Case of Using ab Initio Potential Energy Surfaces and - American

Jun 30, 2010 - Fernando Ayala-Mató§ and Jesús Rubayo-Soneira|. Departamento de Fısica General y Matemáticas. Instituto Superior de Tecnologıas y...
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J. Phys. Chem. A 2010, 114, 9673–9680

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Argon Solid Response upon Rydberg Photoexcitation of the NO Chromosphore: Case of Using ab Initio Potential Energy Surfaces and Comparison to Similar Studied Systems† Juan Carlos Castro-Palacio* Departamento de Fı´sica, UniVersidad de Pinar del Rı´o. Martı´ 270, Esq. 27 de NoViembre, Pinar del Rı´o 20100, Cuba

Keisaku Ishii

‡

Department of Chemical System Engineering. Graduate School of Engineering. The UniVersity of Tokyo, Tokyo 113-8656, Japan §

Fernando Ayala-Mato´ and Jesu´s Rubayo-Soneira

|

Departamento de Fı´sica General y Matema´ticas. Instituto Superior de Tecnologı´as y Ciencias Aplicadas, Quinta de los Molinos, AVe. Carlos III y Luaces, Plaza, C. Habana 10400, Cuba

Koichi Yamashita

⊥

Department of Chemical System Engineering. Graduate School of Engineering, the UniVersity of Tokyo, Tokyo 113-8656, Japan ReceiVed: February 6, 2010; ReVised Manuscript ReceiVed: May 27, 2010

Molecular dynamics simulations of NO-doped Ar solid upon Rydberg photoexcitation of the impurity have been carried out taking into account angular dependent potential energy surfaces (PESs) in the ground and excited states. To go beyond isotropic potentials simulations, the effects of anisotropy of potentials on the structure, dynamics, and energetics are investigated by taking into account two cases, namely, the whole PESs and the isotropic parts. Results have been compared to those obtained in previous works for similar NO-doped rare gas systems. Radial distribution functions (RDF) for the ground and excited state indicate that for both cases the shell structure of the lattice is kept ordered and is characterized by well-defined bands. No influence of the anisotropy of potentials has been detected in the RDFs since the anisotropy is rather manifested at short distances. The well part, which has been proven to be unimportant for the dynamics in previous works, arises here to be important for the right simulation of the spectrum. In general, our results show a reasonable agreement with respect to the experimental values for the dynamics and energetics when ab initio potentials are used, although better results can be obtained if higher level ab initio PESs are used. I. Introduction The rare gas solids’ response upon photoexcitation of impurity molecules or atoms to low-n Rydberg states results in a large blue spectral shift in absorption as compared with the gas phase, which is connected to the strong short-range repulsion between the Rydberg electron and the close shell of the RG atoms.1,2 This strong repulsion is responsible for configurational rearrangements of the cage species surrounding the excited center leading to a new equilibrium configuration from which fluorescence takes place. The large absorption-emission Stokes shifts that are observed reveal the extensive configurational changes around the excited species. The basic mechanism is considered to be a radial expansion of the cage (the so-called electronic “bubble” formation),1-4 which is also seen in RG liquids and clusters.1,3,5 †

Part of the “Reinhard Schinke Festschrift”. * To whom correspondence should be addressed. E-mail: juanc@ geo.upr.edu.cu. ‡ E-mail: [email protected]. § E-mail: [email protected]. | E-mail: [email protected]. ⊥ E-mail: [email protected].

Cage relaxation upon Rydberg excitation of impurity molecules in rare gas solids has been intensively studied over the past few years.1,2,4,6-10 Some examples are (NO, Hg, I2)-doped RG solids2,6,9,11 and H2 solids.6,7,10,12,13 These experimental achievements have motivated the emerging of a wide range of theoretical works. In this respect, computer-based simulations represent a powerful tool since the information offered by experiments is still insufficient for their complete characterization. Several works on molecular dynamics (MD) simulations of the structural relaxation of Rydberg excited NO-doped Ne, Ar, Kr, and Xe solids have been carried out. Primary, a group of these works used isotropic potentials.14-22 The potential energy surfaces (PESs) for NO(X2Π)-RG interactions have been taken from the experimental results of Thuis et al.23 for RG ) Ar, Kr, Xe and from ref 24 for RG ) Ne. However, for the NO(A2Σ+)-RG (RG ) Ne, Kr, Xe) interactions, several approximations have been used since no semiempirical intermolecular potential is available in the literature. To model NO(A2Σ+)-Ne interactions in NO-doped solid Ne, a Born-Mayer potential obtained from a semiclassical projection method has been used.16,17 In the case of modeling NO(A2Σ+)-Kr, Xe

