Antoine Bouthors

Fabrice Neyret

Nelson Max

Eric Bruneton

Cyril Crassin

Interactive multiple anisotropic scattering in clouds

We propose an algorithm for the real time realistic simulation of multiple anisotropic scattering of light in a volume. Contrary to previous real-time methods we account for all kinds of light paths through the medium and preserve their anisotropic behavior.

Our approach consists of estimating the energy transport from the illuminated cloud surface to the rendered cloud pixel for each separate order of multiple scattering. We represent the distribution of light paths reaching a given viewed cloud pixel with the mean and standard deviation of their entry points on the lit surface, which we call the collector area. At rendering time for each pixel we determine the collector area on the lit cloud surface for different sets of scattering orders, then we infer the associated light transport. The fast computation of the collector area and light transport is possible thanks to a preliminary analysis of multiple scattering in planeparallel slabs and does not require slicing or marching through the volume.

Rendering is done efficiently in a shader on the GPU, relying on a cloud surface mesh augmented with a Hypertexture to enrich the shape and silhouette. We demonstrate our model with the interactive rendering of detailed animated cumulus and cloudy sky at 2-10 frames per second.

Introduction

The realistic rendering of clouds is still a challenging problem. Multiple anisotropic scattering must be simulated in a volume, the lack of absorption makes the convergence very slow, and detailed clouds require high resolution volumes. In the scope of real-time rendering this is even worse: volume radiosity or Monte Carlo methods cannot converge in real-time, and volume rendering cannot be achieved with enough resolution for sharp clouds such as cumulus. Precomputations forbid the animation of clouds and light source, and most real-time models do not account for view-dependent effects or miss important visual features such as backscattering.

To solve these problems, our approach represents clouds as surface-bounded volumes and optimizes the calculation of light transport inside the cloud from the illuminated cloud surface to the rendered cloud pixels. For this, we study and characterize the light transport for each order of scattering.

Our contributions are:

-a new model characterizing the light transport (i.e., amount of transmitted energy) between the flat surface of a slab and a point p anywhere in the slab at any given order of scattering (see Figure 1 Contrary to most previous real-time models our multiple scattering simulation:

-does consider the high orders of scattering which are responsible for diffusion and backscatter, as well as the low orders of scattering which are responsible for the glory, the silver lining on the silhouette, and the appearance of thin parts; -uses the physically based strongly anisotropic Mie phase function (not Rayleigh, Gaussian or isotropic) ; -does not need to walk through the volume ; -does not rely on any shape-dependent precomputation.

Representing the cloud shape with a Hypertexture on a surface mesh allows us to efficiently render inhomogeneous boundaries as well as sharp detailed clouds such as cumulus, contrary to methods based on sliced volumes. We can thus render sharp, fluffy or complex wispy clouds at little cost. The size of droplets is characterized at any location by a droplet size distribution (DSD), which is generally modeled in literature by a lognormal or a modified Gamma function [START_REF] Levin | Functions to represent drop size distribution in clouds. the optical density of clouds[END_REF]]. The optical properties of a cloud depend highly on the droplet size. Accounting for the DSD radically changes the resulting phase function, thus the visual appearance.

Still, these data within a cloud is not often available and its physics (e.g., the coalescence mechanism or the evolution of the DSD) is not fully understood. Since computer graphics applications require primarily visual plausibility, approximations of these values are common. As an example, density variations are visually more important on the clouds boundaries -where they are directly visible-than in the cloud core -where they only influence the appearance indirectly, through high-order multiple scattering. Usually, the DSD over a cloud (if using a DSD at all) is assumed constant.

Phase function

The phase function of a cloud droplet is given by the Mie theory.

Common approximations are Gaussian or Henyey-Greenstein functions. As seen in Figure 2 the Mie function combines a strong narrow forward peak (51% of energy), a wide forward lobe (48% of energy), and a complex backward lobe with peaks. These three features all yield very specific and visible effects at the scale of the cloud. The absence of backward peaks means no glory or fogbow. No narrow forward peak means huge underestimation of global transmittance and anisotropy. Gaussian and Henyey-Greenstein functions do encode a lobe and ease calculation but they give far from accurate visual effects. These approximations miss cloud features such as the glory and fogbow, and blur out the narrow forward scattering peak. Rayleigh scattering is even less appropriate since it is symmetrical (50% backward) and it physically corresponds to molecular scattering (giving its blue color to the sky), as opposed to scattering due to droplets.

In the visible spectrum, water cloud albedo can be considered as 1 since there is no absorption (all light is either reflected or transmitted). Note that some atmospheric phenomena commonly credited to clouds are actually caused by other elements (e.g., rainbows are caused by rain, and sundogs by ice crystals in the atmosphere).

Anisotropy

Multiple scattering is strong in clouds and often shows anisotropic behavior. Clouds span hundreds to thousands of meters and the mean free path of a light ray is about 20m. As a result, most rays will be scattered multiple times before exiting the cloud. Because of the highly anisotropic nature of the Mie phase function (99% of the light is scattered in the forward direction), even multiple scattering can be anisotropic. From our analysis of light transport in a slab, we estimate that the light behavior is isotropic only after about 30 scattering events. By isotropic, we mean that multiple scattering behaves as if the phase function of the medium was isotropic, not that the resulting Bidirectional Scattering Distribution Function (BSDF) is isotropic.

Previous Work

Simulating multiple anisotropic Mie scattering through Monte-Carlo integration is not practical in real-time. Previous optimization approaches rely on various simplifications, which we discuss below.

