Probing Lewis Acid–Base Interactions with Born–Oppenheimer

Jun 3, 2015 - Probing Lewis Acid–Base Interactions with Born–Oppenheimer Molecular Dynamics: The Electronic Absorption Spectrum of p-Nitroaniline ...
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Probing Lewis Acid−Base Interactions with Born−Oppenheimer Molecular Dynamics: The Electronic Absorption Spectrum of p‑Nitroaniline in Supercritical CO2 Benedito J. Costa Cabral,*,†,‡ Roberto Rivelino,§ Kaline Coutinho,∥ and Sylvio Canuto∥ †

Grupo de Física Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto, 1049-003 Lisboa, Portugal Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, Av. Professor Gama Pinto 2, 1649-003 Lisboa, Portugal § Instituto de Física da Universidade Federal da Bahia, Campus Universitário de Ondina, CEP 40210-340 Salvador, Bahia, Brazil ∥ Instituto de Física da Universidade de São Paulo, CP 66318, 05314-970 São Paulo, SP, Brazil ‡

ABSTRACT: The structure and dynamics of p-nitroaniline (PNA) in supercritical CO2 (scCO2) at T = 315 K and ρ = 0.81 g cm−3 are investigated by carrying out Born−Oppenheimer molecular dynamics, and the electronic absorption spectrum in scCO2 is determined by time dependent density functional theory. The structure of the PNA−scCO2 solution illustrates the role played by Lewis acid−base (LA−LB) interactions. In comparison with isolated PNA, the ν(N−O) symmetric and asymmetric stretching modes of PNA in scCO2 are red-shifted by −17 and −29 cm−1, respectively. The maximum of the charge transfer (CT) absorption band of PNA in scSCO2 is at 3.9 eV, and the predicted red-shift of the π → π* electronic transition relative to the isolated gas-phase PNA molecule reproduces the experimental value of −0.35 eV. An analysis of the relationship between geometry distortions and excitation energies of PNA in scCO2 shows that the π → π* CT transition is very sensitive to changes of the N−O bond distance, strongly indicating a correlation between vibrational and electronic solvatochromism driven by LA−LB interactions. Despite the importance of LA− LB interactions to explain the solvation of PNA in scCO2, the red-shift of the CT band is mainly determined by electrostatic interactions.

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INTRODUCTION Lewis acid−base (LA−LB) interactions play a major role in supramolecular chemistry, materials science, and biotechnology.1−12 A fundamental and related subject concerns the importance of LA−LB interactions in supercritical solvation.13−18 Specifically, the role played by solute−solvent LA− LB interactions on the electronic properties of “push and pull” dyes solvated at supercritical conditions remains a subject of great interest. “Push and pull” dyes, upon excitation, are characterized by an intramolecular and well-defined charge transfer (CT) band that shows a strong dependence on the solvent polarity.19 Environment effects on the electronic absorption spectra of different molecular species exhibiting CT states have been the subject of numerous works.20−27 A class of model dyes exhibiting CT states are disubstituted benzenes, where the presence of electron donor and electron acceptor substituents connected by a π system contribute to increase intramolecular electronic density transfer upon excitation. These molecules also exhibit large nonlinear optical properties with a wide range of applications in the design of photonic devices.28−32 Several works on the electronic properties of disubstituted benzenes, in particular of pnitroaniline (PNA), where the substituents are the electron © 2015 American Chemical Society

donor amine group (−NH2) and the acceptor nitro group (−NO 2 ), which are linked via a phenyl ring, were reported.20−22,25,26,33−38 The dependence of the CT band shift on the nature of the solute−solvent interactions has been investigated by different works.34,35 In general, solvent effects lead to a bathochromic shift relative to the gas-phase value, which is strongly dependent on the solvent polarity. For PNA in cyclohexane, it is −0.38 eV.38 In polar solvents, such as water, the shift is −0.98 eV20,39 and it is mainly determined by Coulombic interactions.34 Much less is known on CT states in nonpolar environments,37 particularly at supercritical conditions.25 Recently, the origin of the red-shift of the lowest singlet π → π* electronic transition of PNA in supercritical CO2 (scCO2) relative to its gas-phase value was investigated by using microsolvation and also sequential Monte Carlo time dependent density functional theory (TDDFT). 25 The predicted red-shift was, however, underestimated in comparison with the experimental information.25 This disagreement can be possibly explained by the limitations of the microsolvation Received: March 26, 2015 Revised: June 3, 2015 Published: June 3, 2015 8397

