Enabling Forbidden Processes: Quantum and Solvation Enhancement

Article pubs.acs.org/JPCA

Enabling Forbidden Processes: Quantum and Solvation Enhancement of Nitrate Anion UV Absorption Ondřej Svoboda, Lucie Kubelová, and Petr Slavíček* Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, 16628 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: We present simulated electronic absorption spectra of isolated and solvated nitrate anion in the UV region, focusing primarily on the absorption into the first absorption band around 300 nm. This weak absorption band in this spectral region is responsible for the generation of NOx in the polar areas or OH• radicals in the hydrosphere. The 300 nm absorption band is symmetrically strongly forbidden and coupling of at least two vibrational modes is needed to allow the transition in the isolated nitrate anion. Further symmetry breaking is provided by solvation. In this study we model the absorption spectra of nitrate−water clusters using the combined reflection principle path integral molecular dynamics (RP-PIMD) method. Condensed phase UV spectra are modeled within a cluster-continuum model. The calculated spectra are compared with experimental bulk phase measurements and reasonable agreement is found. We also provide a benchmarking of the DFT functionals to be used for a description of the electronically excited states of solvated nitrate anion.

1. INTRODUCTION

It is therefore not surprising that the structure and properties of the nitrate anion have been studied many times using various experimental techniques, focusing on its structure in liquid water13−16 as well as on the interfaces.17−21 The gradual solvation of the nitrate anion was investigated by IR spectroscopy22,23 or photoelectron spectroscopy.24 The nitrate anion has been also extensively studied by means of quantum chemical methods24−30 and methods of molecular simulations.15,31,32 The atmospheric relevance of the nitrate anion stems from the reactions appearing upon the photolysis at around 300 nm.33 The photon absorption in this range triggers two reactions:

Properties of molecular anions are to a large extent controlled by solvation and specifically by hydration.1,2 The hydration mediates the dissociation of neutral precursors into ions and even the very existence of many anions is only possible due to the hydration as the negatively charged molecular species are inherently unstable.3−5 In this contribution, we demonstrate the decisive role of hydration on the UV absorption properties of the nitrate anion. The nitrate anion is one of the more abundant anions on the Earth. Its trace concentrations are found in natural waters. Furthermore, the occurrence of the nitrate anion is extremely enhanced in the areas with intense agriculture due to the use of various nitrate-based fertilizers. Atmospheric solar radiation (with λ > 290 nm) is capable of decomposing nitrate anion, forming in two consecutive reactions OH• radical (see below). The OH• radical can then oxidize organic molecules from polluted water or atmospheric water phases.6,7 There have been also attempts to use nitrate anion for advanced oxidation technology treatment of water using UV radiation.8 It is now generally accepted that nitrate anion is the major chromophore in the Antarctic snow.9,10 The nitrate concentrations have been rather stable through the past centuries and could potentially serve as a key parameter in paleoatmospheric models. Although the nitrate anion has long been considered the end-product of the NOx photochemistry, it has been found that the nitrate photochemistry significantly influences the polar atmosphere.9,10 The OH• radicals formed upon the nitrate photolysis greatly enhance the oxidative capacity of the snow and ice. Nitrate is also a key element in the polar stratospheric clouds.11,12 © 2013 American Chemical Society

λ ≈ 300nm

NO3− + hv ⎯⎯⎯⎯⎯⎯⎯⎯⎯→ NO2− + O(3P) ϕ = 1.1 × 10−3 λ ≈ 300nm

NO3− + hv ⎯⎯⎯⎯⎯⎯⎯⎯⎯→ NO2 + O−

ϕ = 9.2 × 10−3

with the quantum yields measured in the liquid taken from ref 34 (other groups have reported slightly different values35−40). Similar quantum yields have been obtained also for the nitrate anion solvated on ice and pellets and submillimeter ice films.41−43 The oxygen anion further reacts with water, forming OH− anion and the OH• radical, a major oxidative species in the atmosphere. The photochemistry initiated by the absorption of light around 200 nm is quite distinct.44−50 The overview of the nitrate photochemistry can be found, e.g., in refs 39 and 40. The photochemistry of the nitrate anion is also Received: October 4, 2013 Revised: November 15, 2013 Published: November 15, 2013 12868

dx.doi.org/10.1021/jp4098777 | J. Phys. Chem. A 2013, 117, 12868−12877

The Journal of Physical Chemistry A

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different on the surfaces of the aerosol particles20,51 or snow or ice.41−43,52 The photon absorption in the atmospherically important 300 nm region is extremely weak. The nitrate anion UV spectrum consists of two bands; the very weak band at ∼310 nm ( f ∼ 10−4)30,53 corresponds to the symmetrically forbidden n → π* transition whereas the bright state (f ∼ 0.3) appearing around 205 nm results from a π → π* transition. The intensity of the n → π* is controlled by solvation as is experimentally demonstrated by a strong dependence of the spectrum on the polarity of the solvent.54 In the gas phase the nitrate anion exists in a highly symmetrical structure exhibiting the D3h symmetry.55 The absorption into the forbidden band for the nitrate anion in the gas phase is possible only by the coupling of two distinct vibrational modes.56 The nitrate anion loses its high symmetry in the solution. The symmetry breaking can conveniently be visualized within IR spectroscopy. The IR spectra of microhydrated nitrate clusters recorded in the Neumark group clearly indicate the asymmetry of hydration,22,23 which persists in the condensed phase.13,27,31,57 The goal of this study is to model the effect of solvation and quantum vibrational delocalization on the UV absorption characteristics of the nitrate anion. We represent the solvated nitrate anion within a cluster-continuum approach; i.e., the electronic structure calculations are performed for finite size molecular clusters which are embedded in dielectric continuum. Such an approach has been previously successfully used for both UV absorption and photoionization spectra modeling.58,59 Our aim is to model the spectrum quantitatively, including the shape of the spectrum as well as its intensity. This is achieved using the reflection principle method combined with the path integral molecular dynamics simulations (RP-PIMD).58,60,61 The modeling of the spectra at the quantitative level is needed if the ab initio based calculations are to be incorporated into large scale atmospheric model. This would be rather desirable. It is, for example, not known whether the absorption cross section of nitrate on the surface of ice or snow or in the quasiliquid layer is the same as the absorption cross section in the bulk water.62,63 With reliable theoretical techniques, we could model the absorption of the nitrate anion in various structural arrangements.