Phase function

Since the Mie phase function is complex and expensive to compute, it is often approximated using other functions such as Henyey-Greenstein [START_REF] Max | Efficient light propagation for multiple anisotropic volume scattering[END_REF]], Gaussian [START_REF] Premoze | Practical rendering of multiple scattering effects in participating media[END_REF] or even Rayleigh [START_REF] Harris | Real-time cloud rendering[END_REF] (see comments in Section 2.2). [START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF][START_REF] Bouthors | Realtime realistic illumination and shading of stratiform clouds[END_REF]] precompute the Mie phase function for a given DSD, which reproduces real-life features (glory, fogbow, etc.). We use the same approach for our phase function. [START_REF] Kajiya | Ray tracing volume densities[END_REF] and [START_REF] Blinn | Light reflection functions for simulation of clouds and dusty surfaces[END_REF]] consider either low albedo or low density: only single scattering is considered. This neglects all multiple scattering effects. Assuming the transport is mostly forward allows for real-time single-pass algorithms such as slice accumulation [START_REF] Dobashi | A simple, efficient method for realistic animation clouds[END_REF][START_REF] Harris | Real-time cloud rendering[END_REF][START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF]] but this neglects some of the multiple scattering effects such as backscattering. Computing multiple scattering [START_REF] Nishita | Display of clouds taking into account multiple anisotropic scattering and sky light[END_REF] for only the lower orders only has the same effect. The diffusion approximation for multiple scattering [START_REF] Stam | Multiple Scattering as a Diffusion Process[END_REF][START_REF] Jensen | A practical model for subsurface light transport[END_REF]] allows efficient computations of high orders but neglects anisotropy in multiple scattering.

Light transport

[ Premože et al. 2003] introduced the idea of Most Probable Paths (MPP) in participating media. The root idea is that most of the photons arriving at one point in one direction roughly followed the same path. Thus, integrating light transport only along this path is sufficient to account for most of the energy. In addition, [START_REF] Premoze | Practical rendering of multiple scattering effects in participating media[END_REF]] speed up this technique and account for the spatial spreading of light around this mean path through an analytical formulation. This approach has been brought to real-time [START_REF] Hegeman | A lighting model for general participating media[END_REF]] using graphics hardware for volume slicing in a manner similar to [START_REF] Harris | Real-time cloud rendering[END_REF][START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF]]. These methods based on two slicing passes (accumulating the flux from the light source in the slices, then from the slices to the eye) restrict the variety of light paths accounted for.

As mentioned in [Premože et al. 2003;[START_REF] Hegeman | A lighting model for general participating media[END_REF]] the main limitation of the MPP approach is that the paths it computes are mainly of high order, with a small angle change per scattering event. Thus, paths of low order as well as diffusive paths are underestimated. These paths contribute to most of the lighting in thin cloud parts and in the backscattering, and thus should not be neglected (see Figure 4).

We address these limitations by treating light paths of all orders. We also propose a new, faster light transport computation approach that does not rely on slicing or marching through a volume. Our approach is also inspired by the radiative transfer studies on basic shapes such as slabs [START_REF] Chandrasekhar | Radiative transfer[END_REF][START_REF] Krim | Angular distribution of radiation in an isotropically scattering slab[END_REF][START_REF] Mobley | A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces[END_REF][START_REF] Max | Plane-parallel radiance transport for global illumination in vegetation[END_REF]]. We use hardware-friendly representations such as depth maps [START_REF] Dachsbacher | Translucent shadow maps[END_REF] to implement our rendering algorithm on the GPU. Bottom: CG clouds using 3D noise (e) and surfaces with procedural details (f). Adding procedural details gives a less blurry and more contrasted appearance, increasing realism.

Cloud densities representation

Since real cloud density data is difficult to measure or simulate, early work used procedural models [START_REF] Gardner | Visual simulation of clouds[END_REF][START_REF] Dobashi | A simple, efficient method for realistic animation clouds[END_REF]]. Recent approaches have been using fluid simulation techniques [START_REF] Harris | Real-time cloud rendering[END_REF] or atmospheric data [Trembilski and Broßler 2002;[START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF]]. However, fluid simulation can only be computed at coarse level for real-time applications, and atmospheric data have low resolution. As a result, adding high frequency details is necessary to avoid a blurry appearance (see Figure 5). [START_REF] Ebert | A cloud is born[END_REF]] combines Perlin solid noise [START_REF] Perlin | An image synthesizer[END_REF]] and implicit surfaces. [START_REF] Schpok | real-time cloud modeling, rendering, and animation system[END_REF]] advect a noise texture [START_REF] Neyret | Advected textures[END_REF]], but do not account for the noise in the light transport computation, which gives them a uniform appearance (see Figure 5(e)). These ideas inspired us to combine two representations -meshes and 3D textures-to model the clouds at two different scales.

Various rendering primitives have been considered to render clouds. Since clouds are a 3D distribution of droplets, volume grids have often been used to describe them and volume rendering techniques to render them. Methods using billboards or volume slices [START_REF] Harris | Real-time cloud rendering[END_REF][START_REF] Premoze | Practical rendering of multiple scattering effects in participating media[END_REF][START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF][START_REF] Dobashi | A simple, efficient method for realistic animation clouds[END_REF]] result in a lot of overdraw1 , which is computationally expensive. While textured slices are an efficient way of rendering gaseous phenomena, they are not the best option for dense clouds, where most pixels of the back slices are hidden by those in front and therefore wasteful to render. Moreover, 3D texture memory limits the resolution of such models, resulting in blurry silhouettes and a lack of details (see Figures 5(a), 5(b)).

Since cumulus clouds are dense and often have a sharp interface, they also have been represented as surface-bounded volumes such as sets of ellipsoids [START_REF] Gardner | Visual simulation of clouds[END_REF]Elinas and Stürzlinger 2000] or meshes [Trembilski and Broßler 2002]. To avoid the "hard" appearance of polygonal surfaces, they use a procedural shader simulating the detailed silhouette and giving a volumetric impression (see Figure 5(f)). Light transport through the volume is not simulated. [START_REF] Bouthors | Realtime realistic illumination and shading of stratiform clouds[END_REF]] do simulate light transport inside a mesh, but they consider no enrichment at all on silhouettes which thus appear polygonal and opaque.

We take advantage of both volumes and surfaces by representing the high-scale cloud boundary with a mesh and the high-frequency density variations at cloud borders with a Hypertexture [START_REF] Perlin | Hypertexture[END_REF]]. The rest of the cloud interior is considered homogeneous, so only a thin layer of voxels is necessary (see Figure 6).