10.1021/jp101181v  2010 American Chemical Society Published on Web 06/30/2010

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interactions, Lennard-Jones and Born-Mayer potentials have been fitted to reproduce the experimental spectroscopic data available for these systems. For NO(A2Σ+)-Ar interaction a semiempirical potential from Tsuji et al. was used.25 In the case of NO-doped Ar simulations14,15 with isotropic potentials, the internal structure of the molecule has been neglected under the following arguments: (1) the effects on the energy and the structure upon the electronic excitation are little disturbed by the anisotropy of the intermolecular potential in the ground state; (2) at 4 K, which is the experimental temperature, the NO internal vibrations are frozen; and (3) the NO(A2Σ+)-Ar interaction is considered approximately as isotropic because of the nearly spherical 3σs orbital. By these simulations, some steps were given toward the description of the experimental results for the Stokes shift and the bubble dynamics,2,11 although still imprecise. For instance, the value for the Stoke shift was 700 meV versus the experimental value of 580 meV. The simulated first medium response (500 fs) also mismatched the experimental value of 800 fs. On the other hand, the NO(A2Σ+)-Ar potential from Tsuji et al.25 represents a not so good approximation since it was obtained by means of a fitting to a few experimental values of the interaction energy. The general features of the structural relaxation dynamics of the medium where captured. One important conclusion was that the attractive part seems not to be important for the dynamics. This was proven by using a Born-Mayer potential fitted so that matched the Lennard-Jones potential from Tsuji et al.25 in the short distance repulsive bound on the Franck-Condon region. As a result, the general behavior of the first shell response was found to be the same for both cases. This indicated that the global PES in the solid shows new characteristics with respect to the isolated complex. This fact suggests to consider an approach for the PES in the excited state going beyond the isotropic pairwise potentials, for example, anisotropic potentials. In previous works, the dynamics of NO-doped Kr solid has been addressed using ab initio potentials for the NO(X2Π)-Kr and NO(A2Σ+)-Kr interactions.26,27 Results did not improve those obtained with isotropic potentials for the same solid.19-21 Although the general features of the PESs seemed logic and enough for the solid as a first step into the simulation, this study revealed that the correction for quadruple excitation in the excited state plays a fundamental role in the shaping of the PES at short-range. The modeling of the excited state potential at this region has been proved to be crucial for the ulterior dynamics and energy relaxation. In ref 27 the influence of changing the position of the NO molecule axis in the matrix has been tested in the excited state dynamics. Some improvements in the results were obtained for some positions for the NO molecular axis in the matrix. These preferential positions were probably due to the excessive repulsiveness of the excited state PES along some directions, which will be surely corrected by considering properly the corrections for quadruple excitations and bond functions in the ab initio calculations. Recently, in ref 28, the authors performed a more detailed scrutiny of NO-doped Ne matrix response. An isotropic potential has been used for the ground state (Ne-NO(X2Π)) and an a high level ab initio PES29,30 for the excited state (Ne-NO(A2Σ+)). The influence of the anisotropy and manybody effects on the dynamics and energetics have been assessed. In this respect, the energy of the Ne-NO-Ne system was calculated for the NO in the first Rydberg state using ab initio calculations. Results showed that the neglect of higher manybody effects in the excited state NO-Ne potential is not the cause of the disagreement in the molecular dynamics (MD)

