Among the neutral amino acids, arginine had the highest binding free energy (DG) with Au + : À130.7 kcal mol À1 and À140.7 kcal mol À1 , according to RI-MP2/ def2-TZVP and PBE-D3/def2-TZVP, respectively (Table 1).DG was the lowest one for glycine: À60.1 kcal mol À1 and À73.4 kcal mol À1 , according to RI-MP2/def2-TZVP and PBE-D3/ def2-TZVP, respectively.Thus, PBE-D3 tends to overestimate the binding free energy for approximately 10-15 kcal mol À1 as compared to RI-MP2, which is considered as a more precise method.For this reason, PBE-D3 method due to its low computational costs was used for the pretreatment of initial amino acid-Au + geometries (attachment to different sites of amino acid and different conformations were compared) while RI-MP2 was used for the precise calculation of the nal geometries and Gibbs free energy.
Thereby, all amino acids form either monodentate or bidentate complexes with Au + (see Fig. S1 in ESI †).Every amino acid except deprotonated cysteine forms a bond between Au + and the nitrogen of the amino group.Aliphatic amino acids (except methionine), Asp, Glu, Pro, Ser, and Thr form a monodentate complex with Au + .Cys and Met form a bidentate complex while second bond occurs between sulphur and Au.For Arg, His, and Lys, the second site is the nitrogen of the radical side chain; this second site of Au + attraction may become single in a polypeptide since the rst site, amino-group, will participate in the formation of a peptide bond.Trp attaches Au + to one of the carbon atoms of the six-membered ring.Phe, Tyr, and Tyr(ÀH + ) form a cation-pi interaction between Au + and a six-membered ring.Asn and Gln attach Au + to the carbonyl of the side chain (Fig. S1 †).Hence, the Gibbs free energies for the interaction of Au + with Asp, Cys, Glu, Tyr bearing deprotonated side chain radicals appear to be higher than those for the neutral forms of these amino acids (Table 1).

AIM analysis of amino acid complexes with gold cation Au +
Next, we used AIM analysis 62 to study the nature of bonding interactions: amino acid interactions with gold cation Au + were analyzed in terms of electron density and its derivatives.We used several AIM parameters that are presented in Table 2: the density of all electrons (r(r)), the Laplacian of electron density (V 2 r(r)), the Lagrangian kinetic energy term (G(r)), the potential energy density (V(r)), and the energy density (H(r)).
A positive value of V 2 r(r) indicates depletion of electronic charge along the bond, which is typical for electrostatic interaction, while a negative value of V 2 r(r) indicates that electronic charge is located between the nuclei, which is a feature of electron-sharing and covalent interaction.All bond critical points (BCPs) in Table 2 have a positive V 2 r(r) value, which means that all interactions are electrostatic.
The electronic energy density term H(r) is a sum of kinetic and potential components: The virial theorem states that G(r) and V(r) are related to Laplacian through the equation: If H(r) is positive then accumulation of charge at this point is destabilizing.If H(r) is negative then accumulation of charge is stabilizing.The negative value of H(r) indicates the presence of a covalent bond.From Table 2 we may see that in all the cases the electrostatic interactions are stabilizing: all H(r) values are negative.The positive value of V 2 r(r) and negative value of H(r) mean that Au-X bonds are partially covalent and partially electrostatic.That is true for the complexes with both neutral and deprotonated amino acids.For example, AIM parameters calculated for the Au-N bond in the Gly-Au + complex are following: r ¼ 0.11226 hartree, V 2 r ¼ 0.40289 hartree, and V(r) ¼ À0.17388 hartree.The V(r) values allow to calculate the energy of Au-X bond as follows: 63 As expected, arginine had the highest Au-X bond energy value (77.1 kcal mol À1 for the Au-NH bond) among the regarded complexes.This in line with the Gibbs free energy calculations, which show that Au 2 -Arg complex possesses the highest binding energy among neutral AAs.In Au 2 -Arg complex Au interacts both with the nitrogen of the NH 2 group (68.3 kcal mol À1 ) and with the NH group of the side chain (for geometry see Fig. S1 †).Generally,  the deprotonated amino acids had higher bond energy values than the neutral amino acids (this fact is supported by Gibbs free energy calculations): Au-S bond energy was equal to 51.9 kcal mol À1 for Au + -Cys(ÀH + ) and 39.6 kcal mol À1 for Au + -Cys, Au-C bond energy was equal to 41.9 kcal mol À1 for Au + -Tyr(ÀH + ) and 35.4 kcal mol À1 for Au + -Tyr.