Overview of our method

Our shading approach is based on the analysis of light transport for each scattering order. Observing that paths of different orders have different anisotropy and spreading behaviors, we treat them separately:

-order 1 (single scattering), which is the most anisotropic and depends on the finest details, is computed using an analytical form of the scattering equation (see Section 6.2) ; -orders 2-∞ (multiple scattering) are computed in 8 separate sets (2, 3-4, 5-6, 7-8, 9-12, 13-18, 19-30, 31-∞) using our collectorbased algorithm (see Section 6.1) ; -opacity is computed by integrating the extinction function through the cloud volume (see Section 6.3).

Our collector-based approach follows and extends the idea of Most Probable Paths (MPP) [Premože et al. 2003]. We consider one most probable path and spreading per set of scattering orders. More specifically, we consider a collector area, which is the piece of surface through which enters 95% of the light that reaches the current rendered pixel in the view direction (see Figure 7(b)). This collector is defined by its center c on the cloud surface and width σ.

For a given pixel, for each set of scattering orders, we look for this collector, and compute the corresponding light transport.

To find this collector area on the lit cloud surface, we rely on an algorithm that iteratively matches the cloud surface with the most probable collector area. This algorithm is described in Section 6.1. By definition, the role of the cloud surface outside the collector is negligible, thus we can locally approximate the cloud shape as a plane-parallel slab aligned on the collector in order to simplify the computation of light transport (see Figure 7(b)).

φ L ω L ω V d p t y z x φ V ψ V T σ c (a)
Computing anisotropic light transport even for a simple shape like a slab is still very complex [START_REF] Chandrasekhar | Radiative transfer[END_REF]]. To accelerate the light transport computation, we characterize the radiative transfer in a slab through a canonical transport function. This is described in Section 5. We obtain it by analyzing numerous Monte-Carlo simulations for different slab parameters (see Appendix A).

We implement our whole rendering approach on the GPU, using depth maps to represent the cloud surface. This is described in Section 7. In Section 8 we introduce our enrichment of the cloud model and especially of its silhouette in a Hypertexture upon the surface.

The gathering of all steps within a single shader is synthesized in Section 8.1. Then we present our results and performance in Section 9.

5 Characterizing canonical light transport

Simulation

In this section we describe our experimental setup in the canonical case of a plane-parallel slab of thickness t (see Figure 7(a)).

For each set of scattering orders we compute the light transport T (i.e., the proportion of transmitted energy), the collector center c and the collector standard deviation σ. We ran numerous Monte-Carlo simulation of light paths for various values of these 5 parameters (see Appendix A for the details).

We store the results T, c, σ (φV , ψV , φL, d, t) in a 5D Blue: Monte-Carlo simulations. Red: our fitting.

Data compression

These 5D tables (1 per set of scattering orders) encode the canonical transport function, that is, the macroscopic light behavior in a slab of cloud depending on the input parameters (φV , ψV , φL, d, t). Such a set of 5D tables cannot be stored in GPU memory. We compress them by approximating the computed results with empirical functions. Appendix A describes our experimental and fitting setup.

• For the light transport T this fitting yields

T = P • A • X • µL log(d + D) log(B + D) e - (d-B) 2 2C 2 with A = A(t, µV ), B = B1(t, µV )-B2(t, µL), C = C(t, µV ), D = D(t, µV
), X = X(t, µL), P = P(θ), i.e., a 5D table for T reduces to an analytical function and seven 2D tables. P encodes the anisotropy of the result and equals 1 if the light behavior is isotropic (orders 31-∞). X modulates the result according to the lighting angle and is inspired from Chandrasekhar's Xfunction [START_REF] Chandrasekhar | Radiative transfer[END_REF]]. A, B1, B2, C, D the parameters of a "skewed" Gaussian function encoding the light behavior according to the depth of the viewpoint. Figure 8 shows the result of this fitting.

• For the collector center c, our compression results in c = (cx, 0, cz) with

cx = Ax log(1 + E • d) + Bx cz = Az log(1 + E • d) + Bz Ax = F sin ψV sin(G • φL) Bx = H sin ψV sin(φL) Az = I + J[cos ψV sin(K • φL) + LφL] Bz = M + N cos ψV with E = E(µV ), F = F(µV ), G = G(µV ), H = H(µV ), I = I(µV ), J = J(µV ), K = K(µV ), L = L(µV ), M = M(µV ), N = N(µV , µL).
• Our compression of the collector size σ gives

σ = O + Q • t log(1 + R • d) + S log(1 + T • t)
where O, Q, R, S, T are constant for a given set of scattering orders.

Estimating light transport in clouds 6.1 Multiple scattering

Considering a given cloud pixel to be rendered (corresponding to a location p in the cloud), for each scattering order we look for the area (ĉ, σ), i.e., the origin of dispersed light paths on the lit cloud surface which ended at p in eye direction (see Figure 7(b)). Since a cloud is a volume of inhomogeneous densities, defining its surface is difficult. We choose to define it as the boundary where the density ρ crosses a user-defined threshold value ρ0. As explained in the overview, we assume that the cloud behaves locally like a slab tangent to the surface at the collector location. Here, surface orientation is a scale-dependent notion. Since we are interested in the surface of incoming dispersed light paths, our local surface orientation is obtained through filtering the cloud surface according to the dispersion standard deviation σ (dashed cloud shape in Figures 7(b) and9). Sections 7 and 8 give more details on this filtering.

To find this collector location, we iterate as shown on Figure 9. We start at step 1 with a first collector of size σ0 at location c0 which we project in step 2 along the light direction on the cloud surface at c 0 . The corresponding slab is tangent to the surface (filtered according to σ0) at c ′ 0 . View and light parameters (φV , ψV , φL, d, t) according to this slab are obtained by simple geometric transformations. In step 3, the canonical transport function provides us with the collector location c1(φV , ψV , φL, d, t) and size σ1(φV , ψV , φL, d, t) corresponding to such a configuration, which is likely to be different from c ′ 0 We project c1 on the cloud surface filtered by σ1 at c ′ 1 in step 4, and we iterate up to convergence, i.e., cn ≃ c ′ n . We then take (ĉ, σ) = (cn, σn). Once we found the collector, we can the corresponding light transport T (i.e., the amount of energy transmitted from this collector to the eye) with the same input parameters. We run this algorithm for each set of scattering orders on the GPU (see Section 7). This iterative algorithm is in fact a fixed-point method applied on c, i.e., we are looking for value x that satisfies f (x) = x, where x here is our collector parameters (c, σ) and f our canonical transport function. Since the search space of this collector is restricted to the cloud lit surface, this algorithm cannot diverge. However, like any basic fixed point method, it can reach a state where it loops between two values without converging (i.e., ci = ci-1 and ci = ci-2). It can also take too large steps and miss the solution.