principle method65 which has been suggested for treating systems with dissociative final states. Classically, the reflection principle can be interpreted as a reflection of the initial ground state density onto the excited state and further on the energy axis. Formally, the expression for the absorption cross-section within the reflection principle reads66,67 σ (E ) =

π e 2E 3ℏε0c

∑ ∫ ρα |μab |2 δ(E − Eab) dR b

where ρα is the electronic ground state density, μab is a transition dipole moment in the geometry R, and Eab is the difference between the energy of the ground and excited electronic state. Eab is expressed here as Eab = Eb(R) − Ea(R)

that is, we consider the difference between the ground and excited state energies at each geometry (the so-called semiclassical coordinate space representation68). It is also possible to make a kinetic energy correction, accounting thus for zero point energy effects.69 The reflection principle had originally been used mostly for the qualitative interpretation of electronic spectra of simple molecules, it turns out, however, that this approach is capable of modeling quantitatively the absorption spectra of large molecules,70 molecular clusters58,60 or highly anharmonic systems.61,71 The reflection principle has several principal limitations; in particular the vibrational progression of the electronic spectrum is lost. Furthermore, the quality of the calculations is limited by the input quantities obtained from quantum-excited state energies, transition dipole moments and ground state distribution. The excitation energies need to be always carefully benchmarked (see below). The transition dipole moment can be taken to constant and set equal to its value in the equilibrium geometry (Franck−Condon approximation). This would be completely inappropriate for the case of nitrate anion with a zero transition dipole moment in its equilibrium geometry of the D3h symmetry. We instead consider the full transition dipole moment surface within the Monte Carlo evaluation of the integral in the second equation.61 The critical issue is the evaluation of the ground state density. The easiest approach is the sampling based on the ground state harmonic vibrational wave function. This approach would, however, fail for systems with highly anharmonic modes that are always present in the solvated systems. We could alternatively sample the density via classical molecular dynamics simulations. Here, we lose the quantum fluctuations, often dominantly responsible for the width of the electronic spectra. Path integral molecular dynamics (PIMD) sampling takes into account both quantum and thermal effects. The path integral formulation of quantum mechanics makes use of the similarity between the partition function of the classical system and the partition function of the quantum system, where each atom is represented as a chain of fictitious particles (i.e., beads). If the number of beads were infinite, the path integral formulation would be exact. However, this is not possible and the main approximation using the PIMD protocol is then the choice of the number of beads. In this study we have chosen to employ ten beads for an atom. 2.2. Electronic Structure Methods. Description of aqueous systems is in general difficult as the weak intermolecular interactions are involved. The use of highly

2. METHODS 2.1. Absorption Spectra Calculation. The primary goal of this study is to calculate photoabsorption spectra of the nitrate anion and nitrate−water clusters. We start with the general expression for the photoabsorption cross-section σ:64 σ (E ) =

πE 3ℏε0c

∑ Pα |⟨ψβ|R̂|ψα⟩|2 δ(E − Eαβ) α ,β

with ψα and ψβ being initial and final sets of rovibronic states, Pα is probability of finding a particle in the initial state, Eαβ an excitation energy, R̂ a position operator, e the elementary charge, c the speed of light, ε0 the permittivity of vacuum, and finally E an energy of an interacting light. Here we use the dipole approximation, neglecting thus quadrupole and higher order interactions. The formula for the photoabsorption crosssection can be in principle evaluated exactly either within timeindependent approach or using wavepacket dynamics calculations. However, its exact evaluation is only limited to systems with few degrees of freedom and further approximations are needed for larger systems. Here we use the so-called reflection 12869



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3. RESULTS AND DISCUSSION 3.1. Electronic Structure of the Nitrate Anion. Let us begin the results by describing the excited states of the bare nitrate anion. Table 1 shows energies and oscillator strengths of

accurate wave function based methods (e.g., CCSD(T)) is often computationally not feasible due to the increasing system size. The evaluation of the expression for absorption cross section within the RI-PIMD method typically requires many thousands evaluations of energies and forces in the ground state and several hundred evaluations of the excitation energies and transition dipole moments. Therefore, we have to apply density functional methods for both the ground and excited state calculations. For the ground state calculations, one should use a density functional method including dispersion interactions. We decided to describe dispersion using DFT-D corrections developed by Grimme et al.72−74 based on the recent benchmark study by Burns et al.75 keeping in mind that local functionals and relatively small basis sets would facilitate the calculations. Considering all these factors we decided to employ the B97-D functional73 with aug-cc-pVDZ basis for the long path integral molecular dynamics runs. Furthermore, we need to accurately describe the excitation energies and transition dipole moments for the very calculation of the spectrum. To do that, we have made an assessment of several DFT functionals and finally evaluated the CAM-B3LYP one as the best among the functionals tested. The benchmarking of various density functionals with respect to the excited state calculations is described partly in section 3.3 and more extensively in the Supporting Information. 2.3. Modeling Solvation Effects. The UV absorption spectra are modeled within a combined cluster-continuum model. First, small clusters consisting of the nitrate chromophore and several water units are optimized (or its geometries are sampled) in the gas phase. The cluster is then embedded into a dielectric continuum and its properties are calculated. Here, we apply the polarizable continuum model (PCM),76 taking into account the mutual polarization of the solvent and solute molecules. This combined approach is thus capable of accounting for both the specific solvent effects in the first solvation shell and the long-range polarization effects. As the UV absorption is a very fast process, we take into account only the optical part of the solvent response; i.e., we apply the concept of nonequilibrium solvation. The application of the dielectric models in the computational modeling of the electronic spectroscopy was successfully applied both for the absorption spectroscopy77 and in the photoelectron spectroscopy.78 Note, however, that the method has its limitations as the structure of the finite size molecular clusters can be quite distinct from the structure of the first solvation shell for nitrate anion solvated in bulk water. 2.4. Technical Details. The PIMD is implemented as described in ref 79 using up to 10 beads. For each cluster size we have performed the PIMD simulation for 1 ps of the equilibration run followed by a 6 ps production run. The PIMD simulation trajectories were sampled at 2000 randomly generated points for which the excitation energies were calculated. The temperature was set to T = 250 K. A Nosé− Hoover chain (NHC) thermostat (4 thermostats in the chain with a mass of 0.02 au) and the RESPA integrator79 were used. The B97-D/aug-cc-pVDZ method with the resolution of identity approach has been used to calculate the forces in the ground state. The energies and forces for the molecular dynamics calculations have been evaluated in Turbomole 5.10 package80 whereas the excitation energies have been calculated using Gaussian 09 package.81