Interaction of amino acids with Au 2 cluster
Next, we studied the complexes of amino acids with a minimal neutral cluster Au 2 .In the equilibrium geometry of bare Au 2 , the bond length r(Au1-Au2) was equal to 2.465 A, according to RI-MP2/def2-TZVP method.This bond length tends to slightly diminish in the complexes: for example, r(Au1-Au2) was equal to 2.461 A in Au 2 -Gly.
Conformations of amino acids were carefully analyzed both free and in complex with Au 2 (see ESI † for cartesian coordinates).All unionized amino acids attach Au 2 to the nitrogen of the amino group, except arginine and histidine, which attach Au 2 to the nitrogen of the side-chain (these interactions between Au NCs and side-chains of amino acid residues may become even more important in a protein since amino group does participate in the formation of a peptide bond).Also, in the case of arginine gold plays the role of a proton acceptor and forms a nonconventional H-bond with the hydroxyl group (O-H/Au) of the carboxyl (Fig. 2).Amino acid complexes with gold are always monodentate, except for arginine, which forms a bidentate complex and involves hydrogen bonding.The structural parameters of the complex between arginine and Au 2 are presented on Fig. 2.
Thus, arginine forms an Au-N coordination bond with a length of 2.040 A and a valence angle N-Au-Au equal to 170.5 (Fig. 2).For Arg-Au 2 complex the C-NH bond is increased by 0.028 A aer the interaction with Au 2 cluster: the C-NH bond is equal to 1.308 for the Arg-Au 2 complex while for free Arg C-NH bond is equal to 1.280 A. In addition, the stretching mode of n(C-N) undergoes a blue shi with respect to that of the uncoordinated C-N group: from 1730.5 cm À1 to 1635.5 cm À1 .
Amino acids with deprotonated side chain surpass DG values of the neutral amino acids while Cys(ÀH + ) possesses the highest DG among the deprotonated amino acids.Cys(ÀH + ) attaches the cluster through the sulfur atom.Cys(ÀH + ) forms the Au-S bond with a length of 2.260 A and a valence angle C-S-Au equal to 102.6 (Fig. 3).For Cys(ÀH + )-Au 2 complex, the C-S bond stays intact aer the interaction with Au 2 cluster: the C-S bond is equal to 1.821 A for the Cys(ÀH + )-Au 2 complex and the same C-S bond is equal to 1.821 A for the free Cys(ÀH + ).
Cys(ÀH + ) had the highest DG among all amino acids (see Fig. 3 for complex geometry).Generally, the binding affinity of AAs to Au 2 cluster increases in the following order: Cys(ÀH + ) > Asp(ÀH + ) > Tyr(ÀH + ) > Glu(ÀH + ) > Arg > Gln, His, Met [ Asn, Pro, Trp > Lys, Tyr, Phe > His(+H + ) > Asp > Lys(+H + ) > Glu, Leu > Arg(+H + ) > Ile, Val, Ala > Thr, Ser > Gly, Cys.Obviously, we may conclude that Au 2 will preferably bind to the deprotonated residues of the amino acids rather than to the protonated ones in a peptide or protein.Surprisingly, neutral cysteine has the lowest binding energy among all the amino acids, which results in the highest DG difference between the neutral and deprotonated amino acid.Generally, the interaction of Au 2 with protonated and deprotonated AAs do not differ greatly.
It is generally believed that noble metal atoms preferably interact with sulfur in peptides and amino acids. 45,61For cysteine DG was equal to À19.1 kcal mol À1 (À17.7 kcal mol À1 ), and for deprotonated cysteine it was found to be À53.5 kcal mol À1 (À50.8 kcal mol À1 ) (Table 3).Cysteine has a pK a of 8.3, which means that alkalization of the solution containing Cys and Au 2 from neutral to alkaline pH would give the increase in interaction energy equal to 34.4 kcal mol À1 (33.1 kcal mol À1 ).The interaction energy of Au 2 with methionine, which also occurs through the sulfur, was equal to À28.1 kcal mol À1 (À24.5 kcal mol À1 ), which was one of the highest DG among the neutral amino acids.The disulde bond is less favorable for the formation of a complex with the gold cluster: the energy of the interaction between dimethyldisulde and Au 2 was equal to À23.4 kcal mol À1 , according to RI-MP2/ def2-TZVP method (for geometry of the complex see Fig. S2 †); it was equal to À22.7 kcal mol À1 , according to the PBE-D3/def2-TZVP calculation.
In general, our results are in agreement with experimental results showing that gold nanoparticles have the highest binding affinity with the peptides containing Cys, His, Met, and Tyr residues. 33In real experimental conditions, charge repulsion between negatively charged residues Asp(ÀH + ), Glu(ÀH + ) and chloroaurate anions frustrate the reduction reaction.However, some experimental protocols allow Asp and Glu residues to play signicant role in the synthesis of gold nanoclusters. 24Moreover, the stability of Au 2 complexes of all neutral and protonated amino acid residues is rather high (DG is more than À20 kcal mol À1 in absolute values), which indicates that all 20 proteinogenic AAs can stabilize gold NCs.

