Dinuclear Metal-Mediated Homo Base Pairs with Metallophilic Interactions: Theoretical Studies of G₂M₂²⁺ (M = Cu, Ag, and Au) Ions

Abstract

Dinuclear metal-mediated homo base pairs are interesting clusters with highly symmetric structures and significant stabilities. The geometric and electronic structures of G₂M₂ ²⁺ (G = Guanine, M = Cu, Ag or Au) cluster ions were studied with quantum chemical calculations. The lowest-energy isomers of G₂M₂ ²⁺ cluster ions have C_2h symmetries with an approximately antiparallel alignment of two sets of N-M∙∙∙O groups being formed in the planar structures. The M-M distances are shorter than the sum of van der Waals radii of corresponding two homo coinage metal atoms, showing that metallophilic interactions significantly exist in these complexes. They have the large HOMO−LUMO gaps of about 5.80 eV at the DFT level and the bond dissociation energies of more than 5.60 eV at the DFT/B3LYP level, indicating that these cluster dications are highly stable. The second lowest-energy isomers stabilized by an approximately parallel alignment of one set of O-M-O group and one set of N-M-N group are found to be close to the lowest-energy isomers in energy. The barrier between the two isomers of G₂M₂ ²⁺ cluster ions is significantly large, also showing that these lowest-energy isomers are very stable.

Introduction

Metal ion-base pair complexes have attracted tremendous attention because of their importance in the development of nanotechnology and biotechnology^1–8. They have significantly thermal duplex stabilization as well as the conductive property. It has been reported that metal-mediated base pairs can be used as nanowires², novel sensors competent to detect metal ions in aqueous solutions⁹, bifacial nucleobases¹⁰, and logic gates¹¹. In these metal ion-base pair complexes, dual complementary hydrogen bonds between nucleobases are replaced by the metal-nucleobase bonds¹². Dinuclear metal ion-mismatched base pairs have become an interesting class of metal ion-base pair complexes in recent years. There have been many theoretical and experimental investigations on the complexes of dinuclear silver ions and mismatched base pairs^13–19. More recently, dinuclear Cu^II and Hg^II complexes containing an artificial nucleobase (9-ethyl-1, N6-ethenoadenine) have been prepared and their crystal structures have been determined by Mandal et al.^20–22. Their studies show that dinuclear T-Hg ^II ₂ -εA base pair has two sets of parallel M-N bonds with anionic ligands partially compensating the charge of metal ions.

The terms “aurophilic bonding” and “aurophilic interactions” for Au⁺-Au⁺ interactions were introduced by Schmidbaur et al. in 1988^23,24. The weaker attractive interactions between coinage metal cations with closed-shell configurations in coinage metal compounds have been termed as “numismophilicity” (from the Latin word “numisma” meaning a coin) by Vicente et al.²⁵ in 1993, and then extended as “metallophilic interactions” for closed-shell interactions of metal atoms by Pyykkö²⁶ in 1994. Metallophilic interactions are stronger than van der Waals forces but weaker than covalent bonding, close to hydrogen bonding in energy, influencing significantly a number of structural and characteristics of metal compounds. Concerning the intensities of metallophilic interactions, it is generally believed that aurophilic interactions should be stronger than argentophilic bonding due to the strong relativistic effects of Au. Ag ≈ Au seems more reasonable because Ag-Ag distances are very close to Au-Au distances in a family of analogous complexes^27,28.

