Calculations of Electronic Excitation Energies and Excess Electric

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Calculations of Electronic Excitation Energies and Excess Electric Dipole Moments of Solvated para-Nitroaniline with the EOM-CCSD-PCM Method Shih-I Lu, and Li-Ting Gao J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 28 Jun 2018 Downloaded from http://pubs.acs.org on June 28, 2018

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The Journal of Physical Chemistry

1 Calculations of Electronic Excitation Energies and Excess Electric Dipole Moments of Solvated paraNitroaniline with the EOM-CCSD-PCM Method

Shih-I Lu*, Li-Ting Gao Department of Chemistry Soochow University No. 70 Lin-Shih Road, Taipei City, 111, Taiwan Email address: [email protected] Tel: 886-2-28819471 ext 6825 Fax: 886-2-28811053

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2 Abstract In this research, we present computational evidence utilizing vertical electronic excitation energies and the corresponding excess dipole moments of solvated para-nitroaniline (pNA). The properties of interest are calculated by employing the equation of motion coupled-cluster together with single and double excitations (EOM-CCSD). Solvent effects are included through the polarizable continuum model (PCM) with the state-specific (SS) formalism and the perturbation theory energy and density (PTED) approach. We examine the ground state equilibrium geometry of pNA in different environments to yield the symmetry of the stable conformer of solvated pNA is Cs but is also C2v. By employing the calculated vertical excitation energies overestimate experiment, our calculations confirm the consistency of the calculated excess dipole moments with comparable documented results. Lastly, specific to this study, dissimilar environmental models, such as the linear-response (LR), and variants of the corrected linearresponse (cLR and cLR0) formalisms in the context of the EOM-CCSD-PCM-PTED, are assessed against those from the SS formalism.


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3 1. INTRODUCTION Electric properties of molecules can change significantly upon electronic excitation from their ground state (GS) to an excited state (ES). As observed, for example, in the change from the molecular dipole moment of the GS (μg) and the ES (μe), to the purported excess dipole moment (Δμ), these changes are particularly significant. We see this demonstrated in several applications such as: materials with large nonlinear optical response properties;1-3 the semi-quantitative two-state model; 4 and the Stark effect.5 Especially in solution phase, environment complicates the excitation process with an accompanying change of properties. In order to include the solvation effect in quantum chemistry calculations, utilization of the polarizable continuum model (PCM) 6-11 is one of the most recognized approaches. The implementation of coupling with the PCM and wave function-based approach (for example, the coupled-cluster, CC, hierarchy) and, in particular, the time-dependent density functional theory (TD-DFT), have yielded compelling results. While the former is a benchmarked designation, the latter demonstrates a promising alternative for studying larger systems. By employing the perturbation theory energy and density (PTED) scheme to continuum solvation, the coupled-cluster single and double excitations (CCSD)12 and the equation of motion CCSD (EOMCCSD)13-15 deliver precise calculated results for both the GS and the ES. Additionally, approximations of the PTED: the PTE, the PTE(S) and the PTES (where S: singles) are proposed within the CCSD and the EOM-CCSD frameworks. ACS Paragon Plus Environment


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4 Solvation of the ES introduces two complications while using the PCM: (i) time scale of the solvent response to excitation,9, 16-18 and (ii) solvent polarization for the excited state. The first concerns whether or not the solvent molecules have enough time to equilibrate with the new electronic distribution of the solute. Equilibrium (EQ) solvation is applied if both solute and solvent relax simultaneously. If not, the non-equilibrium (NEQ) solvation is employed. For example, we conduct computations of vertical excitation energies and geometry optimization of the ES in the NEQ and the EQ solvation regimes, respectively. Furthermore, there are two principal environmental models for calculating the solvent polarization for the ES: the state-specific (SS) and the linear response (LR) formalisms. The SS 19-20 explicitly considers the excited state wave function and the solvent response to the corresponding electronic density; whereas, the LR21-24 regards the solvent interaction term as the linear response of the GS solvent operator to an external perturbation while ignoring the mutual solute-solvent polarization. In practical implementation, the former involves an iterative cycle over these mutual polarization effects and calculates only one electronic state at a time, while the latter computes multiple states simultaneously. Although the SS delivers a more accurate description for the ES of solvated molecules, it is also much more computationally demanding than its LR counterpart. For excitations involving a large density rearrangement, the LR is determined insufficient because it does not account for the density-dependent relaxation of the solvent polarization. The corrected-LR ACS Paragon Plus Environment

