Dispersion-Corrected Density Functional Theory Study of the Noncovalent Complexes Formed with Imidazo[1,2-a]pyrazines Adsorbed onto Silver Clusters

Abstract

Imidazo[1,2-a]pyrazines are cyclic amidine-type compounds composed of α-amino acid residues. A full structural identification of these molecules constitutes an analytical challenge, especially when imidazo[1,2-a]pyrazines are obtained from physical processes (e.g., sublimation and pyrolysis of amino acids). A valuable source of molecular information can be obtained from absorption spectroscopies and related techniques encompassing the use of metallic substrates. The aim of this study is to provide new knowledge and insights into the noncovalent intermolecular interactions between imidazo[1,2-a]pyrazines and two Ag_n (n = 4 and 20) clusters using density functional theory (DFT) methods. Semiempirical DFT dispersion (DFT-D) corrections were addressed using Grimme’s dispersion (GD2) and Austin–Petersson–Frisch (APF) functionals in conjunction with the 6-31+G(d,p) + LANL2DZ mixed basis set. These DFT-D methods describe strong interactions; besides, in all cases, the APF dispersion (APF-D) energies of interaction appear to be consistently overestimated. In comparison with B3LYP calculations, the mean values for the difference in the energies of interaction calculated are 2.25 (GD2) and 6.24 (APF-D) kcal mol^–1 for Ag₄–molecules, and 2.30 (GD2) and 8.53 (APF-D) kcal mol^–1 for Ag₂₀–molecules. The effect of applying GD2 and APF-D corrections to the noncovalent complexes is nuanced in the intermolecular distances calculated, mainly in the Ag···N(amidine) bonding, which appears to play the most important role for the adsorptive process. Selective enhancement and considerable red shifts for Raman vibrations suggest strong interactions, whereas a charge redistribution involving the metallic substrate and the absorbate leads to a significant rearrangement of frontier molecular orbitals mainly in the Ag₂₀–molecule complexes. Finally, time-dependent DFT calculations were carried out to access the orbital contributions to each of the transitions observed in the absorption spectrum. The corresponding UV–vis spectra involve transitions in the visible region at around 400 and 550 nm for the Ag₄–molecule and the Ag₂₀–molecule complexes, respectively.

Introduction

Imidazo[1,2-a]pyrazines are heterocyclic structures composed of α-amino acid residues contained into a five-membered imidazole fused to a six-membered pyrazine ring with a bridgehead nitrogen atom. These unusual molecules are of great interest from the point of view of amino acid–peptide chemistry because this class of amidine-type compounds might manifest themselves as the central compounds for the whole amidine chemistry.¹ The natural occurrence of imidazo[1,2-a]pyrazines was discovered in bioluminescence sea organisms² involving luciferine³ and coelenterazine^4,5 systems, which constitute the most representative natural imidazopyrazines compounds. Their ability to luminesce under the action of oxidants has allowed the development of chemiluminescent sensors based on the determination of peroxides,⁶ glucose,⁷ and chemiluminescent immunoassay.⁸ A variety of biological activities (e.g., antibacterial, anti-inflammatory, antiulcer, antibronchospastic, cardiac stimulating, and inotropic properties) and cytotoxic effects on cancer cell lines have been also reported for synthetic imidazo[1,2-a]pyrazines derivatives.⁹⁻¹⁶

Several methods from wet-chemistry¹⁶ to sublimation¹⁷ and pyrolysis¹⁸⁻²¹ of amino acids are used to prepare imidazo[1,2-a]pyrazines. However, one of the major difficulties to study these molecules is lack of an adequate technique for a full structural identification. Combinatorial techniques such as gas-phase Fourier transform infrared spectroscopy coupled to gas chromatography and mass spectrometry¹⁷⁻²¹ identified some derivatives, but such methods also exhibited disadvantages because in situ decomposition of imidazo[1,2-a]pyrazines is very notable.¹⁸⁻²¹ The interest to study these cyclic amidine-type molecules lies in the fact that derivatives of glycine have failed to be detected by these techniques. The latter fact can be directly associated with the selective detection, thermochemical stability, or simply because cycle-condensation reactions of amino acids are not able to produce enough amounts of imidazo[1,2-a]pyrazines. Previous quantum chemical calculations²² suggested that the formation of imidazo[1,2-a]pyrazines can proceed overcoming a high reaction barrier of about 49 kcal mol^–1 and only supported by a silica-catalyzed process. This has opened up an area of great dubiety about the formation and the spectroscopic properties²³⁻²⁵ of imidazo[1,2-a]pyrazines, which deserves more definitive answers and novel approaches for experimental identification.