AIM and natural bond orbital (NBO) analysis of amino acid complexes with Au 2 cluster
We used Bader's AIM analysis to study the nature of amino acid interactions with Au 2 cluster in terms of electron density and its derivatives: the density of all electrons r(r), the Laplacian of electron density V 2 r(r), the Lagrangian kinetic energy term G(r), the potential energy density V(r), and the energy density H(r) are presented in Table 4.
One can see that in each case the electrostatic interaction is stabilizing since for each complex H(r) value is negative.The positive value of V 2 r(r) and negative value of H(r) in all cases means that Au-X bonds are partially covalent and partially electrostatic.
Since we know V(r) values we can calculate bond energies.Arginine had the highest Au-X bond energy value equal to 63.1 kcal mol À1 (Table 4), and this fact is supported by Gibbs  energy calculations, which state that arginine has the highest binding energy among neutral AAs.In the Arg-Au 2 complex, gold interacts both with the nitrogen of the side chain and with hydrogen of the carboxyl group.The hydrogen bond energy is pretty small -3.9 kcal mol À1 , but it is a reasonable value for a hydrogen bond. 36ext, we performed the NBO analysis.Natural charges of gold atom and amino acid atom to which the cluster is attached are presented in Table 5 (q Au and q X , respectively).When Au and X both have positive charges (the case of Cys-Au 2 complex), it obliquely indicates that Au-X bond has a covalent nature.When Au and X have opposite charges (all other cases), it indicates that Au-X bond has an electrostatic nature.In all the cases Au 2 cluster had a negative charge (q cluster ), which means that it oxidizes the coordinated amino acid.The bond orders were evaluated by using Wiberg's bond indices, which are presented in Table 5.The Wiberg bond indices were higher for the deprotonated negatively charged amino acid complexes with Au 2 than for the neutral complexes: W Au1-X is equal to 0.366 for Cys-Au 2 and is 0.580 for Cys(ÀH + )-Au 2 , W Au1-X is equal to 0.206 for Tyr-Au 2 and is 0.247 for Tyr(ÀH + )-Au 2 .On contrary, the Au-Au bond order is lower for deprotonated amino acids.
NBO analysis gives useful information when analyzing intramolecular bonding and interaction between bonds.The electron donor orbital and electron acceptor orbital occupancies, as well as the interacting stabilization energy E(2) obtained from the second-order perturbation theory analysis, are reported in Table 6.The larger the E(2) value, the more intensive the interaction between i electron donor orbital and j electron acceptor orbital, which means the more donating tendency from electron donor to electron acceptor.Delocalization of the electron density from occupied bonds or lone pair NBO orbitals to formally unoccupied antibond NBO orbitals indicates a stabilizing donor-acceptor interaction.The intramolecular interaction is formed by the orbital overlap between n, n*, s and s* bond orbitals, which leads to the intramolecular charge transfer (ICT) permitting the stabilization of the system.These interactions are observed as an increase in the electron density in anti-bonding orbital that weakens the respective bonds.
For each i donor orbital and j acceptor orbital, the stabilization energy E(2) of the i / j delocalization was calculated according to the following formula: where e i and e j are NBO orbital energies, and F is the Fock operator.
The amount of transferred charge from i donor orbital to j acceptor orbital was also calculated using the Fock operator and NBO orbital energies as follows: In Table 6, E(2) and q CT for the Au-X and Au-Au bonds of some complexes are presented.The charge is transferred from the lone pair of nitrogen and oxygen or s Au-Au bond to n* orbital of Au, Au-S or Au-Au s* anti-bond.In the case of Arg-Au 2 complex, the charge is transferred from the nitrogen lone pair to the lone pair of Au.In the Gly-Au 2 complex, the charge is transferred from the nitrogen lone pair to Au-Au s* antibonding orbital (Fig. 4).
We focused on the complexes of cysteine and tyrosine with the gold nanocluster since deprotonation of these amino acids gives the strongest energy gain when the AA-Au 2 complex is formed (Table 3).Moreover, only these two amino acids exhibited capability to produce uorescent complexes with silver clusters, as it was show experimentally. 61In the Cys-Au 2 complex, the intramolecular charge transfer occurs from the s Au-Au bond to Au-S s* anti-bonding orbital and leads to delocalization of 113.8 kcal mol À1 , which is the strongest stabilization energy among the regarded complexes.For the Cys(ÀH + )-Au 2 , the same ICT contributes to the stabilization energy of 65.1 kcal mol À1 .In the Tyr-Au 2 complex, ICT of the Paper RSC Advances electron from the nitrogen lone pair to the s* Au-Au anti-bond leads to delocalization of 36.3 kcal mol À1 .In the Tyr(ÀH + )-Au 2 complex, ICT of the n electron of oxygen lone pair to the s* Au-Au anti-bond leads to delocalization equal to 37.8 kcal mol À1 .