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5 (cLR)23, 25-28 approach demonstrates the ability to reduce the gap between the SS and the LR formalisms. The cLR is based upon a "correction" of the linear response transition energy computed in the frozen ground state reaction field together with an SS energy term. While maintaining a computational cost similar to the LR,27, 29 the cLR is seen as the first cycle of the SS iterative scheme and is shown to reduce the difference between the SS and the LR energies substantially. Recently, Ren, Harms and Caricato30 benchmarked the EOM-CCSD-LR model for calculating electronic excitation energies of solvated organic molecules in the NEQ regime. However, employing this model yields results revealing that the method consistently overestimates experimental results by 0.4 - 0.5 eV, a larger than expected error in vacuum. They attributed the deterioration of accuracy to the implicit solvent model used, while ignoring an explicit solvent-solute interaction. Thus, by designing a protocol wherein the H-bonding would be considered explicitly, they were able to achieve consistent improvements. In order to measure a comparison of the LR and the cLR results against full SS calculations, we utilized the EOM-CCSD scheme with the PTED. Two formulations of the cLR correction were considered:27 one that includes the relaxation of the CC T-amplitudes (still designated as the cLR) and one that negates this term (designated as the cLR0). The cLR0 is a computational preference because it allows the calculation of the cLR energy term directly for multiple excited states, thus resulting in a slightly less computational effort than that of the LR formalism. Using methylencyclopropene in ACS Paragon Plus Environment


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6 methanol; trans-acrolein in water; acetone in water; and water in water, Caricato concluded that a marked improvement is obtained while using both the cLR and the cLR0 instead of the LR for all systems being considered. Subsequently, both the cLR and the cLR0 provide promising alternatives for computing excited energies in solution within computationally intensive CC methods. In this study, we examine the Δμ that is dependent upon the rearrangement of electrons upon excitation as well as the excitation energies. We consider the LR, the cLR, the cLR0 and the SS within the framework of the CCSD and the EOM-CCSD with the PTED. For the integrity of the study, we also consider the 0, defined as the excitation energy of the solute molecule actively excited from its GS, as it is in equilibrium with the solvent, to an ES in the presence of a solvent polarization frozen to the initial GS. The resulting calculations of the NEQ and the EQ solvation regimes are found to deliver the same 0. Continuum solvation methodologies yield consistently successful results in cases of weakly interacting solute–solvent couples, whereas a change in strategy is required in order to gain reliable modeling when examining solidly interacting systems, such as those dominated by an explicit hydrogen bonding interaction. Two predominant approaches cited in the literature include explicit solvents to treat local solutesolvent interaction: the hybrid solvation model and the discrete solvation model. The first surrounds the solute with a small number of explicit solvent molecules, and then embeds this cluster into the implicit ACS Paragon Plus Environment

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7 dielectric field.31-32 The second employs a quantum mechanics/molecular mechanics (QM/MM) approach and obtains bulk characteristics of the solvent through molecular dynamics (MD), or Monte Carlo simulations. The quantum mechanics/effective fragment potential (QM/EFP) method 33-35 and the polarizable embedding (PE) scheme

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are conventionally utilized QM/MM approaches. We adopt a

suggested hybrid solvation model for this study wherein a micro-solvated cluster is surrounded by PCM solvent. Then, instead of a complete EOM-CCSD treatment, as in Ref. [30], we implement the TD-DFT to derive an estimate of the explicit solvent-solute interaction. The test molecule chosen for our research is solvated p-nitroaniline (pNA), shown in Figure 1. As a subject of numerous theoretical and experimental studies, 37-56 it is an important prototypical organic push-pull chromophore wherein an electron donor group is connected via the conjugated π-system to an electron acceptor group. pNA possesses a strong π  π* absorption band in the near-ultraviolet to the visible spectra region.57 An experimental 0.98 eV red shift of excitation energy for observation as it traveled from the gas phase, 4.24 eV,58 to the aqueous phase, 3.26 eV.53-54 For pNA dissolved in 1,4dioxane and dimethylsulfoxide, the charge-transfer (CT) absorption band is shown to peak at 355 41 and 389 nm,42 respectively. Also generating a change in the dipole moment of pNA, is the corresponding low-lying singlet ES, which is associated with an intramolecular CT from the amino group to the nitro group across the phenyl ring. At this point, a significant Δμ is expected. Its behavior can be best explained



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8 by the frontier molecular orbitals (Figure S1). Upon photo-excitation, the peak of the π  π* absorption band will be heavily dependent on the solvent polarity due to the increase in the dipole moment. We begin by examining the stable conformation of pNA in different environments. We follow with a comparison of the SS-PTED calculated results to available experimental data. Finally, we measure the 0, the LR, the cLR and the cLR0 approaches by utilizing the full SS data as a benchmark.