In our preceding papers, we have investigated the coinage metal-nucleobase complexes by photoelectron spectroscopy, photodissociation, and theoretical calculations^29–31. G₂M⁺ (G = guanine, M = Cu, Ag or Au) cluster ions prefer planar structures with the metal cations interacting with the N7 atoms of guanine. In my previous papers, metal-to-ligand (MLCT), ligand-to-metal (LMCT), intraligand (LL) charge transfer processes have been found to exist in the photodissociation of G₂M⁺ ions. The bonding and electronic structures of dinuclear coinage metal-mediated base pairs containing divalent metal ions remain elusive. Cu⁺, Ag⁺, and Au⁺ cations have a ¹S electronic ground state with the valence electron configuration nd¹⁰(n + 1)s⁰(n + 1)p⁰. This poses the question about the electron configuration of metal cations in G₂M₂ ²⁺ complexes and the nature of chemical bonding in the metallophilic and nucleobase-M⁺-nucleobase interactions. Gold exhibits larger relativistic effects than those of Cu and Ag, such as 5d relativistic expansion and destabilization, and 6s relativistic stabilization and contraction^32–39. It is interesting to pinpoint whether dinuclear coinage metal-mediated homo base pairs are also stable and in which direction gold-mediated base pairs might deviate from the copper or silver analogues. In this work, we investigate the whole G₂M₂ ²⁺ series for M = Cu, Ag and Au and examine the chemical bonding using various theoretical methods. The calculated results for the G₂M₂ ²⁺ complexes provide new aspects for chemical bonding of the coinage metals and help to find potential applications of metal-mediated base pairs complexes.

Theoretical results

In search of the global minimum of G₂M₂ ²⁺ (M = Cu, Ag or Au) cluster dications, various possible initial geometric structures have been considered. The canonical (K-N9H) tautomer⁴⁰ of guanine was taken into account in the search of their low-energy isomers. The structures, bond lengths, and N-M-O angles of low-energy isomers of these complexes are displayed in Fig. 1 and Table 1. Relative energies (eV), symmetries and electronic states of the low-energy isomers of G₂M₂ ²⁺ cluster ions are shown in Table 2. The optimized structures of G₂M₂ ⁺ cluster ions are in singlet spin states. The triplet and quintet spin states are much less stable than the singlet spin states in energy. All of these complexes are planar structures in guanine-M₂-guanine style, containing one set of nearly linear N–M–N and one group of roughly linear N–M–O bonds.

Figure 1.

Structures and relative energies of the low-lying isomers of G₂M₂ ²⁺ cluster ions. The bond distances are in angstroms.

Table 1.

Optimized Bond Lengths and ∠N-M-O Angles of the Lowest-lying Isomers of G₂M₂ ²⁺ Cluster Ions at the DFT Level^a.

	Distance	Vacuum	COSMO
G2Cu2 2+	Cu-Cu	2.797	2.680
	Cu-N	1.883	1.852
	Cu-O	1.860	1.844
	∠N-Cu-O	168.7	165.3
G2Ag2 2+	Ag-Ag	2.982	2.815
	Ag-N	2.117	2.093
	Ag-O	2.115	2.102
	∠N-Ag-O	174.1	169.7
G2Au2 2+	Au-Au	2.991	2.906
	Au-N	2.032	2.009
	Au-O	2.060	2.040
	N-Au-O	173.0	170.6

^aThe bond distances are in angstroms and the bond angles are in degrees.

Table 2.

Relative Energies (eV), Symmetries and Electronic States of the Low-energy Isomers of G₂M₂ ²⁺ Cluster Ions.

	Isomers	Sym.	State	ΔE (eV)
				PBE/TZ2P	CAMY-B3LYP	COSMO
G2Cu2 2+	1A	C2h	1Ag	0.00	0.00	0.00
	1B	C2V	1A1	0.08	0.07	0.04
	1C	Cs	1A′	1.34	1.32	1.28
G2Ag2 2+	2A	C2h	1Ag	0.00	0.00	0.00
	2B	C2V	1A1	0.05	0.05	0.02
	2C	Cs	1A′	0.68	0.66	0.62
G2Au2 2+	3A	C2h	1Ag	0.00	0.00	0.00
	3B	C2	1A	0.10	0.09	0.06
	3C	Cs	1A′	1.28	1.26	1.23