DOI: 10.1021/acs.jpcb.5b02902 J. Phys. Chem. B 2015, 119, 8397−8405

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The Journal of Physical Chemistry B approach or the inadequacy of classical force fields to model LA−LB interactions. In a recent investigation on the structure and electronic properties of liquid and supercritical CO2, we have stressed the importance of a first-principles approach.40 Considering the fundamental interest in the understanding of the electronic properties of “push and pull” molecules at supercritical conditions, here we adopt a first-principles approach, where the dynamics of a PNA molecule solvated in scCO2 is generated by Born−Oppenheimer molecular dynamics (BOMD).41 Special emphasis is placed on the structure of the PNA−scCO2 solution and on the vibrational and electronic absorption spectra of PNA in scCO2. The electronic absorption spectrum is calculated by using TDDFT.42 Recent developments in density functional theory, specifically, double hybrid density functionals,43 made possible the application of TDDFT to the accurate calculation of excitation energies44 even for systems involving charge transfer excitations. In these cases, it is well-known that widely used approximations for the exchangecorrelation functional present serious limitations.36 This Article is organized as follows. First, we present some details on the computational procedures. The structure and the electronic properties of a few PNA−CO2 complexes illustrating the role played by LA−LB interactions is then reported. This is followed by a discussion on the structure of the PNA−scCO2 supercritical solution and the vibrational properties of PNA in supercritical CO2. The electronic absorption spectrum of PNA in scCO2 is then presented. The presentation of the results is closed by the analysis of the relationship between some geometric distortions of the PNA molecule and the red-shift of the CT band maximum position in scCO2 relative to its gasphase value. We conclude by stressing the excellent agreement with experimental information for the π → π* red-shift and the interest in adopting a first-principles approach to investigate the electronic properties of “push and pull” molecules in scCO2.

(90 000 steps). For temperature control, we employed the canonical sampling velocity rescale thermostat (CSVR).51 Average properties were calculated by using the last 25 ps of the BOMD run. Geometry optimizations for small PNA−CO2 complexes were carried out with the PBE-D3 functional. Excitation energies were calculated with time dependent density functional theory (TDDFT) and the double hybrid B2GP-PLYP functional43,52 with the Tamm−Dancoff approximation to TDDFT excitation energies.53 A Dunning’s correlation consistent double-ζ basis set augmented with a set of diffuse functions (aug-cc-pVDZ or apvdz basis set in a simplified notation)54 was used in the geometry optimizations and TDDFT calculations, which were carried out with all of the electrons. The excitation spectra were constructed by fitting a Lorentzian distribution of 0.05 eV width to the excitation energies and oscillator strengths. Geometry optimizations and TDDFT calculations were carried out with the ORCA program.55 The electronic absorption spectra of PNA in scCO2 were calculated by using 50−100 selected configurations equally separated in time from the last 25 ps of dynamics. To calculate the electronic spectrum, we defined supermolecular structures with the solute (PNA) plus a given number (NQS) of explicit solvent molecules. This quantum system (QS) is embedded (EMB) in the polarizing electrostatic field of the remaining (NS-NQS) solvent molecules, which were represented by atomic charges. The NQS solvent molecules explicitly included in the quantum system are selected by ordering the solvent molecules as a function of their distance to the nitrogen atom of the PNA nitro group. This choice was driven by our interest in investigating the role played by LA−LB interactions in the PNA−CO2 systems. To assess the role played by the electrostatic environment, calculations without the embedding charges (NOEMB) were also carried out. Results for NQS = 0 (EMB) correspond to the PNA molecule embedded in the charge distribution of the CO2 molecules. The embedding charges representing the CO2 molecules correspond to the TraPPE (transferable potential for phase equilibria) model56 where the charges (in a.u.) are qC = 0.70 and qO = −0.35. In keeping with a recent work on liquid and scCO2,40 we have verified that the electronic absorption spectrum of PNA in scCO2 is not significantly dependent on the choice of the electrostatic embedding. Quite similar results are predicted by using charges from different classical force fields, and only results with TraPPE56 embedding charges are presently reported.