2. COMPUTATIONS For our computations, we employ the GAUSSIAN 16.59 GS equilibrium geometries of the pNA molecule in different environments are optimized and verified by using the CCSD/6-31+G(d,p) with the exception of the periodic boundary conditions (PBC) calculation together with the HSE06/6-31G(d,p). 6066

Then, for property calculations, we perform the ES calculations at the GS optimized geometries by

utilizing the response method of the EOM together with the aug-cc-pVDZ basis set. Solvent effects are included through application of the PCM. Additionally, the symmetric isotropic integral equation formalism model (IEFPCM)67-69 together with universal force field (UFF) radii70 is used. We employ the PTED scheme to CCSD-PCM calculations in solution throughout, however, the PBC calculation is applied to crystal at the GS only.


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9 All reported values of the dipole moments are determined by the standard finite field (FF) technique using the four-point approximation with an external electric field (Fk) = 1 × 10−4 a.u. (1 a.u. = 5.1422 × 1011 V m−1): 𝜇 =

= [−𝐸(2𝐹 ) + 8𝐸(𝐹 ) − 8𝐸(−𝐹 ) + 𝐸(−2𝐹 )]⁄12𝐹 .

(1)

Because of the molecular symmetry of the Cs point group for the pNA, the z-component of the dipole moment is expected to disappear. Therefore, we calculate only the x and the y components of the specific dipole moment, followed by an evaluation of the total dipole moment as: 𝜇=

𝜇 +𝜇 +𝜇 =

𝜇 +𝜇 .

(2)

Different solvents are considered beginning with the almost nonpolar 1,4-dioxane (Dioxane,  = 2.2099,  = 2.023222); to the more polar dichloroethane (DCE,  = 10.125,  = 2.087447); to the highly polar dimethylsulfoxide (DMSO,  = 46.826,  = 2.007889).

3. RESULTS AND DISCUSSION 3.1. Ground State Equilibrium Geometry of pNA. Table 1 reports structural parameters, energy differences (ΔE) between the pyramidal (Cs symmetry) and the planar (C2v symmetry) conformers, and the μg of pNA within differing environments. To our knowledge, the only experimental information available concerning the geometry of pNA has been derived from its crystal structure.71-72 The nitrogen-pyramidalized amino group as evidenced by ACS Paragon Plus Environment


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10 the out-of-plane angle (designated as ϕ) around the amino nitrogen (N 14). The torsion angle of H16-N14C6-C1 (designated as ) has also been documented in other research. 43, 50 The crystal structures reported by Trueblood, Goldish, and Donohue,71 and by Colapietro et al.72 presented  of 18.8 and 2.4 degrees, respectively, while both presented a slightly pyramidalized amino group with 3.8 and 5.2 degrees of ϕ, respectively. Although both suggested a slightly nonplanar conformation for pNA in the crystal, comparatively, the former suggested the plane of the amino group is not coplanar with the plane of the phenyl ring. This result has been promoted as justification to assume that pNA adopts C2v symmetry in solution-phase and in vacuum.38, 43, 73 For example, calculations by Kama et al.74 indicated that the choice of optimized versus experimental geometries had only a minor influence on the calculated properties. However, there are two main concerns for adopting planar conformation: (i) the exact positions of hydrogen atoms from such experimental techniques cannot be precisely determined, therefore results remain inconclusive; (ii) no experiment provided affirmative information with respect to the preferred geometrical conformation of solvated pNA. In our first study, we perform a PBC-HSE06/6-31G(d,p) calculation to optimize the geometrical structure and lattice constants of pNA crystal. Calculations for the  and the ϕ are 4.7 and 0.1 degrees, respectively, in part, supporting the nitrogen-planarity of the amino group in pNA crystalline. The stable conformation of solution-phase pNA is considered for our second study. Our results yield a non-planar conformer (Cs symmetry) with a slight energy difference (ΔE) of about 1 kcal/mol, ACS Paragon Plus Environment

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11 when compared to the C2v structure. This difference indicates a flat potential energy surface along the ϕ coordinate. We find the CCSD-calculated molecular geometries of both gas-phase and solution-phase pNA are of Cs symmetry with the  of approximately 26 degrees and the ϕ of approximately 40 degrees. A comparison of the molecular geometries obtained in vacuum and in different solvents, reveals that the presence of solvents, even one with a high dielectric constant, has minimal effect on the optimized geometries and maximal variations of 0.010 Å while passing pNA from vacuum to DMSO. The most stable C2v conformation in solid might possibly be the transition state conformation in both gas and solution phases. Along with an increase of solvent polarity, the g increases from 2.462 au in vacuum to 2.814 au in Dioxane, 3.188 au in DCE and 3.287 au in DMSO. Experimentally, the g in Dioxane and DCE measured are 2.237 and 2.44 au,75 respectively. The corresponding experimental apparatuses employed are the electro-optical absorption and the thermochromic methods. Calculations based on the Cs conformation of 2.814 au for those in Dioxane and 3.188 au for those in DCE, overshoot experiments by approximately 30%. Nevertheless, larger overestimates of more than 50% are derived from the C2v conformation of 3.130 au for those in Dioxane and 3.583 au for those in DCE. This observation provides additional support for the Cs conformation as a preferable option to the C2v in estimating solvated pNA. In conclusion, we surmise that an increase of the solvent polarity will decrease the E; increase the μg; but will not produce a noticeable change to the nitrogen-pyramidalization (ϕ).