As seen in Fig. 1, all the lowest-energy isomers 1A, 2A and 3A of G₂M₂ ²⁺ cations have perfectly planar structures with C_2h symmetries. An approximately antiparallel orientation of two sets of N-M∙∙∙O groups are formed in these isomers 1A, 2A and 3A. The N-M∙∙∙O units have nearly linear arrangements and the order of their angles is Cu < Au < Ag (∠N-Cu-O = 168.7°, ∠N-Ag-O = 174.1°, ∠N-Au∙∙∙O = 173.1°). The Cu-N distances are near 1.893 ± 0.010 Å, and Cu-O distances are 1.855 ± 0.006 Å, depending on the structures. The order of M-N or M-O distances is Cu < Au < Ag, in agreement with the order of the atomic radii increments suggested by Pyykkö⁴¹ (Cu ~ 1.12 Å, Ag ~ 1.28 Å, Au ~ 1.24 Å). Considering the Au-Au distances, aurophilic Au-Au distances can vary from 2.85 Å to 3.50 Å depending on their strength²⁸. The Au-Au distance is 2.991 Å in the lowest-energy isomer 3A, much larger than the single-bond covalent radii (2.48 Å) recommended by Pyykkö⁴¹, indicating that there is hardly strong Au–Au bonding interaction except the aurophilic interaction. The Ag-Ag distance is near 2.982 Å in isomer 2A, significantly longer than the distance of a Ag-Ag single bond (2.53 Å), but shorter than the sum of van der Waals radii (3.44 Å)²⁷. It is very close to the Au-Au distance in isomer 3A, showing that the metallophilic bonding for Ag and Au is very similar. The Cu-Cu distances in isomer 1A are near 2.797 Å, close to the distances of the dimer [{H₃PAgCl}₂] with cuprophilic interactions (2.637–2.809 Å at DFT and ab initio levels)⁴². Concerning metal-metal vibrations, the Cu-Cu vibrational harmonic frequency of isomer 1A is 122.5 cm⁻¹ (force constant F = 0.33 mdyn•Å⁻¹). The Ag-Ag vibrational frequency of isomer 2A is 101.1 cm⁻¹ (force constant F = 0.47 mdyn•Å⁻¹), in accordance with the Ag-Ag vibrations (75–125 cm⁻¹) of crystals of Tl[Ag(CN)₂] detected by a detailed Raman experiment⁴³. The Au-Au vibrational frequency of isomer 3 A is 94.8 cm⁻¹ (force constant F = 0.57 mdyn•Å⁻¹). The order of M-M stretching frequencies is Cu > Ag > Au.

The second lowest-energy isomers 1B, 2B, and 3B of G₂M₂ ²⁺ cluster ions can be considered as derived from isomers 1A, 2A, and 3A, respectively, by revolving guanine about 180° round the C₂ axis. They are stabilized by an approximately parallel orientation of one set of O-M-O group and one set of N-M-N group, close to the lowest-lying isomers in energy at the DFT level. One note that isomer 3B has a nonplanar structure with C₂ symmetry. The M-M distances in isomers 1B-3B are slightly shorter than those in isomer 1A-3A. The third lowest-energy isomers of G₂M₂ ²⁺ cluster ions have planar structures with one metal ion involving in the formation of one set of O-M-N group and another metal ion binding to N7 atom of guanine. Isomers 1C, 2C, and 3C are much higher in energy than the lowest-lying isomers 1A, 2A, and 3A. When the aqueous solvent environment is roughly modeled using the COSMO solvent model, the energy differences of two lowest-energy isomers become closer relative to those in the vacuum environment. All the bond lengths become slightly shorter and the order of ∠N-M-O angles becomes Cu < Ag < Au.