To avoid these cases, we limit the size of each step (we constraint ci such that cici-1 < σi). We start the algorithm with an initial position c0 = p. We use a large initial size σ0. Indeed, if the initial collector spans the whole cloud, the projected result at step 2 will be a first-order approximation of the whole lit cloud surface, which c 0 ,σ 0

Step 1 Step 2

Step 3 Step 4

Step is a good starting point for our algorithm in terms of convergence speed. Subsequent steps will then "refine" the lit cloud surface at the most probable collector location.

Single Scattering

For the first scattering order, which constitutes a degenerate case for our collector-based algorithm, we simply integrate analytically the Mie single scattering along the eye direction. This allows us to account for the inhomogeneous densities and the fine details along the view direction.

This integration is done by considering piecewise linear segments with samples taken on the cloud surface as shown in Figure 10 (i.e., exponentially spaced samples are read along the view direction). For one segment i, the single scattering formula gives Ti = Mie(θ)

x i+1 x i κe -κ(x+l(x)) dx = Mie(θ)(e -κ(x i+1 +l i+1 ) -e -κ(x i +l i ) ) (1)
where Mie is the Mie phase function and κ the extinction coefficient defined in Equation 4, Appendix A. Note that since the Mie phase function is wavelength-dependent, we encode and use Mie as an RGB function. In multiple scattering, this dependence is blurred out, thus T needs only be a scalar.

Opacity

The opacity α is computed by integrating the extinction along the view direction. This results in α = l 0 e -κx dx. Since the extinction coefficient κ is varying in space, we discretize this integration by sampling segments along the view direction as for single scattering. For each segment i, we read κ in the cloud volume and accumulate the opacity

αi = x i+1 x i e -κx dx = e -κx i+1 -e -κx i κ . ( 2
)
This is a standard ray marching procedure.

Implementation on the GPU

rendering time, the cloud mesh is rendered using a fragment shader that computes the light transport from the lit surface as explained in Section 6. Since this process is fairly involved we rely heavily on GPU capabilities to make it efficient, especially for computing distances to the filtered cloud surface, which we explain in this section. 22 intermediate functions A through X in Section 5.2 necessary to compute the canonical transport function are discretized and stored in textures, as well as the Mie phase function used for the single scattering. Overall this gives a few textures occupying less than 2MB in video memory.

To manage efficiently the surface processing (e.g., computing distances) on the GPU we rely on depth maps. We create two depth maps ZminL, ZmaxL and a normal map NL from the light point of view. This is done at each frame to allow for the animation of the cloud shape and of the light.

A convenient way to approximate the filtering of the surface according to a kernel of size σ is to rely on the MIP-mapping of the Z values in the depth map. To compute the MIP-map correctly (i.e., without taking into account pixels where there is no cloud), we add an alpha channel A and we follow the same scheme as for an alpha-premultiplied texture. In fact the premultiplication is done automatically when setting the default Z value to 0. After the MIPmap pyramid (Z 0 , ..., Z n ) is computed, a filtered Z value is obtained by Z i (P )

A i (P ) as in [START_REF] Dachsbacher | Translucent shadow maps[END_REF]]. Computing the distances d (Section 6.1) and li (Equation 1) to the filtered surface in the light direction is done by simply accessing the associated MIP-mapped depth maps. To compute the thickness t, we subtract ZmaxL -ZminL. The orientation of the filtered surface is obtained by reading the MIP-mapped normal map NL. Thanks to this representation, all the parameters (φV , ψV , φL, d, t) can be computed and the whole algorithm described in Section 6 can be implemented in a fragment shader. For each set of scattering orders the shader first finds the collector (ĉ, σ) using our algorithm described in Section 6.1, then computes the associated intensity T using the compressed canonical transport function described in Section 5.

Surface-based cloud approaches generally rely on a transparency shader to fake the effect of inhomogeneities on the silhouette. Volume-based methods are limited in resolution due to the huge memory requirement, which usually makes the silhouette lack details (see Figure 5). Our approach combines the best of both: we define a volumetric Hypertexture in a layer below the surface in order to have high-resolution 3D effects on the cloud edges with low memory requirements (see Figure 6). Thus, the volume representation handles all the frequencies of cloud details that are not handled by the cloud mesh.

The Hypertexture layer is defined through a distance function D(p) to the surface (which equals 0 on the surface and increases inside the cloud). The procedural details are modulating the density N0 (Equation 3) and the extinction coefficient κ (Equation 4) with ρ(p) = S(D(p) + noise(p)) where S is a sigmoid function and noise is a scalar 3D Perlin noise [START_REF] Perlin | An image synthesizer[END_REF]]. Due to the cost of evaluating distance fields, D(p) is computed and stored in a volumetric texture. noise() is evaluated on the fly in the shader. We rely on [START_REF] Crassin | Représentation et algorithmes pour l'exploration interactive de volumes procéduraux étendus et détaillés[END_REF] to compute and voxelize quickly the distance field at high resolution using only the minimal necessary memory usage. This volumetric enrichment is used in three parts of the shader. When computing the cloud opacity (Section 6.3), we perform a ray marching on the GPU [START_REF] Crassin | Représentation et algorithmes pour l'exploration interactive de volumes procéduraux étendus et détaillés[END_REF] through this layer to integrate the cloud density in this part of the cloud. When computing single scattering (Section 6.2), the extinction coefficient κ (Equation 4) is also modulated for each segment according to ρ(p). Finally, to account for these details in the multiple scattering computations (Section 6.1), the depth map ZminL is modulated: we store in ZminL the depth of the first voxel having ρ > ρ0.

Note that for most pixels except on the silhouette and thin parts, strong opacity will stop the ray close to the entry point, so the average marching length is limited.