Binding energies between nucleobases and metals
We calculated the interaction energies of metal cations (Ag + and Au + ), neutral metal atoms (Ag0 and Au0), and diatomic metal clusters (Ag 2 and Au 2 ) with nucleobases, namely cytosine (Cyt) and adenine (Ade).Later, we compared the interaction energies between silver and gold, between different types of metal particles, between nucleobases and selected amino acids (Table 7).Our results are consistent with previously reported data for the nucleobases.Thus, for example, the interaction energy of silver atom Ag0 and cytosine was equal to À3.5 kcal mol À1 , according to Gwinn with co-authors. 53The same complex interaction energy was equal to À7.0 kcal mol À1 , according to Volkov et al. 64 In our case the result was À8.3 kcal mol À1 .The advantage of our work is that the vibrational spectra were calculated and Gibbs free energies of complex formation were determined along with DE total .Thus, for Ag0 complex with cytosine DG is equal to À1.3 kcal mol À1 .We have also investigated the complexes of Au 2 with adenine and protonated cytosine; for the latter it was done for the rst time.Yet, we didn't limit our study to only Me-N bonding, we also analyzed the interactions between metal atoms and the carbonyl oxygen of the cytosine.However, Me-O binding energies concede to Me-N interactions.Thus, for example, in Ag0_Cyt complex DG for the Ag-N binding is equal to À1.3 kcal mol À1 , while for Ag-O binding DG is only   7), so it's highly likely that Ag-O bond doesn't occur.The same is true for Au0_Cyt complex: DG for Au-O interaction is also positive: 0.3 kcal mol À1 .Geometry of the complexes between gold and silver ions and nucleobases, namely cytosine and adenine, are presented on Fig. 5. Ag + _Cyt and Au + _Cyt complexes have certain differences: the silver ion forms bonds with both nitrogen and oxygen while gold ion attaches only to N1.The same is true for Ag + _Ade and Au + _Ade complexes: Ag + forms bonds with N7 of the imidazole ring and nitrogen of the amino-group, Au + forms a bond only with N7.DG binding energy is higher for Au + _Cyt than for Ag + _Cyt complex: À74.3 kcal mol À1 and À55.2 kcal mol À1 , respectively.Au + _Cyt complex with Au-O bonding is less stable than the complex with Au-N bond: À67.9 kcal mol À1 and À74.3 kcal mol À1 , respectively (Table 7).Once again it shows that Me-N bonding is more stable than Me-O bonding.
We compared metal complexes of nucleobases and amino acids.In all the cases amino acid complexes are more stable than analogous nucleobase complexes.Thus, for example, the most stable complex of Au + is with cytosine (À74.3 kcal mol À1 ) while the binding energy of deprotonated cysteine with Au + is equal to À194.1 kcal mol À1 .Probably, the reason is that negative charge of the amino acid residue is favorable for high DG.
The interaction of neutral metal atoms and diatomic clusters with AAs is high for both silver and gold.It is known that aspartic acid residues may play a signicant role in the growth of protein-templated gold nanoclusters. 24For this reason the binding energy between gold and Asp are also high: for Au + , Au0, and Au 2 DG is equal to À169.8 kcal mol À1 , À16.9 kcal mol À1 , and À41.1 kcal mol À1 .