Table 1. Lowest Electronically Excited States in the Gas Phase Nitrate Anion Calculated with the EOM-CCSD Methoda E (eV)/f symmetry

EOM-CCSD/631+g*

EOM-CCSD/aug-ccpVDZ

EOM-CCSD/aug-ccpVQZ

1A1″ 1A2′ 1E″ 1E′ 2E′

4.06/0.00 5.94/0.00 6.16/0.00 6.36/0.17 7.40/0.10

4.05/0.00 5.60/0.00 6.16/0.00 6.25/0.12 6.82/0.13

4.09/0.00 5.39/0.00 6.13/0.00 6.45/0.17 6.07/0.04

a

The oscillator strength f is also shown.

several excited states calculated using three different basis sets and the equation of motion coupled clusters with singles and doubles (EOM-CCSD) method. The lowest excited state of the 1A1″ character is found at 4.09 eV (calculated with the aug-ccpVQZ basis set). The transition into this state from the ground (1A1′) state is symmetrically highly forbidden. This transition mostly corresponds to an excitation of electron from 1a2′ orbital into 2a2′ orbital (Figure 1) and is responsible for the

Figure 1. Electronic transitions in the isolated nitrate anion. In the upper row we present the orbitals occupied in the ground state; in the lower row the virtual orbitals are shown. The dominant transitions for a given state are indicated by arrows. The Rydberg states are omitted in the figure.

weak absorption around 300 nm. Next in energy is a Rydberg transition located in the gas phase at around ∼5.39 eV (1A2′ state). The energy of this state is strongly dependent on the basis set used for the calculation. We can anticipate that this state will be shifted up in energy in water solution due to the Pauli repulsion between the extended excited state wave function and the solvent water molecules. Somewhat higher in energy are located two doubly degenerate states, the 1E″ state at 6.13 eV and the 1E′ state at 6.45 eV. The second pair of degenerate states represents the first allowed transition and we refer to this transition later in the text as a bright state. It is characterized mostly as the transition from the 1e″ orbital into the 2a″ orbital (Figure 1), usually assigned as a π → π* state. The last state considered here is a Rydberg-like 2E′ state. The energy and oscillator strength is strongly basis set dependent, with the f gradually vanishing with the increasing basis set. This state is shifted up in energy in the solution. The electronic 12870



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stable than the other isomer). In general, we observe either symmetrically hydrated clusters or structures where several water molecules bind to a single site (e.g., the second structure of the NO3−···(H2O)5 shown in Figure 2). However, our calculations indicate that both structural arrangements are rather close in energy (e.g., the second structure of the NO3−··· (H2O)5 cluster is stabilized by 0.1 eV). We emphasize the structures chosen here were only used as initial structures for the subsequent molecular dynamics runs. The microhydration of the water clusters was previously studied by Goebbert et al.22 who compared the measured IR spectra with theoretical estimates. They confirm that up to the NO3−···(H2O)3 structure the nitrate tended to be hydrated symmetrically. For larger clusters, however, the most stable are structures with an extended ring or chain of waters linked to the nitrate molecule. The structure of the clusters starts to be generally asymmetrical, with the nitrate anion staying on the surface of the clusters. The globally asymmetrical structures were found to dominate up until the size of 300 water units, for larger clusters and bulk water, the nitrate anion is depleted from the interfacial region.32 3.3. Benchmark of Density Functional Methods for the Excited State Calculations. A large number of electronic structure calculations is required for the UV absorption spectra simulations, and we thus need to find out a computationally feasible yet reliable electronic structure method. The TD-DFT methods represent a reasonable choice yet a careful benchmarking is needed before a particular functional is used for large scale simulations. As the experimental absorption spectrum of the nitrate anion is not available, the benchmarking cannot be based on the experimental reference data. To assess the performance of the tested electronic structure methods, we have calculated excitation energies and transition dipole moments for the minimum energy structures of the NO3− and NO3−···H2O systems. We have used the highly accurate EOM-CCSD method as a benchmark reference. The whole benchmark (with B97-D,73 PBE,82 B3LYP,83 BHandHLYP,84 M06HF,85 CAM-B3LYP,86 ωB97,87 ωB97X,87 ωB97X-D,88 and LC-ωPBE89 functionals) is provided in the Supporting Information. Here we only briefly summarize the most important findings:

structure in the solution is similar, with the exception that the 2E′ state is not in the energetic window anymore. The excitation energies reported here are somewhat lower than the values found in previous studies by Harris30 and McCarthy et al.53 because of the different methodology used. 3.2. Structure of Nitrate−Water Clusters. Figure 2 shows the geometries of NO3−···(H2O)n clusters considered in

Figure 2. Geometries of nitrate−water clusters optimized at the B97D/aug-cc-pVDZ level.

the cluster-continuum models. The structures were optimized at the B97-D/aug-cc-pVDZ level and generally they are consistent with previously published structures. The nitrate anion solvated with a single water molecule forms a planar structure with two hydrogen bonds between the nitrate anion and the water molecule. The nitrate anions with two and three water molecules show similar structural arrangements. The NO3−···(H2O)3 thus again possesses a symmetrical structure with a D3h symmetry. Starting from the NO3−···(H2O)3 cluster, we observe different possible isomers with almost degenerate energies (the first structure in Figure 2 being 0.03 eV more

Figure 3. Convergence of the UV spectrum with the number of beads in the RP-PIMD simulations for the dark (a) and bright (b) states of the NO3− anion. The B97-D/aug-cc-pVDZ method was used for the PIMD simulations; excitation energies and transition dipole moments were recalculated using the TDDFT/CAM-B3LYP/aug-cc-pVDZ method. 12871