Final rendering

The precomputation for the current frame is limited to rebuilding the depth and normal maps. This allows us to change the viewpoint, lighting conditions, and cloud shape.

Terrain and opaque objects are drawn first. Then the cloud mesh is drawn using our pixel shader through deferred shading. This pixel shader:

-iteratively finds the collectors (ĉ, σ) for the 8 sets of scattering orders corresponding to sun illumination (Section 6.1) ; -computes the light transport T associated to each set (as explained in Section 5), and multiplies each by the lighting conditions (intensity, color and visibility) ; -computes the analytical single scattering (Section 6.2) ; -computes the opacity (Section 6.3).

We handle environment illumination like sun illumination. A blue source is added above the cloud and a brown one below the cloud. We use our multiple scattering algorithm with both of these additional sources. Outdoor scenes require accounting for aerial perspective. We rely on the model of [START_REF] Hoffman | Graphics programming methods[END_REF]. Rendering very bright objects such as clouds also require some tone mapping management. We use a simplified, unblurred version of [START_REF] Goodnight | Interactive time-dependent tone mapping using programmable graphics hardware[END_REF]].

Note that our representation allows us to easily account for points of view inside the clouds, since our canonical transport function accounts for this case.

Results

Our tests were conducted on a Pentium 4 at 1.86 GHz with a nVidia 8800 GTS graphics board. All benchmarks were done at resolution 800 × 600.

We tested our method against different cloud shapes: a cloud slab, an animated stratocumulus layer without procedural noise, and a cumulus cloud with procedural noise. The slab allows us to test our algorithm and validate directly its results against the canonical transport function. It also allows us to see features such as anisotropic reflectance, anisotropic transmittance in thin slabs and isotropic transmittance in thick slabs. The stratocumulus layer allows us to test our method against a shape close to the canonical one and to validate the handling of animations. It is composed of 130K triangles, and the framerate is 10fps. We can see on this example all the wanted cloud features: anisotropic scattering, diffusion, backscattering, glory, fogbow. The cumulus cloud model allows us to test our algorithm on an arbitrary shape. It is composed of 5K triangles with a 512 3 Hypertexture. We obtain a framerate of 2fps on this model. Note that most of the time is spent in evaluating the noise on the fly in the hypertexture. Without the procedural noise, the framerate rises to 10fps. This model also displays all the sought cloud features. 10 iterations of our collector-finding algorithm are sufficient in all cases to reach convergence. Figure 12 and the teaser show the result of our method on various cases.

Discussion and Future Work

We address the limitations of other real-time approaches [START_REF] Harris | Real-time cloud rendering[END_REF][START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF][START_REF] Hegeman | A lighting model for general participating media[END_REF]] by treating accurately light paths of all orders and by using a more detailed cloud shape. We use the Mie phase function for cloud droplets, which provides us with the right anisotropy and enables visual effects such as glory and fogbow. Contrary to [START_REF] Schpok | real-time cloud modeling, rendering, and animation system[END_REF]], we account for the procedural details in the light transport calculation. Although similar details could be attained by other real-time approaches [START_REF] Harris | Real-time cloud rendering[END_REF][START_REF] Riley | Efficient rendering of atmospheric phenomena[END_REF][START_REF] Hegeman | A lighting model for general participating media[END_REF]] by increasing the volumetric resolution of their models (at the expense of speed and within memory limits), our method brings features that are not handled by these approaches such as accurate backscattering and diffusion. We allow for the animation of viewpoint, light direction and cloud shape. In case of cloud animation, we rely on the algorithm described in [START_REF] Crassin | Représentation et algorithmes pour l'exploration interactive de volumes procéduraux étendus et détaillés[END_REF] to recompute in real-time the distance field used by our procedural noise.

Like the other methods using a depth-map to solve scattering problems [START_REF] Dachsbacher | Translucent shadow maps[END_REF], this representation has some issues regarding resolution and non-convex shapes. The precision of this representation is limited by the resolution of the depth map. As a result, full scalability of the method would probably require alternative depth maps techniques [START_REF] Stamminger | Perspective shadow maps[END_REF][START_REF] Arvo | Alias-free shadow maps using graphics hardware[END_REF]. In case of non-convex shapes, light transport is slightly underestimated in shadowed regions (see Figure 11(a)): the algorithm incorrectly assumes that there is matter between the shadowed surfaces and the lit surface. In consequence, light is considered more attenuated than it should be. In practice, this error happens on shadowed parts of the cloud, where environment (i.e., sky and ground) illumination is predominant. As mentioned in [START_REF] Dachsbacher | Translucent shadow maps[END_REF]] who suffer from the same issues, this issue can be solved by using a depth peeling technique to treat nonconvex shapes as a collection of convex shapes. Using deep shadow maps [START_REF] Lokovic | Deep shadow maps[END_REF] would also help addressing this issue and increase the accuracy of single scattering.

One limitation of our approach is the assumption that light arriving to the viewer goes through only one connected collector (i.e., one most probable path) per set of scattering orders. As shown on figure 11(b) it is not always the case. In these configurations, our algorithm accounts for only one collector, thus underestimates the amount of light transmitted. Note that since we look for several collectors (one for each of the 8 sets of scattering orders) per pixel, this error concerns only a fraction of the pixel color. One solution might be to look for several collectors per set of scattering orders with different initial values.

Searching for a collector ĉ corresponds to searching for the entry point ĉ on the lit surface of a local maximum of the light transport T . Our iterative algorithm corresponds to a fixed-point method: we look for the fixed point f (c) = c where f represents our canonical transport function. As future work, better techniques from the field of optimization could be used to ensure faster convergence and to handle the case of several maxima of T .

Our light transport computation on GPU using our collector-finding algorithm (i.e., the main contribution of this paper) is fast enough for interactive applications (10fps). The speed of this method can be still be improved. Moreover, the computation of the procedural noise and the GPU ray marching in our implementation is an unoptimized version of [START_REF] Crassin | Représentation et algorithmes pour l'exploration interactive de volumes procéduraux étendus et détaillés[END_REF] and is computationally expensive (80% of the rendering cost).