Vibrational spectroscopy (e.g. Raman) can be the technique of choice for such a molecular identification. In particular, surface-enhanced Raman spectroscopy (SERS)^26,27 dramatically can improve the limit of detection using metallic substrates, resulting in detection even at a single-molecule-level concentration.²⁸ Under such a scenario, it is important to study the adsorptive processes to attempt surface-enhanced Raman detection. Of particular interest is the study of noncovalent intermolecular interactions with metal clusters²⁹ because no mechanism was put forward to account for the adsorption of imidazo[1,2-a]pyrazines onto silver clusters. In the present study, the molecular properties of the noncovalent complexes formed with imidazo[1,2-a]pyrazines and Ag_n (n = 4 and 20) clusters were studied using density functional theory (DFT) methods. The chosen Ag clusters represent to simple models as much as the physical and chemical properties of metallic substrates are of great relevance in SERS.²⁶⁻²⁹ In particular, semiempirical dispersion corrections from Grimme (GD2)³⁰ and Austin–Petersson–Frisch (APF-D)³¹ applied over the exchange–correlation B3LYP^32,33 functional can provide theoretical insights into the strength of the noncovalent intermolecular interactions for these complexes. In addition, DFT calculations were carried out to predict static Raman activities, which further provide a measure of the chemical enhancements that arise during the adsorption onto the metallic substrates. Finally, time-dependent DFT (TD-DFT) calculations were carried out to access the orbital contributions to each of the transitions observed in the absorption spectrum, and molecular excitation energies were obtained for both isolated molecule and metallic cluster-organic compounds. Arising from sublimation of α-amino-acids (e.g., glycine), bi and tricyclic imidazo[1,2-a]pyrazines prepared require the formation of a first intermediate.²² The current series of molecules studied correspond to glycine (Gly, 1), piperazine-2,5-dione (DKP, 2), hexahydroimidazo[1,2-a]pyrazine-3,6-dione (BCA, 3), and hexahydroimidazo[1,2-a]imidazo[1,2-d]pyrazine-3,8-dione (TCA, 4), which all are depicted in Scheme 1.

Scheme 1. Chemical Structures of Glycine (1), Piperazine-2,5-dione (DKP, 2), Imidazo[1,2-a]pyrazine-3,6-dione (BCA, 3), and Imidazo[1,2-a]imidazo[1,2-d]pyrazine-3,8-dione (TCA, 4).

Results and Discussion

In this study, the noncovalent intermolecular interactions occurring on the metallic substrates were addressed using two sizes for the silver clusters, namely, Ag_n (n = 4 and 20). Similarity and differences for these Ag clusters were reported elsewhere.³⁴⁻³⁹ In particular, the Ag₄ and Ag₂₀ clusters were chosen because they are the most stable structures in the potential energy surface, respectively, for small-sized clusters (n < 10) and medium-sized clusters (12 < n < 22).³⁴ Substantial differences with other clusters is the relatively lower symmetry that can lead to metastable isomers. Several DFT methods³⁵ predicted the global minimum for the neutral Ag₄ and Ag₂₀ clusters to be rhombic (D_2h) and tetrahedral (T_d) structures, respectively. Ag₂₀ (T_d) is a relaxed fragment of the face-centered cubic lattice of bulk silver, whereas Ag₄ (D_2h) is a subdomain located at the vertex of Ag₂₀ cluster. Because Ag₄ (D_2h) represents the local minima with respect to other isomers (e.g. T_d, C_2v, see the Supporting Information), this structure was used as a structural criterion for a respective comparison between both clusters. The energy gap between highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital (LUMO), and the Fermi energy level were calculated to characterize the metallic substrates. The HOMO–LUMO gap energies, Δ_GAP, (see Table 1), were calculated to be about 1.8 and 2.5 eV, respectively, for the isolated Ag₄ and Ag₂₀ clusters. It is well known that the large energy gap corresponds to the higher stability for close-shell electron configurations; therefore, Ag₂₀ is more stable than Ag₄ (see Table 1). Empirical dispersion does not affect the properties of the wavefunction³¹ and thus GD2 and APF-D calculations result in similar values for HOMO–LUMO gap energies. The Fermi level (E_F, see the Supporting Information) was calculated to be about −4.36 and −4.44 eV for Ag₄ and Ag₂₀, respectively. Such a difference can be related with a different work function for transferring one quasi-electron from the Fermi level to the vacuum state. For the large size cluster, the value calculated is approximately similar for the bulk metal as obtained from photoelectric measurements on the (111) surface of silver metal surfaces.⁴⁰

Table 1. Orbital Interaction Energies (in kcal mol^–1) for the Noncovalent Intermolecular Interactions between Molecules (1–4) and Ag_n (n = 4 and 20) Clusters As Calculated Using B3LYP and Semiempirical Dispersion Correction with Grimme’s D2 and APF-D Functionals in Conjunction with the 6-31+G(d,p) + LANL2DZ Mixed Basis Set^a.