Castro-Palacio et al. results when compared to the case of using empirically fitted potentials. This point remains to be discussed. However, the general features of the relaxation dynamics were well predicted, and the irrelevance of the well part for the dynamics was also seen. It could be noticed that the Ne solid shows a behavior that is between quantum (e.g., H2 solid) and classical (e.g., Ar, Kr, and Xe) solids. The three-body effects were paradoxically found to be relatively more important in the long-range and not relevant for short distances. This conclusion supported the use of pairwise potentials in that case. Authors suggested that the local disorder and disagreements with respect to experiments could be a consequence of quantum effects influencing the medium response. In this respect, the study of Ar, which is a more classical solid, using anisotropic potentials is expected to bring new insights, by comparison, in the understanding of these issues. In refs 31-33, different levels of ab initio calculations of the Ar-NO(A2Σ+) interactions are shown. In all cases, the PES is repulsive all along the domain, except two shallow wells at linear positions. For distances beyond 7 Å the interaction becomes almost isotropic, however for short distances there is a clear anisotropy in the potential that should influence somehow the dynamics and the energetics once the interaction potential for the complex is taken to the matrix in a pairwise potential approximation. In this work we will investigate by molecular dynamics simulations the structural relaxation of NO-doped Ar solids upon Rydberg photoexcitation of the impurity using PESs that take into account the angular variation of Ar atom direction when moving around the NO molecule. Our model includes the anisotropy of potentials in both the ground and the excited state in order to perform a more complete simulation. A PES for the Ar-NO(X2Π) interactions, which has been optimized to reproduce the microwave spectroscopic data as reported in ref 34 has been used. This PES matched very closely the one published by Alexander,35 using highly accurate ab initio calculations. In the excited state, the Ar-NO(A2Σ+) interactions are modeled using an ab initio PES from ref 33. Our results are compared to those from ref 15, where isotropic potentials were usedin NO-doped Ar simulations and to those for Kr- and Nedoped NO solids using anisotropic PESs,28,36 taking into account the structure, dynamics, and energetics of the nonradiative relaxation process. The outline of the paper is the following. In Section II we show the methodology for modeling the interactions between the species and for the dynamics. In Section III we present the results and discussion for the structure, dynamics and spectrum. All along results are compared to experiments and similar studied systems. Finally some conclusions are drawn in Section IV. II. Methodology A. Potential Energy Surface. The Ar-Ar interactions have been modeled using Lennard-Jones (LJ) pair potentials. The values for the parameters σ and ε37 are registered in Table 1. To model Ar-NO(X2Π) interactions we have used a PES, which has been optimized to reproduce the microwave spectroscopic data as reported in ref 34, and for Ar-NO(A2Σ+) interactions an ab initioPES from ref 33 has been used. The N-O distance was fixed at 1.15 Å, which is the equilibrium bond length of the X2Π state of the diatomic NO molecule. The contour plots for these PESs are shown in Figure 1 (panels a and b). In this work, we use the average PES between A′ and A′′ PESs in the ground state since they almost overlap.34 This

Simulations of NO-Doped Ar with Rydberg Photoexcitation TABLE 1: Parameters for the Intermolecular Interaction Potentials between the Species Forming the Model System Lennard-Jones potential interacting species 37

Ar-Ar NO(X2Π)-Ar23 NO(X2Π)-Ar34 (fit) NO(A2Σ+)-Ar25

σ (Å)

ε (eV)

3.40 3.23 3.50 4.09

0.0104 0.0119 0.0100 0.0073

Born-Mayer potential interacting species 2 +

NO(A Σ )-Ar (fit)

A (eV)

r (Å)

c (Å)

0.53

2.41

0.5

aspect can be noticed in figure 2 where the isotropic parts of A′ and A′′ PESs along with the average curve are shown. The average PES (figure 1, panel a) shows two linear wells at 4.22 Å (R ) 0°) and 3.98 Å (R ) 180°) with energies of -90 and -90 cm-1, respectively, and a perpendicular well at 3.58 Å (R ) 93°) of -115 cm-1. In the case of the NO(A2Σ+)-Ar PES33 (Figure 1, panel b), the energies were calculated at 155 points, in the region of 2.5 e R e 20.0 Å and at R ) 0, 45, 90, 135, and 180°. Jacobicoordinates were employed (r: the NO bond length; R: the distance between the center of mass of NO and the Ar atom; R: the Jacobi angle; 0° corresponds to the linear Ar-NO and 180° to the linear Ar-ON, respectively). The r coordinate was fixed at 1.06 Å, which is the equilibrium bond length of the A2Σ+ state of NO. This PES shows two shallow linear wells located at 4.2 Å (R ) 0°) and 6.08 Å (R ) 180°) with energies of -20 and -15 cm-1, respectively. B. Molecular Dynamics. The structural relaxation of solid Ar upon Rydberg excitation of an NO impurity molecule is

Figure 1. Contour plots of the NO(X2Π)-Ar (panel a) and NO(A2Σ+)-Ar (panel b) PESs. Contour intervals are at 5 cm-1and for energies from -200 to 100 cm-1.