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12 For more conclusive evidence, we re-optimize the isolated pNA molecule in DMSO at the PCMCCSD(T)/cc-pVTZ level of theory. Our computational resources do not allow computations of the Hessian for this scale analysis. Therefore, we compare the energies of molecular geometries constrained to the Cs- and the C2v-symmetries only. The stationary geometry reached in the Cs group is still markedly nonplanar (ψ = 22.4 degree and ϕ = 38.9 degree) and has a total energy substantially lower than the planar stationary geometry (-491.3266070 au versus -491.3275068 au, corresponding to an energy difference of 0.56 kcal/mol). This result is likely a transition state. We conclude that the nonplanar geometry of pNA is also more stable than the planar geometry in the ground state at the PCM-CCSD(T)/cc-pVTZ level of theory.

3.2. Solvent Effects on the Transition-allowed Excited State. Table S1 lists the EOM-CCSD calculated data of vertical excitation energies, oscillator strengths and excess dipole moments of the two lowest excited states for each irreducible representation (A and A) in vacuum. Table S2 provides the calculated results of the corresponding solution-phase EOM-CCSD-SS-PTED. In vertical excitations, the solvent molecules have insufficient time to equilibrate to the new electronic distribution of solute. Therefore, we considered vertical excitation energies in the NEQ regime exclusively. Nevertheless, further examination to evaluate the difference of the  between the calculations in NEQ and EQ regimes is of interest to us.


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13 Figure S2 presents the escape charge phenomenon study wherein EOM-CCSD/aug-cc-pVTZ calculations are analyzed, then followed by a comparison of the results with those of aug-cc-pVDZ. Of the three solvents considered, our calculations demonstrate that the difference in SS-NEQ-PTED excitation energy between the two basis sets is within 0.002 ~ 0.003 eV. Thus, for subsequent property calculations, we utilize the aug-cc-pVDZ basis set. Data provided in Tables S1 and S2, Figure 2 exhibits the order of the ES with excitation energies and the corresponding oscillator strengths of pNA in various environments. Among the low-lying excitations in vacuum, only the fourth lowest excited state (2A) is transition-dipole allowed. This state is associated with the electronic transition from the occupied  orbital to the unoccupied * orbital (Figure S1) corresponding to an intra-molecular CT which delivers an increase in the dipole moment by 2.647 au. In contrast, vertical excitations of pNA in solvents produce different characteristics of ordering states. While passing pNA from in vacuum to organic solvents, the significant   * transition is the second lowest excited state (1A) with an enhanced oscillator strength; a red shift of the excitation energy; and an increase of thee.. The enhancement of the oscillator strength due to solvation is approximately 10%. The red shifts of the excitation energy are: 0.3209, 0.5216 and 0.5630 eV, derived from the solvation of Dioxane, DCE and DMSO, respectively. From the NEQ/EQ calculations, the corresponding increases in the e of particular interest are: 4.320/4.336, 5.208/5.236 and 5.455/5.437 au. As is the case with the g, the more polar solvent produces a larger e. ACS Paragon Plus Environment


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14 Consistent with our findings, the experiment of the significant   * transition, was shown to produce the  of 3.2 au in Dioxane37 are in accordance with the corresponding NEQ/EQ calculated values of 3.422/3.437 au. Together with DCE, the experiment produces the  ranging from 2.81 to 3.97 au.45, 58, 76-77 The calculated value, 3.936 and 3.965 au for the NEQ and the EQ, respectively, is on the upper parameters of the panel. We also observed that there was no discernible difference between the NEQ and the EQ calculated e. The difference between  and  of the solvent has a negligible impact on this observation. In the literature, research was conducted by Kosenkov and Slipchenko 46 targeting the analysis of solvatochromic shifts on singlet and triplet excited states of pNA in water, 1,4-dioxane and cyclohexane through the utilization of the QM/EFP approach. For their study, the MD simulations of pNA and 64 EFP solvent molecules using periodic boundary conditions were chosen to model the condense phase while pNA geometry was frozen. The CIS(D)/6-31+G* level of theory was employed for the quantum region. These CIS(D)/EFP calculations reproduced the red shift of experiment in water (1.0 eV), but produced discrepancies of 0.2 – 0.3 eV in 1,4-dioxane and cyclohexane. Research performed by Schwabe78 explored the solvatochromism of pNA with an explicit consideration of solvents by the PE scheme. The quantum region was treated by the PERI-CC2 79 with the (aug-)cc-PVDZ basis set wherein diffuse functions are added on nonhydrogen atoms only. His calculations delivered a theoretical solvatochromic shift of -0.60 to -0.68 eV compared to -0.71 eV in ACS Paragon Plus Environment