	B3LYP		Grimme-D2		APF-D
complexes	ΔENC	ΔGAP	ΔENC	ΔGAP	ΔENC	ΔGAP
Ag4		1.77		1.85		1.86
Ag4–Gly	–9.69	1.48	–11.62	1.48	–15.51	1.48
Ag4–DKP	–7.03	1.56	–10.02	1.52	–12.78	1.52
Ag4–BCA	–9.05	1.51	–14.07	1.50	–15.66	1.50
Ag4–TCA	–8.20	1.48	–14.25	1.57	–15.00	1.57
Ag20		2.49		2.49		2.50
Ag20–Gly	–14.40	2.93	–18.75	2.43	–23.47	2.44
Ag20–DKP	–11.97	2.45	–18.43	2.43	–20.16	2.43
Ag20–BCA	–14.55	2.43	–21.81	2.43	–23.10	2.44
Ag20–TCA	–13.44	2.33	–20.29	2.27	–21.77	2.28

^aHOMO–LUMO gap energies are reported in eV for each level of theory.

Figure 1 shows the geometries at the stationary points as obtained using DFT-D methods. It was assumed that molecules (1–4) interacted with an ad-atom site located at the vertex of the silver clusters. Previous studies³⁷ showed that this orientation is more stable (∼2.3 kcal mol^–1) that on-top binding onto one of the four faces (111) of the Ag₂₀ cluster. From Figure 1, it becomes evident that mainly two bonds stabilize the adsorptive processes, in which the noncovalent interaction occurs along the Ag···N (BCA and TCA) or Ag···O (DKP) bonds. As a result, one can observe that molecules (1–4) can be adsorbed mainly by cooperative interactions with the participation of NH₂ and COOH groups. The unique exception is Ag₂₀–Gly, in which the interactions arise effectively from both amine and carboxyl groups. For the Ag₄–Gly complex, the calculated bond distance between the N atom and the closest silver atom is 2.382 Å (DFT-D values), whereas this distance is slightly smaller (2.353 Å) for the Ag₂₀–Gly complex. In this complex, it is also observed that NH₂ and COOH groups are coordinated to the metal cluster, in which both O and N atoms lead to form a three-membered ring. Such a bidentate interaction set up the bonding between the O atom and the closest Ag atom (2.423 Å). On other hand, the cyclic derivative DKP (2) forms complexes with Ag clusters via the Ag···O(amide) bond because its N(amide) atom is covalently bounded to the H atom. The resulting Ag···O separation is 2.298 Å for the Ag₄–DKP complex, whereas the intermolecular distance is shortest (2.246 Å) for Ag₂₀–DKP. For BCA (3), the Ag···N separation is longer (2.226 Å) in Ag₄–BCA as compared to Ag₂₀–BCA (2.191 Å). Finally, for the Ag₄–TCA complex the interaction occurred through the imidazole ring, in which the Ag···N separation (2.314 Å) is longer as comparted to the Ag₂₀–TCA complex (2.191 Å). In the case of BCA and TCA, these molecules are adsorbed with an edge-on orientation and the imidazo ring almost lying perpendicular to the Ag clusters. The optimized structures suggested that the interaction of BCA and TCA is governed mainly by the anchoring Ag···N(amine) bonds. Mulliken population analysis indicates that N(amine) is rich in electrons and can be able to donate electron density to the empty 4d and 5s orbitals of silver. The charges on Ag(vertex) and N(amide) atoms calculated upon the formation of the complexes are Ag(−0.101)···N(−0.709), Ag(−0.169)···N(−0.302), and Ag(−0.155)···N(−0.292) for Ag₂₀–Gly, Ag₂₀–BCA and Ag₂₀–TCA complexes, respectively. Therefore, Ag clusters can behave as electron acceptors when charges arise from nitrogen (e.g., Gly, BCA, and TCA). On the other hand, the Ag···O(amine) bond gives rise to a weak interaction, mainly, in the Ag–DKP complexes. The charges on the Ag₂₀–DKP complex are Ag(−0.346)···O(−0.380). The full list of Mulliken population are in the Supporting Information. A reasonable explanation to this is that nitrogen is less electronegative than oxygen, making it a better nucleophile. Finally, the optimized Ag···N(amine) bond lengths are notably shorter in Ag₂₀ clusters than the ones in the Ag₄ cluster. The intermolecular distances for Ag₂₀–molecule complexes are in the order of those calculated in the interaction of amino acids (and short peptides) with small silver clusters.²⁹

Figure 1.