J. Phys. Chem. A, Vol. 114, No. 36, 2010 9675 studied by classical molecular dynamics. The methodology of the simulation has been discussed in refs 14, 15, and 19. To make easier the understanding of the reader, we briefly recall here some points. The simulated system consists of a face centered cubic (fcc) supercell structure with 499 atoms of Ar and an NO molecule placed at a monosubstitutional site. Periodic boundary conditions are applied to simulate an infinite crystal. The supercells contain 10 complete shells of independent neighbors corresponding to 200 particles. At the experimental temperature T ) 4 K the zero-point energy dominates the nuclear motion of the Ar atoms. A scaled temperature approach has been used to model the system,6,38 with an effective simulation temperature T′ for the simulations. This approach consists in regarding the particles as classical harmonic oscillators in thermal equilibrium at an artificial temperature T′, for which, the quantum and classical density matrices have the same value at every point. The resulting expression for T′ is:

T' )

( ( ))

pωD pωD tanh 2kB 2kBT

-1

(1)

where ωD ) 64 cm-1 is the Debye frequency of solid Ar. The new effective temperature for the thermalization system was T′ ) 46 K. This temperature approach has been previously used14-16,19,39 with reasonably good results for heavy rare gas solids. In the case of the weekly bounded systems such as Ne solid, in ref 40, authors have obtained a new correction to Bergsma’s estimation of the effective temperature by considering the anharmonic contributions of the intermolecular interactions. For NO-doped Ar solids, in previous works,14,15 molecular dynamics simulations using Bergsma’s estimation38 have yielded slightly better results with respect to experiments. For heavier systems, such as, NO-doped Kr and Xe solids, the use of Bergsma’s approximation38 is meaningless. In this work, we will use this approximation since it was also used in ref 15m which is eventually brought here for comparison. To elucidate the effects of anisotropy of PESs in the dynamics and energetics, two cases have been considered. The first consists in an approximation to the modeling of the impurity in Ar solids, that is, the NO molecule was considered as a point (its center of mass), placed at a monosubstitutional site and with the oxygen-nitrogen direction fixed at R ) 0° with respect to the z-axis direction during the dynamics. Our reference framework is placed at the NO lattice site and the z-axis is upon the (001) crystallographic direction. This situation involves the use of the whole anisotropic PES while running the dynamics (considering the anisotropies) in the ground (PES from ref 34) and excited (PES from ref 33) states. For the discussion, we will denote the potentials for this case as anisotropic ab initio potentials. In this case, we go beyond previous work14,15 in considering the structure of the molecule, although the N-O distance is fixed since vibrations are assumed unpopulated at the simulation temperature. There are several equivalent positions for the molecule in the crystal that are isotropically distributed in a sphere around the NO. This fact suggests that no difference would be expected in the subsequent evolution of the system. In the case of NO-doped Kr solids modeled with ab initio potentials,26,27 there were small differences for the different equilibrium positions of the NO molecular axis, which came from the excessive repulsiveness of the PES used for the excited state. It was suggested in that study that the level of ab initio calculations for Kr-NO(A2Σ+) should be greatly improved.

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Castro-Palacio et al.

Figure 2. Fit to the isotropic part of the Ar-NO (X2Π) PES from Sumiyoshi et al.34 and to the isotropic part of the Ar-NO (A2Σ+) PES from ref 33 when expanded in Legendre polynomials.

The second case corresponds to the zeroth-order term, f0(R) P0(cos R), of the expansion in Legendre polynomials of the PES. V(R, Ri) ) f0(R), for whatever values of Ri since P0(cos Ri) ) 1. This procedure was applied to NO(X2Π)-Ar and NO(A2Σ+)-Ar 2D analytical PESs. For the isotropic part of the NO(X2Π)-Ar interaction a LJ potential has been fitted, and for the isotropic part of the NO(A2Σ+)-Ar interaction a Born-Mayer of the form V(R) ) A exp(-(r - r0)/c) (see Figure 2). The Levenberg-Marquardt algorithm has been used for both fits.41 The parameters resulting from the fitting are recorded in Table 1. For the discussion we will denote potentials for this case as isotropic ab initio potentials. In the case of the LJ potentials, we have focused on the right modeling of the shortrange repulsive well part rather than on the modeling of the long-range attractive part. This is justified by the fact that the transition takes place from the ground state well (in harmonic approximation) to the repulsive bound in the excited state. The long-range attractive part of the well does not play a significant role in the dynamics since the expansive movement of the bubble is stopped rather by the collective repulsion of Ar-Ar interactions (cage effect). However, its right description should yield a better description of the emission band. All along the paper, we compare our results to those from ref 15. In this previous work, a Born-Mayer form has been fitted to the asymptotic part of a LJ form for the NO(A2Σ+)-Ar25 interaction, and in the case of NO(X2Π)-Ar interactions a LJ form from23 has been used. For both cases the angular variation of the potentials has been neglected. To build up the global PES in the crystal we use a pairwise potential approximation. III. Results and Discussion Figure 3 shows the radial distribution function (RDF) for the ground (panel a) and excited (panel b) states. The figure represents the histogram of equilibrium matrices taken at 3000 time steps in the ground and excited state. Results indicate that both anisotropicab initio potentials and isotropic ab initio potentials keep the shell structure of the lattice ordered, that is, characterized by well-defined bands. Only some small changes between these cases can be noticed for the first shell, which