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15 dichloromethane (DCM) when polarizable force fields and special treatment of hydrogen bonding are applied. In an additional application of the PE scheme with the PERI-CC2/(aug)-cc-pVDZ, Schröder and Schwabe calculated excitation energies of the bright   * transition of pNA in water, methanol, ethanol, and DCM yielding varying results. Compelling evidence was obtained from hydrogen-bonding systems (water, methanol and ethanol). These conclusions verify consistency with experimental values for water and confirm the sufficiency for methanol with a deviation of 0.1 eV and 0.15 eV for ethanol. However, a deviation of more than 0.2 eV is expected for DCM. 80 To explore the preferential solvation effect on the solvatochromic shifts of pNA, Frutos-Puerto, Aguilar, and Galvań

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employed a mean-field sequential QM/MM method, with electron transitions

computed at the CASPT2/cc-pVDZ level of theory. The bulk properties of solvent were simulated by utilizing the ASED/MD (average solvent electrostatic potential from molecular dynamics) method. Calculated solvatochromic shifts from vacuum to cyclohexane and vacuum to trimethylamine (TEA) yielded -0.01 and -0.20 eV, respectively, while additional experimentation produced -0.37 and -0.68 eV. Under these conditions, explicit solvent molecules did not perform satisfactorily. To address the interaction between solute and solvent in our PCM-SS-PTED calculations, we employ the hybrid solvation model. The H-bond shift HB/HB is defined as the change of the



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16 excitation energy/excess dipole moment while passing from the PCM-only system to the explicit solvent + PCM system. We examine the micro-solvated clusters with one and two solvent molecules forming H-bonds with the nitro group. Also embedded in the PCM is the entirety of the micro-solvated clusters. Figure S4 exhibits the geometries obtained through the PCM-CCSD/6-31+G(d,p) level of theory. We consider three exchange-correlation (XC) hybrid functionals for excitations: M06-2X, 81 CAM-B3LYP,82 and B97XD.83 The XC functional results are illustrated in Figure S4. These data reveal the decrease in the excitation energies and the excess dipole moment when H-bonds are treated explicitly. For excitation energy, the average of the red shifts across all functionals is 0.24 eV. Noteworthy in this calculation, is a generally consistent value of the shift produced by all of the functionals, with deviations of 0.01 eV from the average at most. By applying the excess dipole moment, the hybrid-solvation model decreases to 0.81 au. Though our calculations consider DMSO only, similar conclusion would apply to the cases of Dioxane and DCE. A explicit solvent representation will improve the agreement between the experiment and the calculated results. 3.3. Benchmark of the 0, LR, cLR and cLR0. The 0, the LR, the cLR and the cLR0 calculated results are provided in Tables S3 - S6, respectively. For a comparison of results from the SS and its counterparts, we also consider those results in both the NEQ and the EQ regimes. As reported in Figure ACS Paragon Plus Environment

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17 3 (upper and lower panels for the NEQ and the EQ regimes, respectively) the average errors against the SS-PTED excitation energies have been noted. All four environmental models were shown to overestimate the SS results. Furthermore, the average errors for the 0 (0.043 and 0.088 eV in the NEQ and the EQ regimes, respectively) were seen to be markedly larger than for the LR, the cLR and the cLR0. Both the LR and the cLR yield average errors of less than 0.01 eV in the NEQ regime while approximating 0.02 eV in the EQ regime.

Finally, the cLR0 was shown to outperform in the NEQ/EQ

regimes, with average errors of less than 0.002/0.01 eV. Significant results presented in Figure 3 are: (i) the cLR demonstrates an estimate inferior to the SS results over the cLR0 and (ii) the cLR delivers results moderately better than that of the LR. The cLR0 was shown to outperform 4 and 2.5 times better than the cLR for the NEQ and the EQ, respectively, however the cLR0 is actually an approximation of the cLR, with additional physics in the latter. Therefore, our test results for the solvated pNA disagree with Caricato’s assertions27 positing that both the cLR and the cLR0 deliver a similar quantitative approximation of the SS transition energies for their test cases. However, we contend that an improvement to the calculated excited state energy by neglecting the T-amplitudes response to the excitation perturbation in the EOM-CCSD calculation is debatable. One possible explanation might be an incompleteness of the basis set. However, in this instance, the presented aug-cc-pVTZ calculated results reveal that an expansion of the basis set does not impact the vertical



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18 excitation energy. Examination into the potential possibilities responsible for this observation is indicated. Average errors for the Δμ are calculated in Figure 4 (upper and lower panels for the NEQ and the EQ solvation regimes, respectively). In the NEQ regimes, we obtain average errors of -0.043, -0.006, 0.003 and 0.020 au for the 0, the LR, the cLR and the cLR0, respectively. The corresponding quantities in the EQ regime produce -0.057, 0.008, 0.016, and 0.046 au. In a comparison to the SS, the cLR is considered to outperform other environmental models. Additionally, our results demonstrate that the 0 systematically delivers a smaller μ than the SS formalism while delivering a larger μ for both the cLR and the cLR0.