Effective atomic charges of the lowest-energy isomers (1A, 2A, and 3A) of G₂M₂ ²⁺ (M = Cu, Ag, and Au) cluster ions from various population schemes are displayed in Table 3. The charges from the multipole-deformation prescription are slightly larger than those from the Hirshfeld or Voronoi Deformation Density (VDD) prescriptions. Our studies have showed that the Voronoi and Hirshfeld density partitionings are consistent with the chemical shifts of the core-level energies of atoms⁴⁴. According to the Hirshfeld or VDD prescriptions, the coinage metals Cu, Ag, and Au carry large positive charges between 0.18 and 0.34, while the nitrogen and oxygen atoms bonded to the metal atoms carry negatively charges. Thus, strong electrostatic attraction exist in the interactions between the metal atoms and N or O atoms, while the electron-acceptor strength of coinage metal atoms has the order Au > Cu > Ag.

Table 3.

Effective Atomic Charges of the Lowest-energy Isomer (1 A, 2 A, and 3 A) of G₂M₂ ²⁺ Cluster Ions.

	M	Hirshfeld charge	Voronoi charge	MDC-q
G2Cu2 2+	Cu1, Cu2	0.29	0.27	0.39
	N1, N2	−0.11	−0.13	−0.40
	O1, O2	−0.21	−0.22	−0.42
G2Ag2 2+	Ag1, Ag2	0.34	0.30	0.53
	N1, N2	−0.11	−0.13	−0.50
	O1, O2	−0.23	−0.23	−0.49
G2Au2 2+	Au1, Au2	0.22	0.18	0.43
	N1, N2	−0.08	−0.09	−0.50
	O1, O2	−0.20	−0.19	−0.48

To understand the relative stabilities of the lowest-lying isomers and the second lowest-energy isomers of G₂M₂ ²⁺ cluster ions, the possible transition barriers were calculated between them using the Berny method at the DFT/B3LYP level. Obtained transition-state structures were confirmed to connect the correct reactants and products by intrinstic reaction coordinate (IRC). Vibrational analyses show that there is only one imaginary frequency in the transition-state structures. The lowest transition states for the isomers of G₂M₂ ²⁺ cluster ions were determined with conversion barriers of more than 1.00 eV. The barriers between the two low-lying isomers of G₂M₂ ²⁺ cluster ions are significantly large, and it is hard for them to convert at room temperature.

Discussion

The Cu 3d-derived valence MOs and lowest unoccupied molecular orbital (LUMO) 4a_u of the lowest-energy isomer of G₂Cu₂ ²⁺ cation are displayed in Figure S1 and Table 4. The LUMO 4a_u has 95% contribution from the 2p characters of C, N and O atoms, while the 4p orbital of Cu just has 5% contribution to the LUMO. The 3d orbitals of Cu atoms have 90% contribution to the HOMO 5b_u (−11.2 eV), while the 2p orbitals of N and O atoms just have 10% contribution to the HOMO. Three sets of energetically degenerate 4a_g, 2b_g, 4b_u MOs, and one set of 2a_u MO are mainly of the 3d orbitals of Cu atoms. The ds hybridizations of the Cu atoms are mainly involved in three sets of 2a_g, 3a_g, and 3b_u MOs. Seven sets of 3b_g, 3a_u, 1b_g, 2b_u, 1a_u, 1a_g, and 1b_u MOs are the combinations of the 3d orbitals of two Cu atoms and the 2p orbitals of C, N, and O atoms. From these analyses, the cuprophilic interaction occurs mainly through the mutual stabilization of nine sets of 3a_u, 4a_g, 2b_g, 4b_u, 3a_g, 3b_u, 2a_u, 2a_g, and the highest occupied 5b_u MOs.

Table 4.

Characters, Orbital Energies (in eV), and AO Contributions in % (Largest is Bold) of the Cu 3d-derived MOs and Lowest Unoccupied MO of the Lowest-lying Isomer of G₂Cu₂ ²⁺ dication.