lies closest to the active center, for both the ground and excited state. The greatest relative displacement with respect to the ground state is provoked by the potential from Tsuji et al.,25 followed in order by the isotropic and anisotropic ab initio potentials, respectively. This result will be appreciated later in this section in the dynamics of the first shell radius. In the ground state, the third shell is also distorted but to a minor extend. The second does not respond. This means that the third shell atoms are affected by means of an interaction with the first shell atoms and not by the direct influence of the potential. The potential from Thuis et al. was seen in ref 14 to show a RDF overlapping the one of the pure rare gas solid. It happened so because the Ar-NO(X2Π) intermolecular potential23 is very similar to the Ar-Ar intermolecular potential.37 The potential from Tsuji et al. serves here as a pattern for comparison with respect to the pure rare gas. In the excited state, besides the first shell, the third and the forth show differences for the three variants of potentials. These shells are directionally connected to the first, whereas the second, which is not, does not shift. The remaining shells (beyond the fourth) show the same characteristics in the RDFs which indicates that the interaction of potentials does not get that far in the matrix mainly because of the cage effect of Ar-Ar interactions. On the other hand, neither for the ground state nor for the excited, for any of the potentials used, has a splitting of a shell in the RDFs been observed. This indicates that the effects of anisotropy are not manifested in the equilibrium structure of the shells. The effects of anisotropy, if any, should come up in the dynamics of the medium response and in the nonradiative energy dissipation. On the other hand, the fact that anisotropy of potentials does not cause shell splitting at equilibrium structures indicates a long-range insensitivity with respect to the choice of the NO axis position. Before going into the details of the dynamic medium response, we want to refer to the Ar-NO(A2Σ+) PES curves by angular direction as for the expectation for the dynamic results (Figure 4). The curve of the semiempirical isotropic potential from Tsuji et al.,25 which has been used in refs 14 and 15, has been included for comparison. The vertical lines indicate the Franck-Condon (FC) regions for the potentials used to describe the ground state, namely, the potential from Thuis

Simulations of NO-Doped Ar with Rydberg Photoexcitation

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Figure 3. Radial distribution function of the Ar atoms around the impurity in NO-doped Ar solid (a) for the ground and (b) excited states, respectively.

et al.23 (FC1), anisotropic ab initio potentials (FC2), and isotropic ab initio potentials (FC3). These values represent the peaks of the bands for the first shell in the RDFs of the ground state (Figure 3a). There are some aspects of the dynamics that can be predicted, for example, the potential from Tsuji et al. should yield the greatest relative displacement of the first shell since it is the one that shows the steepest slope that is related to the force ejected upon photoexcitation. To a minor extend, it is followed by the isotropic ab initio potentials. In the case of anisotropic ab initio potentials it is difficult to predict the results of the simulations for the dynamics and energetics since there is noticeable change of the potential slopes with the directions at the FC region (FC2). For R ) 90°, the ground state PES shows the deepest well, -115 cm-1. For this direction, the excited state PES shows a slope very similar to the one for isotropic ab initio potentials. Taking into account that initial conditions for the trajectories in the excited state should sample more this zone, the first shell radius increase should be also similar. With respect to the spectrum, it can be also inferred from Figure 4 that results are not expected to be far from experimental results since curves cross the FC peaks at points which lie very close one another.