4. CONCLUSIONS Our calculations assert that while the Cs conformation is the most stable conformation of pNA in vacuum and in solution phase, in the solid conformation, it is not. Vertical excitations of pNA in solvents will exhibit different characteristics of ordering states in vacuum. Citing the EOM-CCSD-LR-NEQ example,30 the EOM-CCSD-SS-NEQ is also shown to overestimate experimental vertical excitation energies of solvated pNA. Both the cLR and the cLR0 were tested for calculations of the excitation energies and Δμ in solution with the CCSD-PCM. Counter to Caricato’s work, 27 we demonstrate that omitting the T amplitudes relaxation (the cLR0) produces more consistency with the SS formalism for ACS Paragon Plus Environment

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19 excitation energies with the cLR delivering exceptional results to the cLR0 in the Δμ. To derive more conclusive evidence confirming the superior performance of the cLR0 against the cLR in the vertical excitation energies for the solution-phase pNA, we propose that additional analysis is warranted.

ACKNOWLEDGEMENTS We are grateful to the National Center for High-performance Computing for computer time and facilities and to the Ministry of Science and Technology, Taiwan (MOST 105-2113-M-031-001) for financial support.

Supporting Information Description: Tables of calculated results for vertical excitation energies, ground state dipole moments and excited state dipole moments. Figures of (i) SS-NEQ-PTED calculated vertical excitation energies using the aug-ccpVDZ and aug-cc-pVTZ basis set; and (ii) TD-DFT calculated results of micro-solvated clusters.



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20 REFERENCE 1. Kanis, D. R.; Ratner, M. A.; Marks, T. J. Design and Construction of Molecular Assemblies with Large Second-Order Optical Nonlinearities. Quantum Chemical Aspects. Chem. Rev. 1994, 94, 195-242. 2. Boyd, R. W. Nonlinear Optics, Third ed.; Academic Press: U.S.A., 2008. 3. Non-Linear Optical Properties of Matter: From Molecules to Condensed Phases; Papadopoulos, M. G.; Sadlej, A. J.; Leszczynski J., Eds.; Springer: The Netherlands, 2010. 4. Oudar, J. L.; Chemla, D. S. Hyperpolarizabilities of the Nitroanilines and Their Relations to the Excited State Dipole Moment. J. Chem. Phys. 1977, 66, 2664-2668. 5. Bublitz, G. U.; Boxer, S. G. Stark Spectroscopy: Applications in Chemistry, Biology, and Materials Science. Annu. Rev. Phys. Chem. 1997, 48, 213-242. 6. Tomasi, J.; Persico, M. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chem. Rev. 1994, 94, 2027-2094. 7. Cramer, C. J.; Truhlar, D. G. Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. Chem. Rev. 1999, 99, 2161-2200. 8. Orozco, M.; Luque, F. J. Theoretical Methods for the Description of the Solvent Effect in Biomolecular Systems. Chem. Rev. 2000, 100, 4187-4226. 9. Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999-3094. 10. Tomasi, J. Selected Features of the Polarizable Continuum Model for the Representation of Solvation. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1, 855-867. 11. Mennucci, B. Modeling Absorption and Fluorescence Solvatochromism with QM/Classical Approaches. Int. J. Quantum Chem. 2015, 115, 1202-1208. 12. Cammi, R. Quantum Cluster Theory for the Polarizable Continuum Model. I. The CCSD Level with Analytical First and Second Derivatives. J. Chem. Phys. 2009, 131, 164104. 13. Caricato, M. Absorption and Emission Spectra of Solvated Molecules with the EOM–CCSD–PCM Method. J. Chem. Theory Comput. 2012, 8, 4494-4502. 14. Caricato, M. Exploring Potential Energy Surfaces of Electronic Excited States in Solution with the EOM-CCCSD-PCM Method. J. Chem. Theory Comput. 2012, 8, 5081-5091. 15. Caricato, M.; Lipparini, F.; Scalmani, G.; Cappelli, C.; Barone, V. Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model. J. Chem. Theory Comput. 2013, 9, 3035-3042. 16. Kim, H. J.; Hynes, J. T. Equilibrium and Nonequilibrium Solvation and Solute Electronic Structure. I. Formulation. J. Chem. Phys. 1990, 93, 5194-5210.