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COMPUTATIONAL DETAILS Born−Oppenheimer molecular dynamics (BOMD) for PNA in scCO2 was carried out for a system of 1 PNA molecule and 64 CO2 molecules (NS = 64) at temperature T = 315 K and density ρ = 0.81 g cm−3 (experimental condition for scCO2) in a cubic box with size L = 17.94 Å and periodic boundary conditions. Additional BOMD was carried out, also at T = 315 K, for an isolated PNA molecule in a cubic box with the same size L. In this case, BOMD was carried out with the Martyna and Tuckerman Poisson solver for nonperiodic boundary conditions.45 The Perdew−Burke−Erzernhof (PBE) exchange correlation functional46 including an empirical correction to the dispersion interactions (D3)47 was adopted for BOMD that was carried out with the hybrid Gaussian and plane-wave method (GPW)48 as implemented in the CP2K program.49 Goedecker, Teter, and Hutter (GTH) norm-conserving pseudopotentials50 were used for representing the core electrons, and only valence electrons were explicitly included in the quantum mechanical density functional theory (DFT) calculations of the forces to generate the dynamics. In the GPW approach, Kohn−Sham orbitals are expanded into atomcentered Gaussian-type orbital functions, whereas the electron density is represented with an auxiliary plane-wave basis set. A double-ζ valence polarization (DZVP) was used to represent the Gaussian orbitals, and the charge density cutoff for the auxiliary basis set was 280 Ry. The self-consistent-field energy threshold for calculating the electronic density was 10−6 hartree. The time step was 0.5 fs, and the total BOMD time was 45 ps

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RESULTS AND DISCUSSION Electronic Spectra of PNA−CO2 Complexes. Before presenting the electronic properties for the PNA−scCO2 solution, we first analyze the electronic absorption spectra of small PNA−CO2 complexes. This can be useful to discuss the PNA−CO2 interactions as well as to estimate how these interactions modify the absorption spectra when a comparison is made with the gas-phase isolated PNA. Three optimized structures of PNA complexes with one CO2 molecule are illustrated in Figure 1. The first complex (I) is a nearly planar structure, where the interaction between the amino group and the aromatic ring leads to a small displacement of the nitrogen atom from the ring plane with a torsional C−C−C−N angle of ∼178°. This complex is energetically stabilized by the interactions between the oxygen atoms (O1) of the nitro 8398

DOI: 10.1021/acs.jpcb.5b02902 J. Phys. Chem. B 2015, 119, 8397−8405

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The Journal of Physical Chemistry B

parameters for the optimized structures, particularly those related to the interactions involving the PNA nitro group with CO2, are reported in the caption of Figure 1. TDDFT B2GP-PLYP/apvdz excitation energies for PNA and PNA−CO2 complexes are reported in Table 1. For isolated PNA, the results for the excitation energies corresponding to the s0 → s2 and s0 → s6 transitions practically coincide with the experimental values.38 Excitation energies for the two PNA− CO2 complexes (I and II) are quite similar. For both complexes, the s0 → s2 excitation that corresponds to the π → π* transition is shifted by ∼ −0.17 eV relative to the isolated gas-phase PNA molecule. This result underestimates the experimental value for the π → π* transition energy shift of PNA in scCO2 (−0.35 eV)33 by −0.18 eV. We notice that the first transition, which is an n → π* forbidden transition for the isolated PNA molecule, becomes weakly allowed in the PNA− CO2 complex II. The electronic absorption spectra of PNA and PNA−CO2 complexes are presented in Figure 1 and exhibit the red-shift of the first absorption band of the complexes relative to the PNA molecule. In contrast with the results for complexes I and II, the maximum position of the CT band for the electronic absorption spectrum of complex III is very close to the one observed in isolated PNA, thus suggesting that this band is not very dependent on hydrogen bonding formation between the amine group and the CO2 molecules. The results for small PNA−CO2 complexes show that, although PNA−CO2 specific interactions are important, they cannot explain the experimental red-shift for the π → π* charge transfer band relative to the isolated gas-phase species. Therefore, the importance of long-ranged electrostatic interactions in the condensed phase should be taken into account. Structure of the PNA−scCO2 Solution and the Vibrational Spectrum of PNA in scCO2. Structure. The structure of the PNA−scCO2 solution is determined by specific solute−solvent interactions and can be analyzed through the calculation of the radial distribution functions (RDFs). We will focus on the RDFs related to interactions between atoms of the PNA nitro group and the CO2 atoms. As stated before, this is driven by our interest in investigating the role played by LA− LB interactions in PNA−CO2 systems. It should be noticed that, despite the relatively long time for a BOMD run (45 ps),