MO	type	ε	occ	Cu(d)	Cu(s)	Cu(p)	N(p)	O(p)	C(p)
1bu	Cu(dsp) + C(2p) + N(2p) + O(2p)	−16.3	2	16	2	3	63	3	13
1ag	Cu(dsp) + C(2p) + N(2p) + O(2p)	−16.1	2	10	3	2	63	7	15
1au	Cu(d) + C(2p) + N(2p) + O(2p)	−14.6	2	11	—	—	63	8	18
2bu	Cu(d) + C(2p) + N(2p) + O(2p)	−14.1	2	20	—	—	8	66	6
2ag	Cu(dsp)	−12.6	2	85	13	2	—	—	—
1bg	Cu(d) + N(2p) + O(2p)	−12.2	2	52	—	—	31	15	2
2au	Cu(d)	−12.2	2	100	—	—	—	—	—
3bu	Cu(ds)	−12.1	2	95	5	—	—	—	—
3ag	Cu(ds)	−11.9	2	94	6	—	—	—	—
4bu	Cu(d)	−11.9	2	100	—	—	—	—	—
2bg	Cu(d)	−11.9	2	100	—	—	—	—	—
4ag	Cu(d)	−11.8	2	100	—	—	—	—	—
3au	Cu(d) + C(2p) + N(2p) + O(2p)	−11.8	2	83	—	—	10	4	3
3bg	Cu(d) + C(2p) + N(2p) + O(2p)	−11.3	2	31	—	—	33	9	27
5bu	Cu(d) + N(2p) + O(2p)	−11.2	2	90	—	—	3	7	—
4au	Cu(p) + C(2p) + N(2p) + O(2p)	−5.6	0	—	—	5	27	9	59

The LUMO 6a_u (−5.4 eV) of G₂Ag₂ ²⁺ cluster ions contains 95% C, N, and O 2p, and 5% Ag 5p characters (Table 5 and Figure S2), similar to the lowest unoccupied 4a_u MO of Ag’s lighter homologue G₂Cu₂ ²⁺. The 2p orbitals of N and O atoms have 97% contribution to the HOMO 5b_g (−11.4 eV), while the 3d orbitals of Ag atoms just have 3% contribution to the HOMO. The characters and bonding of the highest occupied 5b_g MO of G₂Ag₂ ²⁺ dication are completely different from those of the highest occupied 5b_u MO of Ag’s lighter homologue. Seven sets of 6a_g, 4b_g, 5a_u, 5a_g, 1b_g, 1a_u, and 1a_g MOs have major contribution from N 2p character and minor contribution from the 4d orbitals of Ag atoms, 2p orbitals of C and O atoms, while six sets of 1b_u, 3a_g, 2b_g, 4a_g, 3b_u, and 4b_u MOs have significant contribution from the 4d orbitals of Ag atoms and only little contribution from 2p orbitals of C, N and O atoms. The argentophilic interaction occurs mainly through the mutual stabilization of three sets of low 1b_u, 2a_g and 2a_u MOs, two sets of nearly degenerate 3b_g and 2b_u MOs, and two sets of 4a_g, and 4b_u MOs, and also a little stabilized by two sets of 5a_g and 6a_g MOs.

Table 5.

Characters, Orbital Energies (in eV), and AO Contributions in % (Largest is Bold) of the Ag 4d-derived MOs and Lowest Unoccupied MO of the Lowest-lying Isomer of G₂Ag₂ ²⁺ Cluster ion.

MO	ε	occ	Ag(d)	Ag(s)	Ag(p)	N(p)	O(p)	C(p)
1ag	−15.9	2	18	—	2	54	11	15
1au	−14.7	2	37	—	—	48	5	10
1bu	−14.5	2	72	—	—	5	21	2
1bg	−14.4	2	27	—	—	50	4	19
2ag	−14.3	2	94	4	2	—	—	—
3ag	−14.0	2	47	—	—	8	40	5
2au	−14.0	2	100	—	—	—	—	—
2bg	−13.9	2	53	—	—	26	9	12
3au	−13.6	2	30	—	—	32	—	38
3bg	−13.6	2	100	—	—	—	—	—
2bu	−13.6	2	98	2	—	—	—	—
4ag	−13.4	2	77	—	—	3	19	1
3bu	−13.3	2	43	—	—	18	37	2
5ag	−13.0	2	32	—	—	44	18	6
5au	−12.9	2	31	—	—	36	26	7
4bg	−12.9	2	20			61	17	2
6ag	−12.7	2	26	14	—	45	6	9
4bu	−12.0	2	65	10	2	14	9	—
5bg	−11.4	2	3	—	—	50	10	37
6au	−5.4	0	—	—	5	25	12	58