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23 43. Reis, H.; Grzybowski, A.; Papadopoulos, M. G. Computer Simulation of the Linear and Nonlinear Optical Susceptibilities of p-Nitroaniline in Cyclohexane, 1,4-Dioxane, and Tetrahydrofuran in Quadrupolar Approximation. I. Molecular Polarizabilities and Hyperpolarizabilities. J. Phys. Chem. A 2005, 109, 10106-10120. 44. Reis, H.; Papadopoulos, M. G.; Grzybowski, A. Computer Simulation of the Linear and Nonlinear Optical Susceptibilities of p-Nitroaniline in Cyclohexane, 1,4-Dioxane, and Tetrahydrofuran in Quadrupolar Approximation. II. Local Field Effects and Optical Susceptibilitities. J. Phys. Chem. B 2006, 110, 18537-18552. 45. Kawski, A.; Kukliński, B.; Bojarski, P. Excited S1 State Dipole Moments of Nitrobenzene and pNitroaniline from Thermochromic Effect on Electronic Absorption Spectra. Chem. Phys. 2006, 330, 307312. 46. Kosenkov, D.; Slipchenko, L. V. Solvent Effects on the Electronic Transitions of p-Nitroaniline: A QM/EFP Study. J. Phys. Chem. A 2011, 115, 392-401. 47. DeFusco, A.; Minezawa, N.; Slipchenko, L. V.; Zahariev, F.; Gordon, M. S. Modeling Solvent Effects on Electronic Excited States. J. Phys. Chem. Lett. 2011, 2, 2184-2192. 48. Sok, S.; Willow, S. Y.; Zahariev, F.; Gordon, M. S., Solvent-Induced Shift of the Lowest Singlet  → * Charge-Transfer Excited State of p-Nitroaniline in Water: An Application of the TDDFT/EFP1 Method. J. Phys. Chem. A 2011, 115, 9801-9809. 49. Nguyen, P. D.; Ding, F.; Fischer, S. A.; Liang, W.; Li, X. Solvated First-Principles Excited-State Charge-Transfer Dynamics with Time-Dependent Polarizable Continuum Model and Solvent Dielectric Relaxation. J. Phys. Chem. Lett. 2012, 3, 2898-2904. 50. Frutos-Puerto, S.; Aguilar, M. A.; Fdez Galvan, I. Theoretical Study of the Preferential Solvation Effect on the Solvatochromic Shifts of para-Nitroaniline. J. Phys. Chem. B 2013, 117, 2466-2474. 51. Eriksen, J. J.; Sauer, S. P. A.; Mikkelsen, K. V.; Christiansen, O.; Jensen, H. J. A.; Kongsted, J. Failures of TDDFT in Describing the Lowest Intramolecular Charge-Transfer Excitation in paraNitroaniline. Mol. Phys. 2013, 111, 1235-1248. 52. Wielgus, M.; Michalska, J.; Samoc, M.; Bartkowiak, W. Two-Photon Solvatochromism III: Experimental Study of the Solvent Effects on Two-Photon Absorption Spectrum of p-Nitroaniline. Dyes Pigm. 2015, 113, 426-434. 53. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Electronic Absorption Spectra and Solvatochromic Shifts by the Vertical Excitation Model: Solvated Clusters and Molecular Dynamics Sampling. J. Phys. Chem. B 2015, 119, 958-967. 54. Zaleśny, R.; Tian, G.; Hättig, C.; Bartkowiak, W.; Ågren, H. Toward Assessment of Density Functionals for Vibronic Coupling in Two-Photon Absorption: A Case Study of 4-Nitroaniline. J. Comput. Chem. 2015, 36, 1124-1131.