Figure 1. Left: PBE-D3/apvdz optimized structures for two PNA− CO2 complexes (I, II, and III). The atoms of the PNA nitro and amine groups are named C1, N1, O1, and H1. The following geometric parameters are defined (distances in Å and angles in deg): distances (d); angles (θ, ϕ, and η, which is the angle between a vector along the O−C−O axis and another one perpendicular to the PNA plane). I: d(N1−C) = 4.17; d(N1−O) = 4.22; d(O1−C) = 2.99; d(O1−O) = 3.22. θ(N1−O1−C) = 157.9; θ(C1−N1−C) = 102.5; ϕ(N1−O1−C− O) = 179.1; η = 90.0. II: d(N1−C) = 3.41; d(N1−O) = 3.60; d(O1− C) = 3.03; d(O1−O) = 3.26; θ(N1−O1−C) = 96.7; θ(C1−N1−C) = 179.3; ϕ(N1−O1−C−O) = 90.0; η = 0.0. III: d(N1H1···O) = 2.32; d(N1−C) = 4.49; d(N1−O) = 3.31; θ(H1−N1−O) = 11.2. Right: electronic absorption spectra for gas-phase isolated PNA and PNA− CO2 complexes I, II, and III.

group with the carbon atoms (C) of CO2. This structure is a typical structure stabilized by Lewis acid−base interactions where the oxygen atom from the nitro group works as an electron donor to the carbon atom of CO2. The second complex (II) is a nonplanar structure where the CO2 molecule is almost perpendicular to the PNA plane and the carbon atom of CO2 interacts simultaneously with the two PNA oxygen atoms. At the PBE-D3/apvdz level and including zero point vibrational energy corrections, complexes I and II are nearly isoenergetic and II is only 0.45 kcal/mol (1.88 kJ/mol) more stable than I. The third structure (complex III) illustrates the hydrogen bond formation between the PNA amine group and a CO2 molecule. At the PBE-D3 level, this complex is 0.89 kcal/ mol (3.72 kJ/mol) less stable than II. Some geometric

Table 1. Excitation Energies (in eV) and Oscillator Strengths (in Parentheses) for the Optimized Structures of PNA and Three PNA(CO2) Complexes (I, II, and III) Shown in Figure 1a PNA s0 s0 s0 s0 s0 s0 s0 s0 s0 s0 s0

→ → → → → → → → → → →

s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11

n → π* π → π* n → π*

π → π*

π → π*

3.77 4.27 4.39 4.64 5.12 5.48 5.88 6.01 6.19 6.19 6.69

PNA−CO2 (I) 3.76 4.10 4.39 4.60 5.15 5.34 5.96 6.05 6.17 6.18 6.79

(0.456) [4.24] (0.002) (0.001) (0.077) [5.48] (0.004) (0.009) (0.061) (0.304) [5.66] (0.001)

(0.456)

(0.001) (0.082) (0.001) (0.011) (0.044) (0.319) (0.002)

PNA−CO2 (II) 3.79 4.09 4.45 4.60 5.17 5.34 5.94 6.05 6.16 6.14 6.76

(0.012) (0.486)

(0.089) (0.001) (0.017) (0.059) (0.246) (0.001)

PNA−CO2 (III) 3.76 4.22 4.39 4.63 5.15 5.44 5.69 5.94 6.13 6.18 6.58

(0.468) (0.002) (0.079) (0.007) (0.008) (0.049) (0.296) (0.002)

Assignments are made for the transitions with experimentally known excitation energies and for the three transitions defining the first charge transfer band. Geometries optimized with PBE-D3. TDDFT excitation energies were calculated with the B2GP-PLYP exchange correlation functional. The aug-cc-pvdz basis set was used in all the calculations. Experimental values for gas-phase PNA from Millefiori et al.38 are shown in brackets. a