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water molecules. All the calculations are performed with 10 beads in the PIMD simulations, which provide essentially converged quantum results. The two absorption bands (the weak one at 300 nm and the strong one at 200 nm) are treated separately. We compare the calculated spectra with the experiment.54,90 For the forbidden transition (Figure 4), we see very low value of the absorption cross-section of the bare nitrate anion

(1) GGA functionals suffer from spurious charge transfer states and fail to provide correct excitation energies. (2) Mixing of HF exchange significantly improves the results; range-separated hybrids perform better than the global ones. (3) EOM-CCSD and some functionals fail to predict correct oscillator strengths for the transition near 200 nm using middle-sized basis set (e.g., aug-cc-pVDZ). (4) CAM-B3LYP was selected as the best performing functional and was used to calculate excitation energies and transition dipole moments in this work. 3.4. Symmetry Breaking via Molecular Vibrations: UV Absorption Spectrum of the Gas Phase NO3−. The UV absorption spectrum of the isolated nitrate anion should be in principal quite simple as the only optically allowed singlet state is the 1E′ state lying at around 200 nm. All the other states in the energy window below water absorption are forbidden for the nitrate anion in the D3h symmetry. It is, however, known that even forbidden processes can be mediated by molecular vibrations by intensity borrowing from the bright states. Yet the symmetry restrictions are rather strict for the absorption into the A1″ state. The electronic transition dipole moment for the transition is zero, which means that the absorption cross section vanishes within Franck−Condon approximation. However, even the first derivatives of the transition dipole moments have zero value (as well as the second derivatives along the same coordinates), so that no absorption is calculated even within the Herzberg−Teller approximation. It has been pointed out by Strickler and Kasha that a second-order vibronic coupling involving at least two different molecular vibrations is needed to explain the observed spectra.56 With a perturbation analysis they concluded that the oscillator strength f = 3 × 10−7, 3 orders of magnitude lower than the experimental one. The RP-PIMD method allows accounting for the nonCondon effects directly. Figure 3 shows the calculated UV absorption spectrum of the isolated nitrate anion at 250 K. The calculated intensity increases with the number of beads included into the PIMD calculations. The simulation with a single bead is equivalent to the classical molecular dynamics and the vibrational delocalization is given entirely by the thermal agitation. As the number of beads increases, the ground state distribution gradually converges to the quantum limit. It is seen that with 10 beads, the simulation of the dark state absorption spectrum (a) is essentially converged. The calculated value of the absorption cross section is, however, well below the experimental value measured in water solution. The calculated oscillator strength is approximately 2 × 10−6. This is an order of magnitude higher than the theoretical estimate done by Strickler and Kasha,56 on the other hand our calculated value is still 2 orders of magnitude lower than the experimental one. This clearly indicates that vibrational delocalization itself is not able to solely explain the absorption into the first absorption band of the nitrate anion. The intensity of the bright state absorption band (b) is much less dependent on the number of beads. The width of the spectrum increases and the intensity slightly decreases but already the Franck− Condon model is principally able to describe the UV absorption into this band. 3.5. Symmetry Breaking via Solvation: UV Absorption Spectrum Finite Size NO3−···(H2O)n Clusters. In this section we report the calculated photoabsorption spectra for clusters of nitrate anion and water with one to five solvating

Figure 4. Dark state absorption of the nitrate anion with growing cluster size. Sampling was performed with the RP-PIMD method (10 beads) on the B97-D/aug-cc-pVDZ potential energy surface; excitation energies and transition dipole moments were calculated using the TDDFT/CAM-B3LYP/aug-cc-pVDZ method.

(the maximum being at approximately 6 × 10 −22 cm 2 molecule−1). However, even this low value is only possible because of the distorted configurations that can only take place due to the coupling of two independent vibrational modes. After adding an additional water molecule, we observe a very significant increase of 1 order of magnitude of the absorption cross-section. Moreover, the maximum of the absorption peak is blue-shifted, moving from 338 to 323 nm. The explicit addition of more water molecules shows the same trend; i.e., the photon absorption becomes increasingly probable while the peak maximum shifts to lower wavelengths. For the largest cluster considered; i.e., the NO3−···(H2O)5 we observe again an increase in the absorption cross-section and a slight blue shift. We have also calculated the spectra of the bright state photoabsorption (Figure 5). Here we observe that for both the bare nitrate anion and the nitrate−water clusters the absorption first appears near 230 nm. The maximum of the nitrate anion absorption is located approximately at 200 nm. The precise localization of the maximum is, however, difficult because it intersects with the water absorbing near 200 nm.58 On the other hand, we can see clearly that (unlike for the weak absorption band) the onset of the absorption band is independent of the number of water molecules. The solvation plays a decisive role on the absorption into the dark state. It is, however, not clear whether the primary cause of the increased absorption stems from the deformation of the nitrate anion induced by the solvation or whether it is an electronic effect; i.e., it results from a deformation of the electronic cloud in the nitrate chromophore via solvation. To this end, we have performed a PIMD simulation of the NO3−··· H2O cluster with a frozen nitrate anion geometry. The results shown in Figure 6 indicate the shape of the spectrum changes; 12872



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Figure 7. Dark state absorption band of the NO3−·(H2O)5 cluster embedded in the dielectric continuum. Sampling was performed with the RP-PIMD method (10 beads) on the B97-D/aug-cc-pVDZ potential energy surface; excitation energies and transition dipole moments were calculated using the TDDFT/CAM-B3LYP/aug-ccpVDZ method.

Figure 5. Bright state absorption of the nitrate anion with growing cluster size. Sampling was performed with the RP-PIMD method (10 beads) on the B97-D/aug-cc-pVDZ potential energy surface; excitation energies and transition dipole moments were calculated using the TDDFT/CAM-B3LYP/aug-cc-pVDZ method.