The time evolution of the first shell radius upon excitation is shown in Figure 5 for both cases, that is, when anisotropic and isotropic PESs are used, respectively. The curves represent an average over 100 trajectories. The shell dynamics for both cases is characterized by an impulsive ultrafast expansion of the first shell radius in the femtosecond scale. Once the radius gets to a maximum value (Rmax in Table 2), the medium response (cage effect) causes the shell to reverse back its movement. We call the period of time from photoexcitation to the first contraction of the first shell as “femtosecond answer” (fem ans in Table 2). This quantity is a direct indicator of the inertial response of the lattice and has been determined experimentally.42 This is a general behavior that has also been observed in ref 14 and for the other NO-doped RG solids.17-21,28 If we go into more details, when anisotropic ab initio potentials and isotropic ab initio potentials are used, the femtosecond answers (900 and 1000 fs, respectively) are comparable to the experimental value (800 fs).42 Results for the dynamics are registered in Table 2. The maximum expansion (Rmax) occurs at similar times for all potentials, at 260 fs for the isotropic ab initio potentials and at 440 fs for the anisotropic ab initio potentials, against 250 fs in ref 14. The remaining homologous systems behave as: 600 fs

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Figure 4. Potential energy curves for the excited 22A′ state (Ar-NO(A2Σ+) complex), calculated using the multireference singles and doubles configuration interaction method. Ab initio results are indicated by open symbols, where the shape indicates the Ri direction. The figure also includes the isotropic potential from Tsuji et al.25 The vertical lines indicate the FC region for each simulation case.

in Ne,28 320 fs in Kr,19 and 440 fs in Xe.20 The delayed response in Ne with respect to Ar was initially related in ref 28 to the long-range effect of the repulsive part of the potential. Also in this reference, it was proven that is more related to the local disorder probably caused by quantum effects. The expansion time of the electronic bubble has been connected to the normal mode of shortest lifetime and greatest amplitude in the normal mode spectrum for more classical systems, namely, NO-doped Ar, Kr, and Xe.15,20 This connection has to do with the inertial and adiabatic expansion of the first shell within the first ∼200 fs when the rest of the system remains undisturbed. As predicted from figure 4, the potential from Tsuji et al. caused the greatest relative displacement of the first shell, 9.8% (denoted as radius inc. in Table 2, (ReqExc - ReqGround/ReqGround) × 100) as observed in references.14,15 However, for isotropic and anisotropicab initio potentials the quantity radius inc. represents only ∼60% of the value for the isotropic potential from Tsuji et al.,25 which is connected to the slopes at the FC region. We have done the calculation of the slope (force) for 2 points randomly chosen at both sides and very close to the crossing point between the vertical line representing the FC peak and the curve for the different cases (Figure 4). For isotropic ab initio potentials the slope (∆y/∆x) represented the 55.5% and the curve for 90° direction the 49% of the slope for the potential from Tsuji et al.25 It can be seen that results for the percentages in the force approximate results for the percentages in the relative radius increment (radius inc). In ref 2, a moment analysis yielded that values for the radius inc. should range from 4% in the case of NO-doped Xe solid to 15% in NO-doped Ne solid, and that the values for NOdoped Ar solid and for NO-doped Kr solid should take a value in this range and follow the order of the increasing mass of the lattice atoms. In this respect, the value of the bubble size for NO-doped Ar solid should be greater than that for NO-doped Kr solid. From previous theoretical works, based on isotropic semiempirical potentials, the reported values are: 15% in Ne,16 9.8% in Ar,14 6% in Kr,19 and 4.5% in Xe.20 The results presented here are in the range predicted by the moment analysis. The simulated spectroscopic results are shown in Table 3 in comparison to experiments. The value for the Stoke shift (SS