Optimized structures as obtained at the APFD-B3LYP/MBS level of theory for the gas-phase formation of Gly, DKP, BCA, and TCA complexes with Ag₄ and Ag₂₀ clusters. Selected interatomic bond distances in angstroms are included for comparison between dispersive (values in parenthesis) and nondispersive calculations.

Table 1 shows the energies of interaction for the noncovalent complexes, ΔE_NC, calculated in terms of an adiabatic two-state process using B3LYP, GD2 and APF-D functionals (absolute energies are reported in the Supporting Information). In particular, both GD2 and APF-D values account for empirical correction on dispersion through either electron pair bond formation, charge transfer, or polarization mechanisms,^30,31 whereas B3LYP values represent the level of interaction when dispersion corrections are not taken into account. Therefore, GD2 and APF-D interaction energies were benchmarked against B3LYP energies. The mean values calculated for the Ag₄–molecule complexes are 8.5, 12.5, and 14.7 kcal mol^–1, respectively, for B3LYP, GD2, and APF-D, whereas the mean value calculated for the Ag₂₀–molecule complexes are 13.6, 19.8, and 22.1 kcal mol^–1, respectively, for B3LYP, GD2, and APF-D. It is observed that empirical dispersion correction using the APF-D functional resulted in severe strong interactions because in all cases such energies appear to be consistently overestimated in comparison with B3LYP calculations. Differences for the energies of interaction calculated with respect to B3LYP are 2.25 (GD2) and 6.24 (APF-D) kcal mol^–1 for Ag₄–molecules, and 2.30 (GD2) and 8.53 (APF-D) kcal mol^–1 for Ag₂₀–molecules. According to other studies, the dispersion term in the APF-D functional should probably be re-evaluated,³⁸ because deviations can arise from some long-range dispersion that were double-counted by the APF function and the spherical atom model. The HOMO–LUMO gap energies (Δ_GAP, see Table 1) are very similar for GD2 and APF-D calculations, and slightly close with those values calculated without dispersion (i.e., B3LYP). However, the HOMO–LUMO gap energies becomes smaller after complexation with molecules, and this is noticeable for those noncovalent complexes formed with the Ag₄ cluster (in about 0.34 eV). Figure 2 shows the iso-surfaces for HOMO and LUMO (at 0.02 a.u.) depicting the frontier orbitals for the Ag–molecule complexes together with a simplified orbital energy diagram. In the case of Ag₄–molecule complexes (Figure 2A), a small extended distribution occurred in HOMO orbitals, whereas in the Ag₂₀–molecule complexes (Figure 2B) a large portion of HOMO is delocalized, suggesting the formation of electrostatic field gradients around the Ag₂₀ cluster that can induce dipoles in the absorbates because of the changes in the surface charge density. In particular, a significant rearrangement of the frontier molecular orbitals occur in the Ag₂₀–BCA and Ag₂₀–TCA complexes. As regards spatial distribution of frontier orbitals, the following situations can be observed:

• (1)HOMO is found exclusively on Ag metal clusters.
• (2)Both HOMO and LUMO appear on the Ag₄ metal cluster only.
• (3)Traces of LUMO appear on BCA and TCA.
• (4)LUMO is mainly localized in the imidazole ring of BCA and TCA.

Figure 2.

Schematic of the frontier orbital bonding HOMO and LUMO for the complexes formed between Gly and its related imidazo[1,2-a]pyrazines (DKP, BCA, and TCA) when adsorbed onto metallic clusters. (A) Interaction of molecules with the Ag₄ cluster (A) and interaction of molecules with the Ag₂₀ cluster (B).

According to these situations, one can suggest that imidazole rings are responsible for binding imidazo[1,2-a]pyrazines (i.e., BCA and TCA) to Ag clusters.