it is narrower with higher intensity for both states. However, the integrated value of the total absorption is not very affected pointing toward the electronic origin of spectra broadening. The difference between the experimental spectrum measured in bulk water and the calculated UV spectra for the finite size molecular clusters is still relatively large, especially for the 300 nm band. This can be explained by (a) the inadequate level of the electronic structure description. However, our benchmarking in section 3.3 suggests that the difference should be smaller, (b) missing long-range solvation effects, and (c) a different structural arrangement in the first solvation shell in the bulk water and in finite size clusters. 3.6. UV Spectrum of Solvated Nitrate Anion: ClusterContinuum Model. Figure 7 shows the calculated absorption cross section for the NO3−···(H2O)5 cluster embedded in the dielectric continuum. The effect of the long-range interactions on the spectral shape and intensity is not very significant for the forbidden transition. This indicates that the chromophore does not exhibit any strong change in the charge distribution between the ground and excited states. The resulting UV

absorption spectrum is somewhat blue-shifted with respect to the gas phase calculations, yet the implicit solvation does not overwhelmingly affect its absorption cross section. We can expect that further explicit solvation of the nitrate anion would lead to additional increase in the intensity. Furthermore, we might anticipate that the absorption cross section will be rather sensitive to the actual structural arrangement. The absorption on the ice and in the bulk water thus might be quite distinct. On the other hand, the effect of implicit solvation is very pronounced for the bright state photoabsorption (Figure 8). First, we observe a formation of a clear peak corresponding to the nitrate anion; the nitrate excited electronic states are no more mixed with the excited states of water. Noticeably, the intensity of the transition significantly increases upon the embedding of the cluster into the polarizable continuum. The spectral shape still almost does not depend on the explicit solvation (Figure 8a). The calculated UV absorption cross section for the bright peak is in reasonable agreement with the experiment, almost

Figure 6. Disentangling the effect of the NO3− deformation on the UV absorption spectra. Simulations performed in all degrees of freedom (red curves) are compared with simulations using frozen nitrate geometry. Sampling was performed with the RP-PIMD method (10 beads) on the B97D/aug-cc-pVDZ potential energy surface; excitation energies and transition dipole moments were calculated using the TDDFT/CAM-B3LYP/augcc-pVDZ method. 12873



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Figure 8. Bright state absorption of the nitrate anion using the polarizable continuum model. Part a shows the spectrum calculated using TDDFT/ CAM-B3LYP/aug-cc-pVDZ for various cluster sizes. Part b shows the spectrum of the bare nitrate anion immersed in a polarizable continuum, but calculated using the EOMCCSD/aug-cc-pVDZ method. The spectrum is modeled within the RP-PIMD method (10 beads) on the B97-D/aug-ccpVDZ potential energy surface.

experiment to compare against, the path integral molecular dynamics is the most rigorous way (within a reflection principle framework) for the absorption spectra calculation of cluster models. In the absence of the experiment, the PIMD based reflection principle can thus serve as a useful benchmark for more approximate treatments, e.g., within the Wigner transform of a harmonic wave function or classical MD. As the UV absorption of the nitrate anion is extremely important in atmospheric modeling, it would be desirable to extend the present study to larger systems, nitrate anion in bulk water, on the surface of ice or in the quasi-liquid layer on the surface of snow. The asymmetry on the interfaces (or, alternatively, only the partial solvation on the surfaces) can lead to a significantly changed UV absorption profile. The goals set above could be reached using QM/MM approaches for the sampling of the ground state combined with more efficient path integral methods, e.g., those based on the quantum thermostat technique.91 Such a work is currently underway. It would be also interesting to model the UV absorption spectra of the nitrate anion in solvents other than water. It has been shown experimentally that the intensity of the 300 nm absorption band is sensitively controlled by the polarity of the solvent.54 The molecular interpretation of this old observation is nowadays possible.

coinciding in the absolute intensity and position of the peak, with a slightly narrower peak width in the simulations. The peak position is, however, still somewhat blue-shifted. This is an artifact of the electronic structure method as we show in the Figure 8b where we used the more accurate EOM-CCSD approach for the electronic structure description. The EOMCCSD vbased spectrum virtually coincides with the experiment.

4. CONCLUSIONS AND OUTLOOK In the present work, we have used the reflection principle method combined with path integral molecular dynamics to simulate the UV absorption of hydrated nitrate anion, focusing on the spectral region 200−350 nm. The results can be summarized as follows: (1) In the solution, six electronic states can contribute to the UV absorption spectrum of the nitrate anion in the 200− 350 nm spectral range. The strong (200 nm) and weak (300 nm) absorption bands can be ascribed to E1′ and A1″ transitions. (2) The long-range corrected functionals should be used to model UV absorption of hydrated nitrate clusters. The CAM-B3LYP functional with aug-cc-pVDZ basis was used in this work. (3) The absorption into the forbidden A1″ state is mediated by a simultaneous displacement along at least two normal modes. The calculated intensity in the gas phase is, however, still too low to explain the absorption cross section of hydrated nitrate anion in the 300 nm spectral range. (4) Interaction of the nitrate anion with the surrounding water molecules leads to a symmetry breaking, which is the major factor leading to the absorption into the state of nominally A1″ symmetry. (5) The absorption intensity into the bright E1′ state is almost independent of the structure of the first solvation shell; it is, however, heavily influenced by long-range solvent effects. We have shown here that the RP-PIMD method is capable of simulating the forbidden transition of the nitrate anion. The quantum effects are essential for the absorption spectrum modeling of the bare nitrate anion. Because there is no

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ASSOCIATED CONTENT

* Supporting Information S

We provide detailed benchmark of TDDFT excitation energies for bare nitrate anion and nitrate anion with one water together with textual conclusion. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*P. Slavič́ ek: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support of the Grant Agency of the Czech Republic, grant. No. P208/10/1724 and a travel 12874



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grant “Barrande” provided by the Ministry of Education, Youth and Sport of the Czech Republic, no. 7AMB12FR016. Financial support for O.S. from specific university research (MSMT No. 21/2013) is acknowledged. O.S. is a student of the Max Planck international school “Dynamical Processes in Atoms, Molecules and Solids.”