The G₂Au₂ ²⁺ cluster ion has 10 Au 5d AOs, which span a_g (1a_g, 2a_g, 3a_g, and 4a_g MOs) + a_u (low 1a_u, 2a_u, and 3a_u MOs) + b_g (1b_g and the highest occupied 2b_g MOs) + b_u (1b_u and 2b_u MOs) representations in the C_2h symmetry (Figure S3 and Table 6). Suppressing the Au(5d) AO participation, one note that the lowest unoccupied 4a_u MO at −5.7 eV is the combinations of three sets of C(2p), N(2p), O(2p) AOs, and one set of virtual Au(6p) AOs. Mixing of 5d AOs of two gold atoms yields the 2a_u (−13.4 eV) σ bonding orbitals in the middle of the valence band. Due to the relativistic effects, the strong mixing of Au 5d and 6 s AOs in particular the 2a_g (−14.0 eV), 4a_g (−13.0 eV), and 2b_u (−11.6 eV) MOs leads to the significant Au 5d-6s hybridization. It is clear that Au 5d AOs play some role in the highest occupied 2b_g (−11.5 eV) MO as the Au 5d AOs and π_g bonding orbital of C(2p), N(2p), and O(2p) AOs counteract each other. From these analyses, the aurophilic interaction occurs mainly through the mutual stabilization of three sets of 5a_g, 6a_g, and 3b_u δ orbitals, two sets of 3a_u and 3a_g σ orbitals, and also a little stabilized by threee sets of 4b_u, 4a_u and 2b_u MOs, and two sets of degenerate 3b_g and 4b_g MOs. It is worth mentioning that, the bonding interaction in Au₂G₂ ²⁺ cluster ion involves the valence electron configuration 5d⁹6 s¹6p° rather than the nd¹⁰(n + 1)s°(n + 1)p° configuration at Cu or Ag in Au’s homologues. The result seems reasonable because the relativistic effects in the valence shells of gold atom stabilize the s-atomic orbitals (AOs) and destabilize the d-AOs, leading to the drastically reduced 5d-6s gap of Au, and then resulting in Au’s particular electron configuration in the metal-mediated base pairs complexes.

Table 6.

Characters, Orbital Energies (in eV), and AO Contributions in % (Largest is Bold) of the Au 5d-derived MOs and Lowest Unoccupied MO of the Lowest-lying Isomer of G₂Au₂ ²⁺ Cluster ion.

MO	ε	occ	Au(d)	Au(s)	Au(p)	N(p)	O(p)	C(p)	H(s)
1bu	−16.9	2	10	—	2	57	8	16	7
1ag	−16.6	2	11	—	2	50	13	21	3
1au	−15.0	2	34	—	—	50	5	11	—
1bg	−14.7	2	13	—	—	61	6	20	—
2bu	−14.6	2	50	—	—	8	39	3	—
2ag	−14.4	2	33	—	—	7	60	—	—
3ag	−14.0	2	80	20	—	—	—	—	—
2bg	−14.0	2	36	—	—	41	14	9	—
2au	−13.8	2	11	—	—	43	2	44	—
3au	−13.4	2	100	—	—	—	—	—	—
4ag	−13.1	2	30	—	—	57	7	6	—
5ag	−13.0	2	81	19	—	—	—	—	—
3bu	−12.8	2	94	6	—	—	—	—	—
3bg	−12.8	2	64	—	—	29	4	3	—
4bg	−12.8	2	73	—	—	21	5	1	—
6ag	−12.7	2	57	25		10	6	2	—
4au	−12.6	2	59	—	—	18	16	7	—
4bu	−11.6	2	57	26	3	7	7	—	—
5bg	−11.5	2	10	—	—	45	10	35	—
5au	−5.7	0	—	—	3	26	13	58	—