As future work, we would like to take into account higher-scale light effects such as interreflections between clouds and cloud lobes. Also, the method described in [START_REF] Bouthors | Realtime realistic illumination and shading of stratiform clouds[END_REF]] can be applied to this work to compute the interreflections between the clouds and the ground, which have been shown to be of visual importance.

Conclusion

We have proposed a study of light transport yielding a new formulation for the macroscopic behavior of light in participating media that is suited for computer graphics. We have proposed a new way of computing radiative transfer through a volume of homogeneous participating media with a dedicated optional method to handle inhomogeneous boundaries. Contrary to previous approaches, our method only needs to walk the cloud boundaries rather than walking through the whole volume. We have demonstrated this technique on detailed cumulus-type clouds. As shown on our results, we correctly reproduce visual features such as back-scattering, anisotropic multiple scattering, glory, etc.

We believe this approach can be used in other applications where multiple scattering in well-bounded participating media is important such as sub-surface scattering, e.g., as an alternative to the dipole approximation [START_REF] Jensen | A practical model for subsurface light transport[END_REF]. As future research, our approach could also be used in offline rendering, where other rep-resentations (e.g., meshes) can be used for the collector-finding algorithm, which would remove the limitations due to depth maps. It could also be used to find starting paths in a volumetric Metropolis light transport simulation.

A Measuring light transport in a cloud slab

As explained in Section 2, the appropriate phase function for clouds is Mie scattering. It is a complex oscillating function depending of droplet size and wavelength. Like [START_REF] Bouthors | Realtime realistic illumination and shading of stratiform clouds[END_REF], we preintegrate the effect of the DSD on the Mie phase function and we rely on the modified Mie approximation in which the narrow (5 • ) strong forward peak is suppressed out of the phase function and converted into 50% lowered density [START_REF] Lenoble | Radiative transfer in scattering and absorbing atmospheres: standard computational procedures[END_REF]]. This proved to yield equivalent results while needing to consider only half of the scattering events and gave a better conditioned phase function.

For the DSD, we draw on the modified Gamma distribution [START_REF] Levin | Functions to represent drop size distribution in clouds. the optical density of clouds[END_REF]] (adapted to cloud droplets) defined by (3)

N (r) = ρN0 Γ(γ)rn
This function describes the density N (r) of droplets of radius with rn the characteristic radius of the distribution, γ ing its broadness, and N0 is the total density of droplets. Γ is the gamma function. ρ is a modulation factor for the total density brought by our procedural enrichment described in Section 8. A cloud droplet size distribution is then only described by the three parameters N0, rn and γ. In terms of optical properties, the effective radius corresponding to this distribution is re = (γ + 2)rn.

We consider the following typical parameters for cumulus clouds: re = 6µm, γ = 2, N0 = 4.10 8 m -3 .

The extinction coefficient is defined by

κ = ρN0πr 2 e . (4)
It yields the extinction function e -κx which is the probability to traverse the cloud along a path of length x without hitting a droplet. It is used in all scattering equations, including opacity (Equation 2), single scattering (Equation 1) and multiple scattering (Equation 5).

The multiple scattering equation has been extensively discussed in the literature [START_REF] Chandrasekhar | Radiative transfer[END_REF][START_REF] Kajiya | Ray tracing volume densities[END_REF].

It can be written in the form

- ω κ • dT (p, ω) dp = T (p, ω) + 1 4π ω ′ P ( ω • ω ′ )T (p, ω ′ )d ω ′ (5)
for the intensity T reaching a point p in direction ω, with P (θ) the phase function of the media (here, Mie). This integro-differential equation can be solved computationally through Monte-Carlo integration. The contribution of each order of scattering in the intensity T , as as the collector information (c, σ) can be easily tracked during the integration. For our light transport characterization step (Section 5), we computed the solution of Equation 5 in a planeparallel slab for various values of (φV , ψV , φL, d, t) by ray tracing multiple scattering from the eye. We stored the contribution T of each scattering order into a database, along with the collector data (c, σ). These computations were done with an error margin of 5% at the 95% level. We computed them against 10 million different sets of values for (φV , ψV , φL, d, t), resulting in a raw database size of 25GB. These computations took several weeks on a 100nodes, dual-core 900MHz Itanium-2 cluster. The database and fitting results will be made accessible online.

The analysis of these results (i.e., finding lower-dimensional functions fitting the results) was done empirically by plotting T, c, σ against the input parameters and looking for remarkable behaviors.

It was inspired by previous approaches such as Chandrasekhar's Xand Y -functions. The fitting itself was done using classical nonlinear least square optimization with MATLAB.

Figure 12: Some results of our method.

Figure 1 :

 1 Figure 1: Overview of our contributions. (a): In an preliminary analysis, we characterize light transport in a slab via a collector area representing location of incoming light for each scattering order. (b): We use this characterization to find collectors on an arbitrary cloud shape and compute the light transport. (c): Our cloud model is represented by a Hypertexture, with procedural details on the boundary and a homogeneous core.

Figure 2 :

 2 Figure 2: Log plots (inset: polar log plots) of commonly used phase functions. Red: Rayleigh. Green: Henyey-Greenstein with g = .99. Blue: Mie.2 Cloud physics2.1 Density and size of droplets in cloudsReal convective clouds are not blurry on boundaries, they are usually sharp or wispy (see Figures5(c), 5(d)). Collapsing cloud turrets or weak clouds may have a larger wispy layer. These inhomogeneities in the cloud liquid water content (i.e., mass density) are a strong visual feature of clouds. Inside the cloud, this density can also vary -especially near rain condition -due to coalescence of droplets.

Figure 3 :

 3 Figure 3: Some results of our light transport analysis. Left: BSDF for a point of view at a depth d = 100m inside a cloud slab of thickness t = 1000m, with an incident illumination angle φ L = 75 • . Areas represent the contribution of different orders of scattering. Even high orders (up to 30 scattering events) show an anisotropic behavior, while orders > 30 show an isotropic behavior. Right: Contribution of different orders of scattering for the reflectance (in red) and transmittance (in blue) of a slab of varying thickness. Isotropic orders (31-∞) begin to appear at thicknesses > 100m. Anisotropic orders (1-30) play a role up to 1000m in transmittance and contribute to 30% -100% of the reflectance.