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(19) Krepelova, A.; Newberg, J. T.; Huthwelker, T.; Bluhm, H.; Ammann, M. The nature of nitrate at the ice surface studied by XPS and NEXAFS. Phys. Chem. Chem. Phys. 2010, 12, 8870−8880. (20) Richards, N. K.; Wingen, L. M.; Callahan, K. M.; Nishino, N.; Kleinman, M. T.; Tobias, D. J.; Finlayson-Pitts, B. J. Nitrate Ion Photolysis in Thin Water Films in the Presence of Bromide Ions. J. Phys. Chem. A 2011, 115, 5810−5821. (21) Gankanda, A.; Grassian, V. H. Nitrate Photochemistry in NaY Zeolite: Product Formation and Product Stability under Different Environmental Conditions. J. Phys. Chem. A 2013, 117, 2205−2212. (22) Goebbert, D. J.; Garand, E.; Wende, T.; Bergmann, R.; Meijer, G.; Asmis, K. R.; Neumark, D. M. Infrared Spectroscopy of the Microhydrated Nitrate Ions NO3−(H2O)1−6. J. Phys. Chem. A 2009, 113, 7584−7592. (23) Asmis, K. R.; Neumark, D. M. Vibrational Spectroscopy of Microhydrated Conjugate Base Anions. Acc. Chem. Res. 2012, 45, 43− 52. (24) Wang, X. B.; Yang, X.; Wang, L. S.; Nicholas, J. B. Photodetachment and theoretical study of free and water-solvated nitrate anions, NO3−(H2O)n (n=0−6). J. Chem. Phys. 2002, 116, 561− 570. (25) Pathak, A. K. Theoretical study on microhydration of NO3− ion: Structure and polarizability. Chem. Phys. 2011, 384, 52−56. (26) Pathak, A. K. Normal modes for probing the local solvation environment of nitrate anion during step wise hydration: A theoretical study. Chem. Phys. 2012, 400, 86−92. (27) Ramesh, S. G.; Re, S. Y.; Hynes, J. T. Charge transfer and OH vibrational frequency red shifts in nitrate-water clusters. J. Phys. Chem. A 2008, 112, 3391−3398. (28) Grana, A. M.; Lee, T. J.; Headgordon, M. Ab-Initio Calculations of Singlet and Triplet Excited-States of Chlorine Nitrate and NitricAcid. J. Phys. Chem. 1995, 99, 3493−3502. (29) Peterson, K. A.; Li, Y. M.; Francisco, J. S.; Zou, P.; Webster, C. E.; Perez, L. M.; Hall, M. B.; North, S. W. The role of triplet states in the long wavelength absorption region of bromine nitrate. J. Chem. Phys. 2003, 119, 7864−7870. (30) Harris, L. E. Lower Electronic States of Nitrite and Nitrate Ion, Nitromethane, Nitramide, Nitric-Acid, and Nitrate Esters. J. Chem. Phys. 1973, 58, 5615−5626. (31) Lebrero, M. C. G.; Bikiel, D. E.; Elola, M. D.; Estrin, D. A.; Roitberg, A. E. Solvent-induced symmetry breaking of nitrate ion in aqueous clusters: A quantum-classical simulation study. J. Chem. Phys. 2002, 117, 2718−2725. (32) Miller, Y.; Thomas, J. L.; Kemp, D. D.; Finlayson-Pitts, B. J.; Gordon, M. S.; Tobias, D. J.; Gerber, R. B. Structure of Large NitrateWater Clusters at Ambient Temperatures: Simulations with Effective Fragment Potentials and Force Fields with Implications for Atmospheric Chemistry. J. Phys. Chem. A 2009, 113, 12805−12814. (33) Daniels, M.; Meyers, R. V.; Belardo, E. V. Photochemistry of Aqueous Nitrate System. I. Excitation in 300-mμ Band. J. Phys. Chem. 1968, 72, 389−399. (34) Warneck, P.; Wurzinger, C. Product Quantum Yields for the 305-nm Photodecomposition of NO3− in Aqueous-Solution. J. Phys. Chem. 1988, 92, 6278−6283. (35) Bayliss, N. S.; Bucat, R. B. Photolysis of Aqueous Nitrate Solutions. Aust. J. Chem. 1975, 28, 1865−1878. (36) Zepp, R. G.; Hoigne, J.; Bader, H. Nitrate-Induced Photooxidation of Trace Organic-Chemicals in Water. Environ. Sci. Technol. 1987, 21, 443−450. (37) Zellner, R.; Exner, M.; Herrmann, H. Absolute Oh Quantum Yields in the Laser Photolysis of Nitrate, Nitrite and Dissolved H2O2 at 308 and 351 Nm in the Temperature-Range 278−353 K. J. Atmos. Chem. 1990, 10, 411−425. (38) Alif, A.; Boule, P. Photochemistry and Environment XIV. Phototransformation of Nitrophenols Induced by Excitation of Nitrite and Nitrate Ions. J. Photochem. Photobiol. A 1991, 59, 357−367. (39) Mark, G.; Korth, H. G.; Schuchmann, H. P.; vonSonntag, C. The photochemistry of aqueous nitrate ion revisited. J. Photochem. Photobiol. A 1996, 101, 89−103.