TDDFT calculations were carried out on 15 electronic transitions for the ground-state complexes. Table 2 shows the most important excitation energies (i.e., those with the largest oscillator strength) as calculated for vertical excitation at using DFT-D methods. It is observed that the Ag₄–molecules complexes exhibited the highest oscillator strengths, whereas very small oscillator strengths were calculated for the Ag₂₀–molecules complexes. On one hand, the excitations for electronic transitions in Ag₄–molecule systems are found at energies in the proximity of the absorption maxima (i.e., 386 nm relative to the Ag₄ cluster), that is, Ag₄–Gly, 408 nm (f = 0.795); Ag₄–DKP, 362 nm (f = 0.639); Ag₄–BCA, 379 nm (f = 0.879); and Ag₄–TCA, 393 nm (f = 0.601). Therefore, these metal-molecule transitions should occur from orbitals below the HOMO (HOMO – N, with N = 1 and 2) of Ag₄ to the LUMO of each molecule. On the other hand, the calculated absorption spectrum for Ag₂₀–molecule complexes involves excitations in the visible region and they are very close to the absorption maxima (i.e., 537 nm, relative to the Ag₂₀ cluster); that is, Ag₂₀–Gly, 554 nm (f = 0.021); Ag₂₀–DKP, 543 nm (f = 0.025); Ag₂₀–BCA, 547 nm (f = 0.024); and Ag₂₀–TCA, 647 nm (f = 0.019). Figure 3 shows the simulated absorptive spectrum of the studied complexes. The absorption showed changes as a function of both the molecule and the cluster size. For the Ag₄–molecules complexes, the corresponding spectra involve transitions in the visible region that might occur at about 400 nm, which are blue-shifted regarding the transitions for the Ag₂₀–molecule complexes occurring at around 550 nm.

Table 2. Principal Molecular–Cluster Complexes’ Excitation Energies As Obtained from TDDFT Calculations.

complex	MOsa	energy/wavelengthb	fc	wave function
Ag4–Gly	58 → 61	3.039/408	0.7952	0.521 |H → L + 2⟩
	58 → 65	3.609/344	0.2350	0.569 |H → L + 6⟩
	57 → 59	3.776/328	0.3328	0.456 |H – 1 → L⟩
Ag4–DKP	68 → 75	3.405/364	0.3103	0.400 |H → L + 6⟩
	68 → 75	3.421/362	0.6388	0.506 |H → L + 6⟩
	66 → 69	3.886/319	0.2111	0.419 |H – 2 → L⟩
Ag4–BCA	78 → 84	3.267/379	0.8792	0.478 |H → L + 5⟩
	78 → 88	3.811/325	0.1773	0.654 |H → L + 9⟩
	77 → 79	3.847/322	0.1541	0.387 |H – 1 → L⟩
Ag4–TCA	88 → 95	3.157/393	0.6007	0.474 |H → L + 6⟩
	88 → 96	3.521/352	0.2121	0.508 |H → L + 7⟩
	87 → 90	3.712/334	0.1105	0.490 |H – 1 → L + 1⟩
Ag20–Gly	208 → 213	2.179/569	0.0137	0.624 |H – 2 → L + 2⟩
	206 → 212	2.232/556	0.0187	0.466 |H – 4 → L + 1⟩
	206 → 211	2.236/554	0.0209	0.518 |H – 4 → L⟩
	207 → 212	2.253/550	0.0181	0.602 |H – 3 → L + 2⟩
	208 → 214	2.295/540	0.0155	0.545 |H – 2 → L + 3⟩
Ag20–DKP	216 → 221	2.229/556	0.0132	0.594 |H – 4 → L⟩
	216 → 222	2.258/549	0.0109	0.461 |H – 4 → L + 1⟩
	218 → 223	2.285/543	0.0250	0.486 | H – 2 → L + 2⟩
Ag20–BCA	229 → 231	1.939/639	0.0138	0.486 |H – 1 → L⟩
	226 → 232	2.234/555	0.0170	0.417 |H – 4 → L + 1⟩
	226 → 231	2.241/553	0.0136	0.346 |H–4 → L⟩
	227 → 232	2.261/548	0.0133	0.330 |H – 3 → L + 1⟩
	229 → 233	2.265/547	0.0238	0.385 |H – 1 → L + 2⟩
Ag20–TCA	239 → 241	1.844/672	0.0107	0.545 |H – 1 → L⟩
	240 → 242	1.916/647	0.0192	0.593 |H → L + 1⟩
	236 → 241	2.166/572	0.0129	0.486 |H – 4 → L⟩
	236 → 242	2.210/561	0.0163	0.474 |H – 4 → L + 1⟩
	237 → 242	2.235/555	0.0135	0.529 |H – 3 → L + 1⟩

^aMolecular orbitals.