Castro-Palacio et al. in Table 3) when anisotropic ab initio potentialsare used (610 meV) is in fair agreement to the experimental value of 580 meV. The Stoke shift is a very important experimental quantity since it represents the amount of energy transmitted to the lattice in the absorption-emission process. The Stoke shifts depends on the energy gap existing between the ground and excited state potential energy surfaces at the well positions where the FC transitions takes place. The absorption energy is shifted to the red since an extra energy is used in overcoming the coulomb repulsion arising from the overlap between the Rydberg electron and the electronic clouds of the first shell atoms.1,2 For a better understanding, in Figure 6, it is shown a schematic representation of the absorption-emission process in the matrix. The quantities ∆x1 and ∆x2 (also in Table 3) correspond to the excess of energy dissipated in the excited state after the absorption and in the ground state after fluorescence, respectively. In ref 14, where semiempirical isotropic potentials were used, these quantities were calculated and compared to the results from moment analysis of the absorption-emission line shape, in the configuration coordinate model in the harmonic approximation, performed by Chergui et al.2 For all cases, the excess of energy in the excited state, ∆x1, is greater that the excess of energy in the ground state, ∆x2, which is a fact observed in the moment analysis results. However, the absorption peak is not well reproduced by the anisotropic ab initio potentials. This is suggested from Figure 4, where it can be seen that curves for R ) 0°, R ) 45°, and R ) 180° cross the FC line (FC2) at energy values smaller than for the isotropic ab initio potential and for the potential from Tsuji et al.25 curves. The well part seems to play an important role in the description of the spectrum, even when it is not relevant for the dynamics as proved in refs 15, 19, and 20 In ref 15, the authors argued that the NO molecule recovers a higher symmetry in the matrix because of the trapping geometry and configuration interaction does not take place. The authors concluded that the attractive part of the potential disappears once the Ar-NO(A2Σ+) potential is taken to the matrix. However, in the present work, isotropic ab initio potentials, which were modeled by a LJ in the ground state and by a Born-Mayer in the excited state, do not show good results for the Stoke shift. This quantity is rather small with respect to the experimental value, although the absorption peak is reproduced. This mismatch may come from the fact that the emission energy is higher than the experimental one. This suggests that the well part may play certain role. The anisotropy at short-range of the excited state PES is expected to have effects on the absorption peak. The anisotropy causes differences in the energy depending on the position of the Ar atom in the FC region, which make direct influence on the absorption peak. On the other hand, the changes of slope over the FC determine the width of the absorption band and constitute an important initial condition for the evolution of each individual trajectory on the excited state PES. On the other hand, the effect of the well part on the emission energy can not be disregarded either. The latter has been demonstrated in NOdoped Ar solid14,15 and NO-doped Kr19 solid simulations where only LJ potentials (which have attractive part) have been able to fairly approach the experimental results for the spectrum. On the other hand, in NO-doped Ar solid,15 a normal-mode analysis allowed to explain the insights of the transition process, such as details of the time response of the medium. A similar analysis was done for NO-doped Kr21 and Xe solids20 yielding reasonable good results; however, some tests at that moment

Simulations of NO-Doped Ar with Rydberg Photoexcitation

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Figure 5. Time evolution of the first shell radius following X2Π f A2Σ+ transition of NO in Ar solids. The curves represent an average of 100 individual trajectories. The open cicles indicate the values of the maximum expansion (Rmax) of the shell and the time for the first contraction (femtosecond answer).

TABLE 2: Results for MD Simulations in Comparison with Femtosecond Spectroscopya case

ReqGround (Å)

ReqExc (Å)

radius inc (%)

Rmax (Å)

fem ans (fs)

isotropic ab initio pot. anisotropic ab initio pot. from refs 14, 15 experiments42

4.09 3.91 3.67

4.34 4.14 4.03

6.1 5.8 9.8 4 - 15%2

4.54 4.38 4.45

900 1000 500 800

a ReqGround and ReqExc are the equilibrium radii for the ground and excited state, respectively; Rmax is the maximum value of the cage radius after photoexcitation; “radius inc.” is the relative increment of the cage radius, defined as ((ReqExc - ReqGround)/ReqGround) × 100; and “fem ans” is the time value for the first cage contraction.

TABLE 3: Spectroscopic Energy Results from MD Simulations in Comparison with Experimental Measurementsa case

Eab (eV)

Eem (eV)

SS (meV)

∆x1 (meV)

∆x2 (meV)

isotropic ab initio potentials anisotropic ab initio potentials from refs 14, 15 experiments2

6.19 5.80 6.30 6.30

5.90 5.19 5.60 5.75

290 610 700 580

160 390 430 330

130 220 330 250

a

Eab and Eem are the absorption and emission peak energies, and SS is the Stokes shift. The quantities ∆x1 and ∆x2 correspond to the excess of energy dissipated in the excited state after the absorption and in the ground state after fluorescence, respectively.