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24 55. Cabral, B. J.; Rivelino, R.; Coutinho, K.; Canuto, S. Probing Lewis Acid-Base Interactions with Born-Oppenheimer Molecular Dynamics: The Electronic Absorption Spectrum of p-Nitroaniline in Supercritical CO2. J. Phys. Chem. B 2015, 119, 8397-8405. 56. Cabral, B. J.; Coutinho, K.; Canuto, S. A First-Principles Approach to the Dynamics and Electronic Properties of p-Nitroaniline in Water. J. Phys. Chem. A 2016, 120, 3878-3887. 57. Benjamin, I. Electronic Spectra in Bulk Water and at the Water Liquid/Vapor Interface.: Effect of Solvent and Solute Polarizabilities. Chem. Phys. Lett. 1998, 287, 480-486. 58. Millefiori, S.; Favini, G.; Millefiori, A.; Grasso, D. Electronic Spectra and Structure of Nitroanilines. Spectrochim. Acta, Part A 1977, 33, 21-27. 59. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H., et al. Gaussian 16, Revision A.03; Gaussian, Inc.; Wallingford, CT, 2016. 60. Heyd, J.; Scuseria, G. E. Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd-Scuseria-Ernzerhof Screened Coulomb Hybrid Functional. J. Chem. Phys. 2004, 121, 11871192. 61. Heyd, J.; Scuseria, G. E. Assessment and Validation of a Screened Coulomb Hybrid Density Functional. J. Chem. Phys. 2004, 120, 7274-7280. 62. Heyd, J.; Peralta, J. E.; Scuseria, G. E.; Martin, R. L. Energy Band Gaps and Lattice Parameters Evaluated with the Heyd-Scuseria-Ernzerhof Screened Hybrid Functional. J. Chem. Phys. 2005, 123, 174101. 63. Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum: “Hybrid Functionals Based on a Screened Coulomb Potential” [J. Chem. Phys. 118, 8207 (2003)]. J. Chem. Phys. 2006, 124, 219906. 64. Izmaylov, A. F.; Scuseria, G. E.; Frisch, M. J. Efficient Evaluation of Short-Range Hartree-Fock Exchange in Large Molecules and Periodic Systems. J. Chem. Phys. 2006, 125, 104103. 65. Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E. Influence of the Exchange Screening Parameter on the Performance of Screened Hybrid Functionals. J. Chem. Phys. 2006, 125, 224106. 66. Henderson, T. M.; Izmaylov, A. F.; Scalmani, G.; Scuseria, G. E. Can Short-Range Hybrids Describe Long-Range-Dependent Properties? J. Chem. Phys. 2009, 131, 044108. 67. Cancès, E.; Mennucci, B.; Tomasi, J. A New Integral Equation Formalism for the Polarizable Continuum Model: Theoretical Background and Applications to Isotropic and Anisotropic Dielectrics. J. Chem. Phys. 1997, 107, 3032-3041. 68. Mennucci, B.; Cancès, E.; Tomasi, J. Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications. J. Phys. Chem. B 1997, 101, 10506-10517. 69. Lipparini, F.; Scalmani, G.; Mennucci, B.; Cances, E.; Caricato, M.; Frisch, M. J. A Variational Formulation of the Polarizable Continuum Model. J. Chem. Phys. 2010, 133, 014106. ACS Paragon Plus Environment

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26 Table 1. Structure parameters, energy difference between Cs and C2v conformers, and molecular dipole moments of the ground state pNA in different environmentsa Vacuum

Dioxane

DCE

DMSO

PBC-HSE06

X-ray71

X-ray72

rC3-C2

1.396

1.396

1.398

1.398

1.404

1.392

1.391

rC2-C1

1.391

1.390

1.389

1.389

1.376

1.370

1.368

rC1-C6

1.407

1.408

1.410

1.410

1.420

1.412

1.407

rC6-N14

1.395

1.392

1.389

1.389

1.342

1.353

1.355

rN14-H16

1.009

1.009

1.010

1.010

1.017

0.750

0.847

rC3-N11

1.466

1.462

1.457

1.456

1.413

1.454

1.434

rN11-O13

1.234

1.235

1.237

1.237

1.242

1.229

1.237

ϕb

40.1

39.9

39.6

39.9

0.1

3.8

5.2

c

25.8

25.7

25.6

25.7

4.7

18.8

2.4

Ed

-1.17

-1.04

-0.92

-0.89

g (Cs)

2.462

2.814

3.188

3.287

g (C2v)

2.713

3.130

3.583

3.721

a: Bond distances in Å, dihedral angle in degree, energy in kcal/mol, and dipole moment in au b: Out-plane-angle of nitrogen pyramidalization (Figure 1) c: Torsion angle of H16-N14-C6-C1 (Figure 1) ACS Paragon Plus Environment

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27 d: Energy difference of the ground state pNA between Cs and C2v symmetry: E = E(Cs) – E(C2v)



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28 Figure 1. The structure and atomic numbering scheme for the pNA. The out-of-plane angle of nitrogen pyramidalization is designated as the . The x-axis is perpendicular to the molecular plane of the benzene ring, atoms C3, C6, N11 and N14 lie along the y-axis, and C2 and C4 lie along the z-axis.


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29 Figure 2. Excitation energies and oscillator strengths (in the parenthesis) of the lowest excited states of pNA in different environments calculated with the EOM-CCSD in vacuum and the EOM-CCSD-SSPTED in solution phase with non-equilibrium solvation



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30 Figure 3. Cumulative average error (in eV) in the vertical excitation energy compared to the SS results for pNA in Dioxane, DCE and DMSO


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31 Figure 4. Cumulative average error (in au) in the excess dipole moment compared to the SS results for pNA in Dioxane, DCE and DMSO



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32 TOC graphic


Calculations of Electronic Excitation Energies and Excess Electric

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