Figure 4 :

 4 Figure 4: Various kinds of light paths in participating media, brought by different orders of scattering. Low orders of scattering bring short, steepturning paths (red). Higher orders bring long, slow-turning paths (green). Highest orders bring complex, spread, diffusive paths (blue). The Most Probable Paths approach [Premože et al. 2003] reproduces the green ones, but underestimates red and blue ones.

Figure 5 :

 5 Figure 5: Top: real-time (a) and interactive (b) CG cumulus clouds using billboard or slices. Middle: wispy (c) and sharp (d) real cumulus clouds. Bottom: CG clouds using 3D noise (e) and surfaces with procedural details (f). Adding procedural details gives a less blurry and more contrasted appearance, increasing realism.

hFigure 6 :

 6 Figure 6: cloud representation. A mesh is used to describe the outer cloud boundaries at low resolution. A procedural volumetric hypertexture adds details under the boundary up to a certain depth h inside the cloud. The core is considered homogeneous.

Figure 7 :

 7 Figure 7: (a): Setup and notation for the canonical light transport T through a collector area (c, σ) between a lit slab surface and a point p in the slab, depending on the input parameters (φ V , ψ V , φ L , d, t) for each set of scattering orders. Note that ψ L is always zero (the reference frame is aligned with the light direction). (b): Light transport in the cloud between its lit surface and a point p. For each set of scattering orders the incoming light at p is assumed to come from a collector area. We characterize this transport by looking for a fitting slab, then relying on the canonical transport function.

  These values T, c, σ are computed against 5 input parameters: slab thickness t, viewpoint depth d, viewing angles (φV , ψV ) and lighting elevation angle φL, in the reference frame shown in Figure7(a). We define µV = cos(φV ), µL = cos(φL), ωV = view direction, ωL = light direction, cos θ = ωV • ωL, p = (0, -d, 0) = viewpoint location. Since we want to characterize light transport up to any point p within the volume, we consider values of the viewpoint depth d the slab (0 ≤ d ≤ t). Viewpoints outside the slab correspond to d = 0 or d = t.

Figure 8 :

 8 Figure8: Some resulting BSDF of our light transport analysis. T is plotted against φ V (ψ V fixed at 0 • ) for various input parameters (φ L = 25 • ).

Figure 9 :

 9 Figure 9: Summary of our iterative algorithm to locate the collector (blue area). Solid cloud shape: unfiltered cloud surface. Dashed cloud shape: surface filtered according to σ. Dashed box: slab matching the filtered surface at collector position c. Orange boxes represent the use of our canonical transport function.

Figure 10 :

 10 Figure 10: Piecewise linear integration of the single scattering paths.

Figure 11 :

 11 Figure 11: (a): Limitation of using depth maps. The radiance of the red surface is slightly underestimated. However, this error is of low visual importance. (b): Limitation of searching for only one collector per set of scattering orders. In this example two collectors of equal importance exist, but our method will find only one.

i.e., a given pixel is rasterized many time by different rendered primitives.

Acknowledgments

We thank Guillaume Piolat for the days and night of coding, Florent Moulin and Laurence Boissieux for the week-ends spent modeling the clouds, Sébastien Barbier, Paul Kry, and the reviewers for the comments on the paper. INRIA provided the clusters and databases, managed by Eric Ragusi and Frédéric Saint-Marcel. The Mie phase function was generated by Philip Laven's MiePlot. This work was partially funded by the Exploradoc fellowship and the Fund.


Martín I Taccone

Andrés Cruz

Jordan Dezalay

Satchin Soorkia

Michel Broquier

Gilles Grégoire

Cristián G Sánchez

Gustavo A Pino

UV photofragmentation of cold Cytosine-M + complexes (M + : Na + , K + , Ag + )

The UV-photofragmentation spectra of cold Cytosine-M + complexes (M + : Na + , K + , Ag+) were recorded and analyzed through comparison with geometry optimizations and frequency calculations of the ground and excited states at the SCS-CC2/Def2-SVPD level of theory. While in all complexes, the ground state minimum geometry is planar (Cs symmetry), the * state minimum geometry has the NH2 group slightly twisted and an out-of-plane metal cation. This was confirmed by comparing the simulated * Franck-Condon spectra with the vibrationally resolved photofragmentation spectra of CytNa + and CytK + . Vertical excitation transitions were also calculated to evaluate the energies of the CT states involving the transfer of an electron from the Cyt moiety to M + . For both CytK + and CytNa + complexes, the first CT state corresponds to an electron transfer from the cytosine aromatic  ring to the antibonding * orbital centered on the alkali cation. This * state is predicted to lie much higher in energy (> 6 V) than the band origin of the * electronic transition (around 4.3 eV) unlike what is observed for CytAg + complex for which the first excited state has a nO* electronic configuration. This is the reason for the absence of the Cyt + + M charge transfer fragmentation channel for CytK + and CytNa + complexes.