^bIn eV/nm.

^cOscillator strength.

Figure 3.

Absorption spectra of the complexes formed between Gly, DKP, BCA, and TCA molecules with metallic clusters. (A) Predicted spectra using the Ag₄ cluster and (B) predicted cluster using the Ag₂₀ cluster. Spectra are broadened by a Lorentzian having a width of 12 nm.

Theoretical Raman spectra for neutral Gly (1), DKP (2), BCA (3,) and TCA (4) molecules obtained using DFT-D methods are shown in Figure 4. Frequencies at the gas-phase with the corresponding band assignments and the absolute Raman cross sections are respectively listed in Tables 3–6. Raman spectra were calculated only for neutral molecules, as it was demonstrated that Raman spectra of amino acids do not depend on the pH values.⁴¹ In detail, Raman spectral profiles contain bands grouped in two regions, namely, bands between 200 and 1000 cm^–1 and bands within the range of 1000–2000 cm^–1. However, peak intensities at the second range are slightly smaller than the peaks located at the first range. Taking into account the basis set effect on fundamental frequencies, the wavenumber scaled was used for the full assignment on the vibrational modes. In particular, the Raman spectra profile of Gly (1) shows bands associated with COO^– bend + CH₂ bend at 494 and 586 cm^–1, stretching-type modes of CH₂ at 1190, 1398, and 1462 cm^–1, and stretching of C=O at 1674 cm^–1. In-plane deformation bending δ(C=O) was at 807 cm^–1, and δ(NH₂) and wagging ρ_w(NH₂) at 1092 and 1591 cm^–1, respectively. A number of additional bands because of CH₂ and C=N and C=O vibration modes are evident in the case of BCA (3) and TCA (4) molecules, whereas the spectra of DKP (2) showed the presence of NH bands that remained as the spectral characteristics of Gly (1). The fingerprint region (i.e., 200 and 800 cm^–1) for DKP, BCA, and TCA molecules is constituted by peaks corresponding to the bands that all belong to deformation modes involving ring distortions (i.e., deformations of pyrazine and imidazo rings) as well as in-plane and out-of-plane bending of C=O moieties. The strongest bands because of rings’ breathing of DKP, BCA, and TCA molecules are located at 755, 707, and 702 cm^–1, respectively.

Figure 4.

Simulated normal Raman scattering spectra of Gly, DKP, BCA, and TCA molecules as calculated at the APFD-B3LYP/MBS level of theory. Differential cross sections of molecules in units of 10^–31 cm²/sr were calculated at an incident wavelength of 514.5 nm based on static polarizability derivatives. Bands are given a Lorentzian width of 20 cm^–1. Frequencies were scaled with a 0.959 factor.

Table 3. Selected Gas-Phase Normal Raman Active Modes, Scattering Factors (S_i), Absolute Raman Cross Sections (dσ/dΩ) at an Incident Wavelength of 514.5 nm Based on Static Polarizability Derivatives, Together with Their Corresponding Band Assignments for Gly (1).

νia	Sib	dσ/dΩc× 10–31	band assignment
66	0.31	0.21	molecule deform
162	3.32	0.46	NH deform out-of-plane
376	2.28	0.09	molecule deform
452	1.70	0.07	COOH bending
494	3.82	0.11	COO– bend + CH2 bend
586	3.62	0.09	C–C stretch
807	9.60	0.13	COOH bending
1092	6.48	0.08	NH deform out-of-plane
1190	9.64	0.11	C–H bending
1266	5.37	0.05	C–H bending
1398	3.91	0.03	C–H bending
1462	15.72	0.10	C–H bending
1591	3.76	0.02	NH bending
1674	6.16	0.03	C=O stretch

^aIn cm^–1.

^bIn Å⁴/amu.

^cIn cm²/sr.

Table 6. Selected Normal Raman Active Modes, Scattering Factors (S_i), Absolute Raman Cross Sections (dσ/dΩ) at an Incident Wavelength of 514.5 nm Based on Static Polarizability Derivatives, Together with Their Corresponding Band Assignments for Hexahydroimidazo[1,2-a]imidazo[1,2-d]pyrazine-3,8-dione (4).