AIM analysis of metal complexes with cytosine
We used Bader's AIM analysis to study the nature of nucleobase interactions with metal ions, atoms, and nanoclusters in terms of electron density and its derivatives: r(r), V 2 r(r), G(r), V(r), and H(r) are presented in Table 8.Metal/nucleobase complex energy density H(r) value is negative for most of the complexes, which means that the electrostatic interaction between metal atoms and cytosine is stabilizing.The positive value of the Laplacian of electron density V 2 r(r) and negative value of H(r) in most of the cases means that Me-X bonds are partially covalent and partially electrostatic.In the case of Ag0_Cyt(+H + ) with Ag/ HN1 interaction and Ag 2 _Cyt(+H + ) with Ag-O interaction the local kinetic energy G(r) outweighs V(r): internuclear charge concentration is destabilizing, which is typical for a nonbonded situation, which in the case of Ag0_Cyt(+H + ) is also conrmed by positive DG value (1.9 kcal mol À1 ).
Ag + _Cyt complex attracted our interest since silver cation forms bonds with both nitrogen and oxygen atoms while Au + forms a bond only with N1 atom of cytosine.The higher energy of potential energy density for Au-N BCP results in the higher ), which is supported by Gibbs energy calculations (see Table 7).In the case of neutral metal atoms the situation is similar: for Ag0_Cyt complex Ag-N bond energy is equal to 21.6 kcal mol À1 while Au-N bond energy in Au0_Cyt complex is much higher: 40.53 kcal mol À1 .The same is true for Ag 2 _Cyt and Au 2 _Cyt complexes: bond energies are equal to 33.8 kcal mol À1 and 59.6 kcal mol À1 , respectively.These data are in agreement with Gibbs free energies for metal binding with nucleobases (Table 7): the binding energies are higher for gold atoms than for silver.