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the PNA nitro group. Integration of the N1−C RDF up to 5.7 Å leads to 8.5 which is the average number of CO2 molecules in the first coordination shell of the nitro group. The N1−O RDF shows a first maximum a 4.1 Å and a first minimum at ∼5.5 Å. Integration up to the first maximum yields an average number of 5.12, whereas the average number of oxygen atoms estimated by integration up to the minimum is 15.8. The O1−C RDF shows a first maximum at ∼3.3 Å and integration up to this distance leads to 1.2 CO2, which is the average number of CO2 molecules in close interaction with the oxygen atom of the PNA nitro group. Integration of this RDF up to the first minimum at ∼4.7 Å leads to an average coordination number of 4.9. The O1−O RDF shows a first maximum at 3.4 Å, and integration up to this distance leads to an average number of 2.8 CO2 molecules. Integration of this RDF up to 4.6 Å leads to an average coordination number of ∼9.4. It should be observed that the calculated coordination numbers of the CO2 carbon and oxygen atoms around the PNA nitro group are closely related. As expected, the average number of coordinating oxygen atoms is approximately 2 times the average number of carbon atoms. The results for the structure including maxima and minima positions of the RDFs as well as the corresponding coordination numbers are also gathered in the caption of Figure 2. Further information on the PNA−CO2 interactions in scCO2 can be obtained by calculating the distribution of some specific structural parameters. To this purpose, we have identified in the first coordination shell of the nitro group (d(N1−C) < 5.7 Å) the CO2 molecule which is closest to the N1 atom. Driven by the analysis of the gas-phase optimized structures of PNA−CO2 complexes previously discussed (see Figure 1), we have calculated the distributions of the N1−C distances (N[d]) and N1−O1−C angles (N[θ]) for PNA in scCO2. In addition, we have defined an angle that we call η, which is the angle between a vector normal to the PNA plane and the O−O axis of the CO2 molecule. Thus, a value of η close to zero is related to the presence of a CO2 molecule that is perpendicular to the

the statistics for the structural solute−solvent correlations is limited due to the presence of a single solute molecule. However, as discussed below, the main structural features characterizing the solute−solvent correlations are adequately described. Denoting by N1 and O1 the nitrogen and oxygen atoms of the nitro group and by C and O the carbon and oxygen atoms of CO2, the RDFs related to the N1−C, N1−O, O1−C, and O1−O correlations are illustrated in Figure 2. The N1−C RDF

Figure 2. Radial distribution functions (RDFs) related to the interactions between the N1 and O1 atoms of the PNA nitro group and the atoms of the CO2 molecule. Data for the RDF first maxima and minima positions (in Å) and coordination numbers (in parentheses) are N1−C 4.1 (2.8) and 5.5 (8.7); N1−O 4.1 (5.1) and 5.5 (15.8); O1−C 3.3 (1.2) and 4.7 (4.9); O1−O 3.4 (2.8) and 4.6 (9.4).

is characterized by a first broad maximum with a main peak at ∼4.1 Å and a first minimum at 5.7 Å. Integration of the N1−C RDF up to 4.1 Å leads to 2.8 CO2 molecules, which represents the average number of CO2 molecules in close interaction with

Figure 3. Distributions of structural parameters from BOMD of PNA in scCO2. Left: Distribution of the d(N1−C) bond distance between the N atom of the nitro group and the closest CO2 carbon atom in the first coordination shell. Middle: Distribution of the θ(N1−O1−C) angle for CO2 molecules. Right: Distribution of the angle η between a normal to the PNA plane and the O−C−O axis for molecules in the first coordination shell of the nitro group. 8400

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observed. The secondary maxima for both the amine and nitro groups seem to reflect different regimes for the dynamics of PNA, as illustrated by the time evolution of the C−N bond distances (left panels). No significant differences are observed when we compare ν(C−N) frequency distributions for the isolated PNA molecule and for PNA in scCO2. The N−O bond distance distribution (N[d(N−O)], inset panel) and the frequency distribution of ν(N−O) are presented in Figure 5. Results for both isolated PNA at T = 315 K (black