νia	Sib	dσ/dΩc× 10–31	band assignment
44	1.11	0.17	pyrazine ring deform
197	3.05	0.52	rings deform
236	3.04	0.39	rings deform
401	5.99	0.24	pyrazine ring deform
509	3.23	0.20	rings deform
612	11.51	0.32	rings deform
702	15.97	0.48	rings breath
1019	7.28	0.10	CH2 rock
1134	10.29	0.13	CH2 wagging
1179	5.15	0.09	CH2 wagging
1235	6.50	0.14	CH2 wagging
1270	4.29	0.10	CH2 wagging
1325	15.83	0.17	CH2 wagging
1407	35.42	0.33	CH2 scissors
1469	15.01	0.17	CH2 scissors
1624	32.29	0.25	C=N stretch
1669	20.85	0.16	C=O stretch

^aIn cm^–1.

^bIn Å⁴/amu.

^cIn cm²/sr.

Table 4. Selected Normal Raman Active Modes, Scattering Factors (S_i), Absolute Raman Cross Sections (dσ/dΩ) at an Incident Wavelength of 514.5 nm Based on Static Polarizability Derivatives, Together with Their Corresponding Band Assignments for Piperazine-2,5-dione (2).

νia	Sib	dσ/dΩc× 10–31	band assignment
60	0.69	0.56	ring deform
174	1.31	0.20	ring deform
428	4.23	0.18	ring deform
506	4.34	0.19	CH2 stretch
577	6.31	0.16	ring stretch
755	18.32	0.28	ring breath
1125	3.39	0.04	ring deform
1217	13.83	0.13	CH2 rocking
1296	11.65	0.12	CH2 wagging
1346	13.21	0.11	CH2 bending, NH bending
1427	8.59	0.09	CH2 scissors, NH bending
1477	11.77	0.10	CH2 scissors
1642	15.43	0.08	C=O stretch

^aIn cm^–1.

^bIn Å⁴/amu.

^cIn cm²/sr.

Table 5. Selected Normal Raman Active Modes, Scattering Factors (S_i), Absolute Raman Cross Sections (dσ/dΩ) at an Incident Wavelength of 514.5 nm Based on Static Polarizability Derivatives Together with Their Corresponding Band Assignments for Hexahydroimidazo[1,2-a]pyrazine-3,6-dione (3).

νia	Sib	dσ/dΩc× 10–31	band assignment
55	0.86	0.83	rings deform
167	1.54	0.27	rings deform
202	1.24	0.22	rings deform, CH2 rock
233	1.62	0.20	rings deform, CH2 rock
416	6.56	0.26	pyrazine ring deform
521	3.29	0.16	CH2 rock, NH deform out-of-plane
569	8.37	0.26	CH2 rock, NH deform out-of-plane
678	8.59	0.30	CH2 rock, NH deform out-of-plane
707	11.28	0.27	rings breath
823	2.31	0.05	pyrazine ring deform
1017	2.71	0.05	CH2 rock, NH deform out-of-plane
1133	5.70	0.07	CH2 rock
1211	7.47	0.13	pyrazine ring deform
1305	11.39	0.14	CH2 wagging
1360	6.29	0.10	NH bending
1472	16.24	0.16	CH2 scissors
1627	19.89	0.15	C=N stretch
1669	10.41	0.09	C=O stretch

^aIn cm^–1.

^bIn Å⁴/amu.

^cIn cm²/sr.