For G₂Cu₂ ²⁺ cluster dication, the HOMO (Cu d) → LUMO (G₂ π) excitation can be classified as metal-metal-to-ligand charge transfer (MMLCT), while for G₂Ag₂ ²⁺ and G₂Au₂ ²⁺ cluster dications, the HOMO → LUMO excitations are able to be classified as ligand-to-ligand (LL) charge transfer. These charge transfer processes are different from those in mononuclear metal-mediated base pairs^28,31, modified significantly by the presence of the Cu–Cu, Ag-Ag, and Au-Au interactions. It may provide valuable information for their absorption or photodissociation experiments.

The lowest-energy isomer 2A of G₂Ag₂ ²⁺ dication has larger HOMO−LUMO gap of 5.98 eV at the DFT level, as compared to Ag’s heavier (HOMO-LUMO gap nearly 5.80 eV) and lighter homologue (HOMO-LUMO gap nearly 5.58 eV). However, the bond dissociation energies (BDEs) of G₂M₂ ²⁺ cluster ions calculated based on the differences between the total energy of the parent ion (G₂M₂ ²⁺) and the total energies of all the fragments (G and M⁺) at the DFF/B3LYP level (G₂M₂ ²⁺ → 2 G + 2 M⁺) are 8.52, 5.66, 8.50 eV, for Cu, Ag, and Au, respectively. This indicates that the sum of N-M, M-O, and metallophilic interactions in G₂Ag₂ ²⁺ cluster ion is much weaker than those in Ag’s heavier and lighter homologues.

Because dinuclear metal-mediated base pairs can be introduced as DNA sequences, it is interesting to compare the structural parameters of isolated G₂M₂ ²⁺ cluster ions with those of TGM₂GT²⁺ (M = Cu, Ag and Au) cluster ions. Structures and M-N, M-O and M-M bond lengths of optimized TGM₂GT²⁺ (M = Cu, Ag and Au) cluster ions have been shown in Fig. 2. The Cu-N and Cu-Cu bond lengths of TGCu₂GT²⁺ ions have been slightly shortened relative to those of G₂Cu₂ ²⁺ cluster ions, while the Ag-N bond lengths of TGAg₂GT²⁺ ion are slightly shorter than those of G₂Ag₂ ²⁺ ions. TGAu₂GT²⁺ ion has slightly longer Au-Au bond length when compared with G₂Au₂ ²⁺ ions. Lengthened sequences containing G₂Cu₂ ²⁺ and G₂Au₂ ²⁺ cluster ions have slightly weaker metallophilic interactions relative to the isolated G₂M₂ ²⁺ cluster ions. However, lengthened sequences containing G₂Ag₂ ²⁺ cluster ions have almost the same argentophilic interactions relative to the isolated G₂M₂ ²⁺ cluster ions.

Figure 2.

Structures and M-N, M-O and M-M bond lengths of TGM₂GT²⁺ (M = Cu, Ag and Au) cluster ions.