PNA plane, as is the case of complex II shown in Figure 1. The distributions of these parameters are presented in Figure 3. The distribution of d(N1−C), [N(d)], shows a maximum near 4.2 Å, which practically coincides with the average d(N1− C) distance, and also with the first maximum of the N1−C RDF. By including the CO2 molecules in the first coordination shell, the average value of θ is 104.6 ± 0.2°, which is still close to the value observed for complex II of 96.7°. However, the distribution of η (right panel) is a broad distribution and the average η is 99.8 ± 0.2°, which is close to the observed value for complex I. Therefore, our results strongly indicate that, in scCO2, although the distribution of CO2 molecules relative to the PNA dipole axis is compatible with a picture of competing interactions between gas-phase structures I and II, the CO2 molecular axis shows a preferential orientation that is parallel to the plane of the PNA ring. This result can be possibly explained by the competition between solute−solvent and solvent− solvent interactions as well as by thermal effects. Vibrational Spectrum. As in previous BOMD studies,40,57 the vibrational spectrum is presently investigated through the calculation of time correlation functions. For example, the distribution of the ν(C−N) stretching frequency of PNA in scCO2 can be analyzed by calculating the Fourier transform of the average velocity autocorrelation function defined as CAA(t) = ⟨A(t)A(ti)/A(ti)A(ti)⟩, where A = (dx/dt), ti is a time origin, and, in the present case, x = d(C−NO2), x = d(C−NH2), and x = d(N−O2). The time evolution of the C−N bond distances for the nitro (C−NO2) and amine (C−NH2) groups of PNA in scCO2 and the corresponding frequency distributions are presented in Figure 4. The average d(C−N) bond distances are 1.386 and

Figure 5. Left panel: Distribution N[d(N−O)] of the N−O bond distance of the nitro group for PNA (black line) and PNA−scCO2 (red line). Right panel: distribution of the ν(N−O) stretch frequency for PNA (black line) and PNA−scCO2 (red line).

line) and for PNA in scCO2 (red line) are presented. Although the average d(N−O) distances for isolated (1.251 Å) and solvated PNA (1.254 Å) are similar, the N[d(N−O) distance distribution suggests a small displacement of the d(N−O) bond distance to larger values for PNA in scCO2 (see inset of Figure 5). As next illustrated, this effect (small displacement of the bond length to larger values) reflects the role played by PNA− CO2 interactions in scCO2 and can be related to a red-shift of the ν(N−O) stretching frequency. The [ν(N−O)] frequency distribution is presented in Figure 5. For isolated PNA (black lines), two doublet peaks are observed at 1490/1506 and 1298/1306 cm−1. These values can be compared with the experimental values of 1503 and 1317/ 1332 cm−1 for the asymmetric and symmetric stretching modes, respectively.60 For PNA in scCO2, the frequency distribution shows two main peaks at 1468/1477 and 1281/1288 cm−1. Therefore, our results indicate that in comparison with isolated PNA the frequencies associated with the asymmetric and symmetric stretching modes for PNA in scCO2 are red-shifted by −29/−22 and −18/−17 cm−1, respectively. Experimental data for the vibrational frequencies of PNA in different solvents have been reported.21,61−64 From these data, it appears that the νs(NO2) stretch frequency is red-shifted by ∼ −30 cm−1 when we move from PNA in DMSO to PNA in cyclohexane.64 Data for the νs(NO2) stretch frequency shifts for PNA solvated in DMSO−CCl4 and toluene−CCl4 mixtures have also been reported.63 These data also strongly indicate that νs(NO2) is dependent on the solute−solvent interactions and that it is shifted by ∼25 cm−1 when we move from PNA in pure CCl4 to PNA in pure DMSO. Moreover, Dreyer et al.63 also provided evidence that there is a correlation between vibrational and electronic solvatochromism. Specifically, the

Figure 4. Left panels: Time evolution of the C−N distances for the nitro (C−NO2) and amine (C−NH2) groups. Right panels: Distribution of the ν(C−N) frequencies associated with the time evolution of the C−N distances.