REFERENCES

(1) Ehrler, O. T.; Neumark, D. M. Dynamics of Electron Solvation in Molecular Clusters. Acc. Chem. Res. 2009, 42, 769−777. (2) Jungwirth, P.; Tobias, D. J. Ions at the air/water interface. J. Phys. Chem. B 2002, 106, 6361−6373. (3) Pluharova, E.; Oncak, M.; Seidel, R.; Schroeder, C.; Schroeder, W.; Winter, B.; Bradforth, S. E.; Jungwirth, P.; Slavicek, P. Transforming Anion Instability into Stability: Contrasting Photoionization of Three Protonation Forms of the Phosphate Ion upon Moving into Water. J. Phys. Chem. B 2012, 116, 13254−13264. (4) Hendricks, J. H.; de Clercq, H. L.; Freidhoff, C. B.; Arnold, S. T.; Eaton, J. G.; Fancher, C.; Lyapustina, S. A.; Snodgrass, J. T.; Bowen, K. H. Anion solvation at the microscopic level: Photoelectron spectroscopy of the solvated anion clusters, NO−(Y)n, where Y=Ar, Kr, Xe, N2O, H2S, NH3, H2O, and C2H4(OH)2. J. Chem. Phys. 2002, 116, 7926−7938. (5) Wang, X. B.; Wang, L. S. Photoelectron Spectroscopy of Multiply Charged Anions. Annu. Rev. Phys. Chem. 2009, 60, 105−126. (6) Stemmler, K.; von Gunten, U. OH radical-initiated oxidation of organic compounds in atmospheric water phases: part 1. Reactions of peroxyl radicals derived from 2-butoxyethanol in water. Atmos. Environ. 2000, 34, 4241−4252. (7) Stemmler, K.; von Gunten, U. OH radical-initiated oxidation of organic compounds in atmospheric water phases: part 2. Reactions of peroxyl radicals with transition metals. Atmos. Environ. 2000, 34, 4253−4264. (8) Schenck, G. O. Handbook of Water Purification; Ellis Horwood Ltd.: Chichester, U.K., 1987. (9) Domine, F.; Shepson, P. B. Air-snow interactions and atmospheric chemistry. Science 2002, 297, 1506−1510. (10) Grannas, A. M.; Jones, A. E.; Dibb, J.; Ammann, M.; Anastasio, C.; Beine, H. J.; Bergin, M.; Bottenheim, J.; Boxe, C. S.; Carver, G.; et al. An overview of snow photochemistry: evidence, mechanisms and impacts. Atmos. Chem. Phys. 2007, 7, 4329−4373. (11) Peter, T. Microphysics and heterogeneous chemistry of polar stratospheric clouds. Annu. Rev. Phys. Chem. 1997, 48, 785−822. (12) Donsig, H. A.; Herridge, D.; Vickerman, J. C. Static SIMS studies of reactions on mimics of polar stratospheric clouds III: Mechanism of chlorine nitrate decomposition and reaction. J. Phys. Chem. A 1999, 103, 9211−9220. (13) Waterland, M. R.; Kelley, A. M. Far-ultraviolet resonance Raman spectroscopy of nitrate ion in solution. J. Chem. Phys. 2000, 113, 6760−6773. (14) Hudson, P. K.; Schwarz, J.; Baltrusaitis, J.; Gibson, E. R.; Grassian, V. H. A spectroscopic study of atmospherically relevant concentrated aqueous nitrate solutions. J. Phys. Chem. A 2007, 111, 544−548. (15) Xu, M.; Larentzos, J. P.; Roshdy, M.; Criscenti, L. J.; Allen, H. C. Aqueous divalent metal-nitrate interactions: hydration versus ion pairing. Phys. Chem. Chem. Phys. 2008, 10, 4793−4801. (16) Thogersen, J.; Rehault, J.; Odelius, M.; Ogden, T.; Jena, N. K.; Jensen, S. J. K.; Keiding, S. R.; Helbing, J. Hydration Dynamics of Aqueous Nitrate. J. Phys. Chem. B 2013, 117, 3376−3388. (17) Wren, S. N.; Donaldson, D. J. Glancing-angle Raman study of nitrate and nitric acid at the air-aqueous interface. Chem. Phys. Lett. 2012, 522, 1−10. (18) Brown, M. A.; Winter, B.; Faubel, M.; Hemminger, J. C. Spatial Distribution of Nitrate and Nitrite Anions at the Liquid/Vapor Interface of Aqueous Solutions. J. Am. Chem. Soc. 2009, 131, 8354− 8355. 12875



Article

(40) Mack, J.; Bolton, J. R. Photochemistry of nitrite and nitrate in aqueous solution: a review. J. Photochem. Photobiol. A 1999, 128, 1−13. (41) Dubowski, Y.; Colussi, A. J.; Hoffmann, M. R. Nitrogen dioxide release in the 302 nm band photolysis of spray-frozen aqueous nitrate solutions. Atmospheric implications. J. Phys. Chem. A 2001, 105, 4928−4932. (42) Dubowski, Y.; Colussi, A. J.; Boxe, C.; Hoffmann, M. R. Monotonic increase of nitrite yields in the photolysis of nitrate in ice and water between 238 and 294 K. J. Phys. Chem. A 2002, 106, 6967− 6971. (43) Chu, L.; Anastasio, C. Quantum yields of hydroxyl radical and nitrogen dioxide from the photolysis of nitrate on ice. J. Phys. Chem. A 2003, 107, 9594−9602. (44) Madsen, D.; Larsen, J.; Jensen, S. K.; Keiding, S. R.; Thogersen, J. The primary photodynamics of aqueous nitrate: Formation of peroxynitrite. J. Am. Chem. Soc. 2003, 125, 15571−15576. (45) Thogersen, J.; Gadegaard, A.; Nielsen, J.; Jensen, S. K.; Petersen, C.; Keiding, S. R. Primary Formation Dynamics of Peroxynitrite Following Photolysis of Nitrate. J. Phys. Chem. A 2009, 113, 10488− 10494. (46) Wagner, I.; Strehlow, H.; Busse, G. Flash-Photolysis of Nitrate Ions in Aqueous-Solution. Z. Phys. Chem. (Muenchen, Ger.) 1980, 123, 1−33. (47) Shuali, U.; Ottoleng., M.; Rabani, J.; Yelin, Z. On Photochemistry of Aqueous Nitrate Solutions Excited in 195-nm Band. J. Phys. Chem. 1969, 73, 3445−3451. (48) Barat, F.; Gilles, L.; Hickel, B.; Sutton, J. Flash Photolysis of Nitrate Ion in Aqueous Solution - Excitation at 200 Nm. J. Chem. Soc. A 1970, 11, 1982−1986. (49) Petriconi, G.; Papee, H. M. Decomposition of Sodium Nitrate Solutions under Ultra-Violet Irradiation at 25 Degrees C. J. Inorg. Nucl. Chem. 1968, 30, 1525−1535. (50) Strehlow, H.; Wagner, I.; Busse, G. On Some Properties of the Nitrate Ion in Its Excited-States. Z. Phys. Chem. (Muenchen, Ger.) 1982, 132, 55−65. (51) Finlayson-Pitts, B. J. Reactions at surfaces in the atmosphere: integration of experiments and theory as necessary (but not necessarily sufficient) for predicting the physical chemistry of aerosols. Phys. Chem. Chem. Phys. 2009, 11, 7760−7779. (52) Jacobi, H. W.; Annor, T.; Quansah, E. Investigation of the photochemical decomposition of nitrate, hydrogen peroxide, and formaldehyde in artificial snow. J. Photochem. Photobiol. A 2006, 179, 330−338. (53) McCarthy, M. I.; Peterson, K. A.; Hess, W. P. Electronic structure of sodium nitrate: Investigations of laser desorption mechanisms. J. Phys. Chem. 1996, 100, 6708−6714. (54) Rotlevi, E.; Treinin, A. The 300-Mmu Band of NO3−. J. Phys. Chem. 1965, 69, 2645−2648. (55) Relph, R. A.; Bopp, J. C.; Johnson, M. A.; Viggiano, A. A. Argon cluster-mediated isolation and vibrational spectra of peroxy and nominally D3h isomers of CO3− and NO3−. J. Chem. Phys. 2008, 129, 064305. (56) Strickler, S. J.; Kasha, M. Molecular Orbitals in Chemistry, Physics and Biology; Olov, P., Pullman, B., Eds.; Academic Press: New York, NY, 1964; pp 241−261. (57) Vchirawongkwin, V.; Kritayakornupong, C.; Tongraar, A.; Rode, B. M. Symmetry Breaking and Hydration Structure of Carbonate and Nitrate in Aqueous Solutions: A Study by Ab Initio Quantum Mechanical Charge Field Molecular Dynamics. J. Phys. Chem. B 2011, 115, 12527−12536. (58) Svoboda, O.; Oncak, M.; Slavicek, P. Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. I. Photoabsorption. J. Chem. Phys. 2011, 135, 154301. (59) Svoboda, O.; Oncak, M.; Slavicek, P. Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. II. Photoionization. J. Chem. Phys. 2011, 135, 154302. (60) Della Sala, F.; Rousseau, R.; Gorling, A.; Marx, D. Quantum and thermal fluctuation effects on the photoabsorption spectra of clusters. Phys. Rev. Lett. 2004, 92, 183401.