Conclusions

The geometric and electronic structures of G₂M₂ ²⁺ (G = Guanine, M = Cu, Ag or Au) cluster ions have been investigated with DFT approaches. The lowest-lying isomers of the presently investigated species have C_2h symmetries with an approximately antiparallel alignment of N-M∙∙∙O groups being formed in the planar structures. Their HOMO-LUMO gaps significantly above 5.50 eV at the DFT level, indicating that these cluster dications are highly stable. The Ag-Ag, and Au-Au distances in these isomers are very similar, slightly longer than the Cu-Cu distance. Cu-Cu, Ag-Ag and Au-Au distances are shorter than the sum of van der Waals radii of corresponding two homo coinage-metal atoms, showing that metal-metal bonding can be characterized as weak but significant metallophilic interactions. From above-mentioned orbital analyses, s and d orbitals of metal atoms and p orbitals of C, N and O atoms all significantly participate in the orbital interactions. The compositions and bonding of the HOMO of G₂Cu₂ ²⁺ dication are completely different from those of the highest occupied MOs of Cu’s heavier homologues. The bonding interactions in Au₂G₂ ²⁺ dication involve the valence electron configuration 5d⁹6s¹6p° rather than the nd¹⁰(n + 1)s⁰(n + 1)p⁰ configuration at Cu or Ag in Au’s homologues, although it may not be attached as an absolute physical meaning. The second lowest-energy isomers stabilized by an approximately parallel alignment of one set of O-M-O group and one set of N-M-N group are found to be close to the lowest-energy isomers in energy. The barrier between the two isomers of G₂M₂ ²⁺ cluster ions is significantly large, also showing that these lowest-energy isomers are very stable.

Theoretical methods

To investigate the geometric structures and energetics of G₂M₂ ²⁺ (G = guanine, M = Cu, Ag or Au) cluster dications, DFT calculations were performed with Amsterdam Density Functional program (ADF 2013.01)^45–47. The geometries were fully optimized using the generalized gradient approximation (GGA)⁴⁸ of Purdue-Becke-Ernzerhof (PBE), converging to an energy gradient <10⁻⁵ Hartree∙nt Å⁻¹ at an Kohn-Sham SCF criterion <10⁻⁸ a.u. The uncontracted Slater basis sets with the quality of triple-plus two polarization functions (TZ2P) were used, with the frozen core approximation applied to the [1s²-2p⁶] core for Cu, the [1s²-3d¹⁰] core for Ag, the [1s²-4f¹⁴] core for Au, [1s¹] core for H and the [1s²] cores for C, N and O. The scalar relativistic was taken into account by the Zero Order Regular Approximation (ZORA). Optimized minimum structures were verified with nonexistence of imaginary frequencies in the analyses of vibrational frequencies. For more reliable energies, the single-point energy was calculated using the CAMY-B3LYP/TZ2P⁴⁹ density functional method at the PBE/TZ2P geometries. The corrections of zero-point energy (ZPE) were also included in calculating the relative energies. To determine the atomic charges of Cu, Ag, Au, relevant N, and O atoms in these clusters, the population partitioning schemes of Hirshfeld^50,51, Voronoi⁵², and multipole derived charges (MDC-q)⁵³ were calculated.

The conductor-like screening model (COSMO) was also used to approximately explore the influence of a aqueous solvent environment on the geometries and energetics of the G₂M₂ ²⁺ cluster cations⁵⁴. The following atomic COSMO-default radii from the ADF code were used: H 1.350, C 1.700, N 1.608, O 1.517, Cu 1.883, Ag 2. 025, and Au 2.025⁵⁵. The parameters for water solvent were used in the COSMO calculations as water was the most common solvent used in the experimental studies for comparison.

The structures of G₂M₂ ²⁺ ions and transition states between two nearly degenerated isomers of G₂M₂ ²⁺ cluster dications were optimized using the GAUSSIAN 09 program⁵⁶. The Becke 3-parameter-Lee-Yang-Parr (B3LYP)^57,58 density functional method with the 6–31 + + G(d,p) basis set was chosen for nucleobases. The ECP10MDF, ECP28MDF, ECP60MDF relativistic effective core potential (RECP) developed by the Stuttgart-Cologne groups were chosen for Cu 1s-2p (3spd4s), Ag 1s-3d (4spd5s), and Au 1s-4f (5spd6s), respectively⁵⁹. Gaussian type one-electron basis sets of MDF_VDZ were used for Cu, Ag and Au^59,60.

Author Contributions

G.-J.C. conceived the idea, performed the calculations and wrote the manuscript.

Competing Interests

The author declares that they have no competing interests.