Figure 5 shows the effect of using Ag clusters on the Raman spectra of molecules (1–4). As observed, evident spectral differences resulted in bands that appeared at different wavenumbers. In particular, selective enhancement and considerable red shifts for several Raman vibrations suggest that for some signal enhancements such a result effectively corresponds to the presence of local interactions occurring between the active site of the adsorbate (i.e., imidazole ring) and the effective ad-atom of the metal surface. In particular, for the Ag₄–Gly complex, the bands observed are δ(NH₂), ρ_w(CH₂), δ(NH₂), and ν(C=O) located at 862, 1277, 1598, and 1672 cm^–1, respectively. Tenorio et al.⁴¹ calculated similar Raman spectra for glycine but using a silver eight-atom cluster. For the Ag₄–DKP complex, the most characteristic absorption bands present intense peaks at 764, 1306, 1354, 1454, and 1641 cm^–1 assigned to ν(NH), δ(CH₂), ν(NH), ν(N=C), and ν(C=O) vibrations, respectively. For both Ag₄–BCA and Ag₄–TCA complexes, the most intense bands were observed in a particular region between 1000 and 1500 cm^–1. Absorption bands were predicted corresponding to δ(CH₂) at 996 cm^–1, rings’ deformations at 1013 cm^–1, ρ_w(CH₂) at 1208 cm^–1, pyrazine ring-deformation at 1277 cm^–1, bending δ(NH) at 1362 cm^–1, imidazo ring-deformation at 1424 cm^–1, bending δ(N=C) at 1613 cm^–1, and bending δ(C=O) at 1638 cm^–1. Finally, the Raman spectra of the molecules adsorbed onto the Ag₂₀ cluster are much more similar than those of isolated molecules. This is the case of the Ag₂₀–Gly complex, in which the most intense bands are δ(CCO), δ(NH₂), and δ(CH₂), δ(CH₂), ω(CH₂), δ(NH₂), and δ(C=O) located at 629, 1147, 1386, 1435, and 1628 cm^–1, respectively. The predicted absorptions for the interval between δ(NH₂) and δ(C=O) stretching is 193 cm^–1, whereas in the case of Ag₄–Gly, it was 74 cm^–1. In Ag₂₀–DKP, the principal absorption bands correspond to ring breathing (764 and 889 cm^–1), which is more evident than that in the Ag₄ complex. The bands δ(CH₂), ν(NH), and ν(N=C) were also observed at 1217, 1356, and 1429 cm^–1, respectively. However, C=O bands are much weaker and thus they cannot be distinguished in the predicted spectrum. Because BCA and TCA are molecules with the same chemical nature, the interaction energies are similar, and form noncovalent complexes through the same active site, the predicted Raman spectra for both Ag₂₀–BCA and Ag₂₀–TCA complexes showed similar bands in the 800–1500 cm^–1 region. According to the interaction energies calculated (∼20 kcal mol^–1), it is expected that such values overpass a threshold required to observe the SERS effect.⁴¹ However, further studies should address other variables such as the effect of pH, charge of Ag clusters and molecules, different metallic substrates, as well as calculations of Raman activities using different laser wavelengths.

Figure 5.

(A) Raman spectra using the Ag₄ cluster and (B) Raman spectra using the Ag₂₀ cluster. For the simulated static normal Raman spectra of the Gly, DKP, BCA, and TCA complexes with a metallic cluster the differential cross sections of molecules (in units of 10^–31 cm²/sr) were calculated on the basis of static polarizability derivatives and using an incident wavelength of 514.5 nm. The bands showed are given by a Lorentzian width of 20 cm^–1.

Conclusions

Theoretical calculations of the noncovalent intermolecular interactions between imidazo[1,2-a]pyrazines and silver clusters were reported in the framework of dispersion-corrected DFT methods. The main conclusions can be summarized as follows:

• In terms of a computational modeling that compensates resource and time, the Ag₂₀ cluster is a very useful model to study the interactions of Ag nanoparticles with imidazo[1,2-a]pyrazines. In terms of an accurate prediction, dispersion-corrected DFT methods are required to estimate interaction energies in the noncovalent complexes studied.

• The mean values for the difference in the interaction energies calculated appeared to be consistently overestimated with APF-D, especially when complexes are formed with the Ag₂₀ cluster.

• Mulliken population analysis suggests a transfer of charge across the Ag···N(amine), red shifts for Raman vibrations suggest strong interactions, and charge redistribution involving HOMO and LUMO orbitals give rise to the formation of stable noncovalent complexes that can surpass a dissociation limit.

• These simulations constitute a useful and valuable first element for further experimental characterization of these unusual classes of cyclic amidines.

Computational Methodology

To account for dispersive interactions in the electron density of the noncovalent molecule-metal cluster systems, all the electronic structure calculations were studied through DFT using the Grimme³⁰ and the APF³¹ dispersion correction methods over the B3LYP functional. A mixed basis set (MBS) was set using the 6-31G+(d,p) basis set for C, H, O, and N atoms plus the LANL2DZ basis set for Ag. Details of relative interaction energies, normal modes frequencies, Kohn–Sham HOMO and LUMO orbitals, vertical excitation energies, Raman intensities calculations, basis-set superposition error, and the details of the computational methodology adopted for the present work are given in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.9b03127.

• Details of computational methods; representative structures for Ag₄ clusters; total density-of-states calculated for Ag₄ (a) and Ag₂₀ (b) clusters; frontier orbitals HOMO and LUMO for molecules (1–4); absolute electronic energies (in Ha) for the isolated molecules (1–4) and metallic cluster-organic molecule systems HOMO and LUMO energies calculated for the isolated molecules; and Mulliken atomic charges for the Ag₂₀–molecule complexes (PDF)

The author declares no competing financial interest.