Conclusion
Binding energies between 19 amino acids and gold nanoparticles have been studied previously using molecular dynamics. 66In this study, Gibbs free energies of interaction of gold cation Au + and diatomic neutral Au 2 cluster with the full set of proteinogenic a-amino acids have been calculated by two methods: RI-MP2 and PBE-D3.The complexes of Au + and Au 2 with deprotonated side chains of all 20 amino acids exhibit the higher values of DG than that with the neutral and protonated amino acids, which is in agreement with the data obtained earlier for triatomic gold nanocluster Au 3 complexes with glycine and cysteine. 45However, the stability of Au 2 complexes with neutral and protonated amino acid residues is also rather high (DG is more than À20 kcal mol À1 in absolute values), which indicates that practically all 20 amino acids can stabilize gold NCs and nanoparticles.The binding affinity of AAs to the Au 2 cluster increases in the following order: Cys(ÀH + ) > Asp(ÀH + ) > Tyr(ÀH + ) > Glu(ÀH + ) > Arg > Gln, His, Met > Asn, Pro, Trp > Lys, Tyr, Phe > His(+H + ) > Asp > Lys(+H + ) > Glu, Leu > Arg(+H + ) > Ile, Val, Ala > Thr, Ser > Gly, Cys.Generally, the interaction of gold atoms with protonated and deprotonated amino acid residues do not differ greatly, which is in agreement with the experimental evidences that gold cluster synthesis occurs in a wide range of pH. 24,67The fact that deprotonated cysteine has the highest binding energy with both Au 2 and Au + among all the amino acids explains the ne synthesis of gold nanoclusters on thiolates. 68,69ur results suggest that binding energy between neutral silver clusters and DNA is rather weak (DG is equal to À1 to À9 kcal mol À1 ) as compared to charged particles (À55 to À63 kcal mol À1 ).1][52] The interaction between Au0 atoms and nucleobases is also rather weak (À4 to À6 kcal mol À1 ); however, the binding energy between diatomic cluster and DNA is higher (À25 to À26 kcal mol À1 ).This obstacle explains the existence of neutral gold nanoclusters stabilized by poly-cytosine and poly-adenine. 54peaking about protein templates, the interaction of neutral metal atoms and diatomic clusters with amino acid residues is high for both silver and gold.7]22 Moreover, the signicant difference in the binding energy of neutral gold and silver atoms with nucleobases and amino acids apparently means that unlike DNA template neutral metal atoms are strongly bound to amino acid residues and can't freely diffuse in a polypeptide globula.This fact allows to make a conclusion that formation of metal nanoclusters in proteins occurs through the nucleation of Au atoms located on the neighboring amino acid residues, and the exibility of the amino acid residue side chains and protein chain as a whole plays a signicant role in this process.
Finally, based on the AIM analysis, we have found that for all complexes amino acid-Au 2 bonds are partially electrostatic and partially covalent, the same is true for amino acid complexes with Au + .

Fig. 1
Fig. 1 Geometries of deprotonated anionic amino acids bound to gold cation.

Table 2
Amino acid complexes with Au + ; bond critical point (BCP) data from AIM analysis

Table 4
Amino acid complexes with Au 2 ; bond critical point (BCP) data from AIM analysis

Table 5
Calculated natural population analysis (NPA) charges and Wiberg bond indices of the optimized structures of amino acid-Au 2 complexes This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 34149-34160 | 34155

Table 6
Second order perturbation theory analysis of Fock matrix in NBO basis for some selected amino acid-Ag 2 complexes

Table 7
Gibbs free energy (G) and total energy (E) in kcal mol À1 for metal binding with amino acids and nucleobases; the table contains both literature data and results calculated in this study with RI-MP2/ def2-TZVP method This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 34149-34160 | 34157 Paper RSC Advances energy of the bond equal to 70.4 kcal mol À1 as compared with Ag-N (24.3 kcal mol À1 ) and Ag-O (21.5 kcal mol À1