indicated that very different results would have been obtained if Born-Mayer potentials had been used instead of LJ ones. IV. Conclusions A more complete study of the structural relaxation of NOdoped Ar solids upon Rydberg photoexcitation of the impurity has been carried out taking into account the angular variation of the potentials in the ground and excited state. In this respect, high level ab initio potentials have been included and their effects on the structure, dynamics and energetics have been evaluated. As for the structure in the RDFs, no influence of the anisotropy of potentials has been detected. The first shell shifted with respect to the pure rare gas in the case of isotropic and anisotropic ab initio potentials. In the excited state the fourth shell was also disturbed, but to a minor extend when compared to the first. The well part, which has been proven to be unimportant for the dynamics in previous works, at the same time seems to important for the right description of the absorption emission process. In general, there is a reasonable fair agreement with respect to the experimental values for the

Figure 6. Schematic representation of the absoption emission process of the NO molecule in the matrix. The quantities δx1 and δx2 correspond to the excess of energy dissipated in the excited state after the electronic transition and in the ground state after fluorescence, respectively.

dynamics and energetics when ab initio potentials are used. Because the Ar solid is more classical than the Ne solid, our

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results support the conclusion of the authors in ref 28 for NOdoped Ne solid, when they state that the disagreement with respect to the experiments may be due to the quantum effects. We still think that ab initio potentials can allow a better understanding of the structural relaxation of NO-doped rare gas classical solids upon photoexcitation of the impurity. One important thing in it is the adequate description of the potential at short distances in the FC region where anisotropy is manifested. This could be reached by going beyond in the level or in considering a different methodology, for the ab initio calculations, mainly for the excited state. Acknowledgment. We would like to thank Dr. Yoshihiro Sumiyoshi and Professor Yasuki Endo from the Department of Basic Science, Graduate School of Arts and Sciences, the University of Tokyo, Komaba for fruitful discussions on the Ar-NO(X2Π) PES. This work has been supported by a Grantin-aid (No. 21245004) and for Scientific Research (A) the Global COE Program for Chemistry Innovation from the Ministry of Education, Culture, Sports, Science and Technology of Japan. References and Notes (1) Schwentner, N.; Koch, E. E.; Jortner, J. Electronic Excitation in Condensed Rare Gas Solids; Springer: Berlin, 1985. (2) Chergui, M.; Schwentner, N.; Chandrasekharan, V. J. Chem. Phys. 1988, 89, 1277. (3) Jortner, J. Femtochemistry, Ultrafast Chemical and Physical Processes in Molecular Systems; Chergui, M., Ed.; World Scientific: Singapore, 1996; p 15. (4) Ya. Fugol, I. AdV. Phys. 1978, 37, 1. (5) Wo¨rmer, J.; Karabach, R.; Joppien, M.; Mo¨ller, T. J. Chem. Phys. 1996, 104, 8269. Bjorneholm, O.; Federmann, F.; Fo¨sing, F.; Mo¨ller, T. Phys. ReV. Lett. 1995, 74, 3017. Bjorneholm, O.; Federmann, F.; Fo¨sing, F.; Mo¨ller, T.; Stampfli, S. J. Chem. Phys. 1996, 104, 1876. Lengen, M.; Joppien, M.; von Pietrowski, R.; Mo¨ller, T. Chem. Phys. Lett. 1994, 229, 362. (6) Schwentner, N.; Apkarian, V. A. Chem. ReV. 1999, 99, 1481. (7) Vigliotti, F.; Chergui, M.; Dickgiesser, M.; Schwentner, N. Faraday Discuss. 1997, 108, 139. (8) (a) Goodman, J.; Brus, L. E. J. Chem. Phys. 1977, 67, 933. (b) Goodman, J.; Brus, L. E. J. Chem. Phys. 1978, 69, 4083. (9) Portella-Oberli, M. T.; Jeannin, C.; Chergui, M. Chem. Phys. Lett. 1996, 259, 475. (10) Jeannin, C.; Portella-Orbeli, M. T.; Vigliotti, F.; Chergui, M. Chem. Phys. Lett. 1997, 279, 65. (11) Chergui, M.; Schwentner, N.; Bo¨hmer, W. J. Chem. Phys. 1986, 85, 2472. (12) Bonacina, L.; Larre´garay, P.; van Mourik, F.; Chergui, M. Phys. ReV. Lett. 2005, 95, 015301. (13) Bonacina, L.; Larre´garay, P.; van Mourik, F.; Chergui, M. J. Chem. Phys. 2006, 125, 054507. (14) Jimenez, S.; Pasquarello, A.; Car, R.; Chergui, M. Chem. Phys. 1998, 233, 343.

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