(61) Oncak, M.; Sistik, L.; Slavicek, P. Can theory quantitatively model stratospheric photolysis? Ab initio estimate of absolute absorption cross sections of ClOOCl. J. Chem. Phys. 2010, 133, 174303. (62) Domine, F.; Bock, J.; Voisin, D.; Donaldson, D. J. Can we model snow photochemistry? Problems with the current approaches. J. Phys. Chem. A 2013, 117, 4733−4749. (63) Boxe, C. S.; Saiz-Lopez, A. Multiphase modeling of nitrate photochemistry in the quasi-liquid layer (QLL): implications for NOx release from the Arctic and coastal Antarctic snowpack. Atmos. Chem. Phys. 2008, 8, 4855−4864. (64) Crespo-Otero, R.; Barbatti, M. Spectrum simulation and decomposition with nuclear ensemble: formal derivation and application to benzene, furan and 2-phenylfuran. Theor. Chem. Acc. 2012, 131, 1237. (65) Schinke, R. Photodissociation Dynamics; Cambridge University Press: Cambridge, U.K., 1995; p 436. (66) Lee, S. Y.; Brown, R. C.; Heller, E. J. Multidimensional Reflection Approximation - Application to the Photo-Dissociation of Polyatomics. J. Phys. Chem. 1983, 87, 2045−2053. (67) Lee, S. Y. Energy Shift Correction for the Reflection Approximation. J. Chem. Phys. 1985, 82, 4588−4594. (68) Lee, S. Y. Semi-Classical Theory of Radiation Interacting with a Molecule. J. Chem. Phys. 1982, 76, 3064−3074. (69) Prakash, M. K.; Weibel, J. D.; Marcus, R. A. Isotopomer fractionation in the UV photolysis of N2O: Comparison of theory and experiment. J. Geophys. Res., Atmos 2005, 110, D21315. (70) Sistik, L.; Oncak, M.; Slavicek, P. Simulations of photoemission and equilibrium redox processes of ionic liquids: the role of ion pairing and long-range polarization. Phys. Chem. Chem. Phys. 2011, 13, 11998−12007. (71) Thurmer, S.; Seidel, R.; Winter, B.; Oncak, M.; Slavicek, P. Flexible H2O2 in Water: Electronic Structure from Photoelectron Spectroscopy and Ab Initio Calculations. J. Phys. Chem. A 2011, 115, 6239−6249. (72) Grimme, S. Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 2004, 25, 1463−1473. (73) Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787−1799. (74) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (75) Burns, L. A.; Vazquez-Mayagoitia, A.; Sumpter, B. G.; Sherrill, C. D. Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals. J. Chem. Phys. 2011, 134, 084107. (76) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum mechanical continuum solvation models. Chem. Rev. 2005, 105, 2999−3093. (77) Gustavsson, T.; Banyasz, A.; Lazzarotto, E.; Markovitsi, D.; Scalmani, G.; Frisch, M. J.; Barone, V.; Improta, R. Singlet excited-state behavior of uracil and thymine in aqueous solution: A combined experimental and computational study of 11 uracil derivatives. J. Am. Chem. Soc. 2006, 128, 607−619. (78) Jagoda-Cwiklik, B.; Slavicek, P.; Cwiklik, L.; Nolting, D.; Winter, B.; Jungwirth, P. Ionization of imidazole in the gas phase, microhydrated environments, and in aqueous solution. J. Phys. Chem. A 2008, 112, 3499−3505. (79) Tuckerman, M. E. Path Integration via Molecular Dynamics. Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes 2002, 10, 269−298. (80) TURBOMOLE V5.10 2009, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989−2007, TURBOMOLE GmbH, since 2007; available from http://www. turbomole.com. 12876



Article

(81) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (82) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (83) Becke, A. D. Density-Functional Thermochemistry III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (84) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (85) Zhao, Y.; Truhlar, D. G. Density functional for spectroscopy: No long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states. J. Phys. Chem. A 2006, 110, 13126−13130. (86) Yanai, T.; Tew, D. P.; Handy, N. C. A new hybrid exchangecorrelation functional using the Coulomb-attenuating method (CAMB3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (87) Chai, J. D.; Head-Gordon, M. Systematic optimization of longrange corrected hybrid density functionals. J. Chem. Phys. 2008, 128, 084106. (88) Chai, J. D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (89) Vydrov, O. A.; Scuseria, G. E. Assessment of a long-range corrected hybrid functional. J. Chem. Phys. 2006, 125, 234109. (90) Maria, H. J.; Mcdonald, J. R.; Mcglynn, S. P. Electronic Absorption-Spectrum of Nitrate Ion and Boron Trihalides. J. Am. Chem. Soc. 1973, 95, 1050−1056. (91) Morrone, J. A.; Markland, T. E.; Ceriotti, M.; Berne, B. J. Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances. J. Chem. Phys. 2011, 134, 014103.

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