1.465 Å for the amine and nitro groups, respectively, and they are quite similar to the distances observed in isolated PNA. For the amine group, the ν(C−N) frequency distribution shows a main peak at 1300 cm−1 and two other maxima at ∼1490 and 1600 cm−1. The value at 1300 cm−1 is similar to those observed in aromatic amines58 and can be compared to the experimental result of 1305 cm−1 for PNA in tetrahydrofuran (THF).59 The ν(C−N) frequency distribution for the nitro group is characterized by a main peak at 1300 cm−1. However, in this case, two secondary peaks at ∼1000 and ∼1050 cm−1 are also 8401

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The Journal of Physical Chemistry B νs(NO2) frequency shift and the electronic shift of the CT band of PNA are correlated.63 An interesting aspect concerning the νs(NO2) stretching frequency of PNA is the presence of a doublet with a spectral separation between the maxima in the 8.6−16.7 cm−1 range.63 Our predictions for the spectral separation of the isolated PNA doublets are 8 and 16 cm−1 for the symmetric and asymmetric stretching, respectively. The origin of this doublet is not well understood, and two different explanations were proposed. The first is Fermi resonance,63 where the presence of a doublet is related to the coupling between the symmetric NO2 stretch and another totally symmetric vibrational mode or overtone. The second relies on the hypothesis of two kinds of stretching vibrations related to specific solute−solvent interactions. Although it is not our purpose here to further investigate this issue, the present results show that the ν(NO2) vibrational stretching doublet is observed even for the isolated PNA molecule. Electronic Absorption of PNA in scCO2. The theoretical electronic spectrum of PNA in scCO2 is presented in Figure 6.

molecule. This prediction practically coincides with the experimental value of −0.35 eV.33 Although our results show the importance of explicitly taking into account the solvent molecules in close interaction with the PNA nitro group, it appears that the main contribution to the observed red-shift of the CT band is determined by polarization effects. These effects also lead to an ∼ 20% increase of the ground state (GS) dipole moment of PNA from the isolated molecule to PNA in scCO2. The gas-phase dipole moment of the PNA molecule at the B2GP-PLYP/apvdz//PBE-D3/apvdz level is 7.07 D, which is ∼0.8 D above the experimental data for PNA in liquid benzene (6.29 D).38 The average dipole moment of PNA in scCO2 is presently estimated as 8.6 ± 2 D. The inset panel of Figure 6 illustrates the contributions of the three lowest excitations to the CT band of PNA in scCO2. It should be observed that at the B2GP-PLYP/apvdz theoretical level the first and third n → π* transitions are forbidden in the gas-phase optimized PNA (see Table 1). However, due to geometry distortions induced by thermal effects and interactions with the CO2 molecules in scCO2, these transitions become weakly allowed, leading to the spectra shown in Figure 6, where the intensities of the first and third excitations (I1 and I3) were normalized to the intensity of the second excitation (I2). Although this is an interesting feature, our results clearly indicate that the structure of the CT band of PNA in scCO2 is mainly determined by the s0 → s2 excitation that corresponds to a π → π* transition. One relevant issue concerning the electronic absorption of PNA in scCO2 is the dependence of the excitation energies on the structural distortions of the solute induced by thermal effects and also by the interaction with the solvent. To further investigate this issue, we first selected different sets of configurations satisfying some specific geometry constraints. Then, we calculated the average absorption spectra for these configurations. Figure 7 (left panel) shows the spectra for the C−N distances of the PNA nitro group satisfying the criteria d(C−NO2) > 1.58 Å (black line) and d(C−NO2) < 1.37 Å (dashed blue line). The results indicate that the absorption spectrum of PNA in scCO2 is very dependent on the d(C−

Figure 6. Electronic absorption spectra of PNA in scCO2. The quantum system includes the PNA molecule plus NQS solvent molecules. Results with EMB (NOEMB) correspond to calculations with (without) embedding charges. The inset illustrates the contribution of the first three excitations to the CT band of PNA in scCO2. The intensities for the first and third excitations (s0 → s1 and s0 → s3) were normalized to the intensity of s0 → s2.

Comparison between the results for NQS = 0 with (EMB) and without (NOEMB) electrostatic embedding shows that the electrostatic embedding leads to a 0.15 eV red-shift of the CT band maximum position. The results for different values of NQS allow us to discuss how the calculated spectra depend on the explicit inclusion of the CO2 molecules in close interaction with the PNA nitro group. A small red-shift (0.06 eV) of the CT band is observed when we move from NQS = 0 to NQS = 5. The explicit inclusion of 10 CO2 molecules (NQS = 10), which is nearly the number of solvent molecules in the first coordination shell of the nitro group (∼8.5), shifts the maximum position to 3.9 eV. In this case, only the five excited states that define the excitation energies in the first CT band were calculated. At the B2GP-PLYP/apvdz level, the maximum position for the absorption spectrum of isolated PNA is 4.27 eV (see Table 1 and Figure 1). Therefore, we predict that the maximum position of the first CT band of PNA in scCO2 is red-shifted by −0.37 eV relative to the gas-phase isolated PNA

Figure 7. Dependence of the electronic absorption spectra of PNA in scCO2 on specific geometry parameters. Left panel: Spectra for the C− N distances in the nitro group satisfying d(C−NO2) > 1.58 Å (full black line) and d(C−NO2) < 1.37 Å (blue dashed line). Right panel: Spectra for the N−O distances satisfying d(N−O) > 1.26 Å (full black line) and d(N−O) < 1.24 Å (blue dashed line). 8402

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molecular species of great interest in materials science, specifically in the controlled design of photonic devices.

NO2) distance and that it is significantly red-shifted for small distances. However, as has been previously discussed, the average d(C−NO2) in scCO2 is quite similar to what is observed for the isolated PNA molecule. Moreover, only for a very small number of configurations, d(C−NO2) is smaller than the lower threshold value (see Figure 4). Therefore, the average spectrum in scCO2 should not be very dependent on the d(C− NO2) distance. In the right panel of Figure 7, we present the spectra for two sets of configurations satisfying the criteria d(N−O) > 1.26 Å (black line) and d(N−O) < 1.24 Å (dashed blue line). The results show that the spectrum for larger d(N−O) is red-shifted relative to that for the smaller distances. The [ν(N−O)] frequency distribution for PNA in scCO2 shows that the peaks corresponding to the symmetric and asymmetric stretching are significantly red-shifted in comparison with the isolated PNA molecule, which reflects the interactions of the PNA nitro group with the CO2 molecules. Therefore, the above results provide further evidence on the relationship between vibrational and electronic solvatochromism.63 Moreover, our results for PNA in scCO2 strongly indicate that this correlation is driven by LA−LB interactions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Work partially supported by FCT (Portugal), CNPq, CAPES, FAPESP, INCT-FCx, and nBioNet (Brazil).

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REFERENCES

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CONCLUSIONS Born−Oppenheimer molecular dynamics of PNA in scCO2 were carried out, and the electronic absorption spectrum of PNA was investigated by TDDFT calculations. The analysis of the structure of the PNA−scCO2 solution indicates that LA− LB interactions involving the PNA nitro group and the electron deficient carbon atom of CO2 play a significant role and explain some specific structural and vibrational features. The orientational order of the CO2 molecules in close interaction with the PNA nitro group keeps some similarity with what is observed in PNA−CO2 complexes. Vibrational evidence on the role played by LA−LB interactions in the PNA−scCO2 solution was also provided through the analysis of the ν(N−O) asymmetric and symmetric stretching frequencies that are red-shifted relative to the values for the PNA molecule at the same temperature In keeping with several experimental works on the vibrational spectra of PNA in different solvents, our results for the νs(NO2) stretching frequency of PNA in scCO2 indicate the presence of a doublet with a small spectral separation between the maxima. In addition, we are providing evidence that the doublet is also observed for an isolated PNA molecule, a result that lends credence to the possibility that its origin is not related to the interactions with the solvent. The maximum of the charge transfer (CT) absorption band of PNA in scSCO2 is at 3.9 eV, and the predicted red-shift of the π → π* electronic transition relative to the isolated gasphase PNA molecule reproduces an experimental value of −0.35 eV. An analysis of the relationship between geometry distortions and excitation energies of PNA in scCO2 indicates that the π → π* transition is very sensitive to the value of the N−O bond distance. Taking into consideration the feature that thermal induced geometry changes significantly influence vibrational properties, our results are in agreement with the experimental evidence on the correlation between vibrational and electronic solvatochromism for PNA in scCO2.63 Despite the importance of LA−LB interactions in explaining the solvation of PNA in scCO2, the red-shift of the CT band is mainly determined by electrostatic interactions. In conclusion, the present results also stress the importance of adopting a firstprinciples approach to investigate the electronic properties of 8403

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