INTRODUCTION

Purine and pyrimidine bases (Adenine, Guanine, Thymine and Cytosine) are the building blocks of DNA. The DNA damage upon UV photoexcitation is an important cause for mutagenic effects in biological systems [START_REF] Schreier | Early Events of DNA Photodamage[END_REF][START_REF] Pfeifer | Mutations Induced by Ultraviolet Light[END_REF][START_REF] Bera | Radicals Derived from the Guanine•cytosine Base Pair Cause DNA Subunit Lesions[END_REF][START_REF] Boudaı̈ffa | Resonant Formation of DNA Strand Breaks by Low-Energy (3 to 20 eV) Electrons[END_REF] and further possible development of different types of cancer. 5- 7 A useful strategy to understand these processes is a bottom-up approach by means of studying the excited state photodynamics of the building blocks. [START_REF] Ullrich | Electronic Relaxation Dynamics in DNA and RNA Bases Studied by Time-Resolved Photoelectron Spectroscopy[END_REF][START_REF] Serrano-Andrés | Are the Five Natural DNA/RNA Base Monomers a Good Choice from Natural Selection?: A Photochemical Perspective[END_REF][START_REF] Barbatti | Relaxation Mechanisms of UV-Photoexcited DNA and RNA Nucleobases[END_REF][START_REF] Middleton | DNA Excited-State Dynamics: From Single Bases to the Double Helix[END_REF][START_REF] Improta | Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases[END_REF][START_REF] Berdakin | Excited States of Protonated DNA/RNA Bases[END_REF][START_REF] Kleinermanns | Excited State Dynamics of DNA Bases[END_REF][START_REF] Boldissar | How Nature Covers Its Bases[END_REF][START_REF] Gustavsson | DNA/RNA: Building Blocks of Life Under UV Irradiation[END_REF] It is also known that the interaction of the DNA bases with cations (H + or metal cations M + ) can induce the formation of non-canonical structures [START_REF] Lippert | Promotion of Rare Nucleobase Tautomers by Metal Binding[END_REF][START_REF] Cristofari | Driven Conformational Switch between Non-Canonical DNA Structures in a C-Rich Domain of EGFR Promoter[END_REF][START_REF] Berdakin | Gas Phase Structure of Metal Mediated (Cytosine)2Ag + Mimics the Hemiprotonated (Cytosine)2H + Dimer in i-Motif Folding[END_REF][START_REF] Berdakin | Effect of Ag + on the Excited-State Properties of a Gas-Phase (Cytosine)2Ag + Complex: Electronic Transition and Estimated Lifetime[END_REF] as well as to facilitate proton transfer (PT) reactions within base pairs. [START_REF] Sponer | Interaction of Metal Cations with Nucleic Acids and Their Building Units[END_REF][START_REF] Cruz-Ortiz | Fingerprints of Both Watson-Crick and Hoogsteen Isomers of the Isolated (Cytosine-Guanine)H + Pair[END_REF] During the last years we have studied the UV spectroscopy and excited state dynamics of protonated DNA bases [START_REF] Berdakin | Excited States of Protonated DNA/RNA Bases[END_REF][START_REF] Broquier | Excited State Dynamics of Cold Protonated Cytosine Tautomers: Characterization of Charge Transfer, Intersystem Crossing, and Internal Conversion Processes[END_REF][START_REF] Féraud | Excited States of Proton-Bound DNA/RNA Base Homodimers: Pyrimidines[END_REF] as well as the effect of substituting H + by Ag + on the structure and reactivity of Cytosine and its dimeric form. [START_REF] Berdakin | Gas Phase Structure of Metal Mediated (Cytosine)2Ag + Mimics the Hemiprotonated (Cytosine)2H + Dimer in i-Motif Folding[END_REF][START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF][START_REF] Berdakin | Effect of Ag+ on the Excited-State Properties of a Gas-Phase (Cytosine)2Ag + Complex: Electronic Transition and Estimated Lifetime[END_REF] In this regard, it was recently shown that the first excited state of CytAg + complex is a charge transfer (CT) state in which an electron from a nO orbital of Cyt is transferred to a * orbital on Ag + . The excitation of the complex to the nO* state at 3.93 eV leads to ionized cytosine Cyt + and neutral Ag fragments. [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF] Since ionization of DNA bases could induce PT reactions by reducing the energy barrier, [START_REF] Bertran | Proton Transfer in DNA Base Pairs[END_REF][START_REF] Nir | Pairing of Isolated Nucleic-Acid Bases in the Absence of the DNA Backbone[END_REF] the presence of CT states producing Cyt + at low excitation energies could alter the fidelity of DNA inducing mutagenic effects. [START_REF] Li | Tautomerism Provides a Molecular Explanation for the Mutagenic Properties of the Anti-HIV Nucleoside 5-Aza-5,6-Dihydro-2'-Deoxycytidine[END_REF][START_REF] Wang | Structural Evidence for the Rare Tautomer Hypothesis of Spontaneous Mutagenesis[END_REF] Moreover, the ground state fragmentation of CytAg + by infrared multiphoton dissociation (IRMPD) produces HNCO loss as the only fragmentation channel [START_REF] Berdakin | On the Ag + -Cytosine Interaction: The Effect of Microhydration Probed by IR Optical Spectroscopy and Density Functional Theory[END_REF] at variance with the fragmentation by IRMPD of CytM + complexes (M = Li, Na, K, Rb, Cs) for which the only fragmentation channel was the neutral Cyt loss. [START_REF] Yang | IRMPD Action Spectroscopy of Alkali Metal Cation--Cytosine Complexes: Effects of Alkali Metal Cation Size on Gas Phase Conformation[END_REF] Considering this difference and the remarkable CT character of the first excited state of CytAg + , the goal of this work was to study the effect of some of the two most abundant metal cations in biological systems, e.g. Na + and K + on the UV photofragmentation of the CytNa + and CytK + complexes as compared to CytAg + by means of photofragmentation spectroscopy of cold ions.

EXPERIMENTAL AND THEORETICAL METHODS

The experiments have been conducted at the Centre Laser of the Université Paris-Sud (CLUPS) in Orsay. The experimental setup has been previously presented [START_REF] Broquier | A Comprehensive Study of Cold Protonated Tyramine: UV Photodissociation Experiments and Ab Initio Calculations[END_REF] and is briefly summarized here. It comprises an electrospray ion source (ESI), a 3D-quadrupole ion trap QIT (Jordan TOF, Inc.) mounted on a cold head of a compressed helium cryostat (CH-204S, Sumitomo) that maintains the temperature of the trap around 10-15 K, and a linear time-of-flight mass spectrometer (TOF-MS). The complexes of interest are produced in the ESI source from a water/methanol solution (50/50 by volume) of Cytosine and alkali salt (NaCl and KI) or AgNO3 at 100 µM. The complexes are first stored in an octupole trap for 100 ms and then extracted, mass-selected and transferred into the 3D-QIT where they are thermalized through collisions with helium buffer gas introduced by a pulsed valve (General valve, series 9) a few ms before the entrance of the ions. Two UV lasers were used for the photodissociation of the ions, either a ps OPA laser (EKSPLA PG 411) with 8 cm -1 bandwidth and 16 ps time resolution, or the output of a frequency doubled ns dye laser (Quantel TDL 90) whose resolution is 0.2 cm -1 . Both lasers operated at 10 Hz and are triggered at least 40 ms after the entrance of the ions in the QIT to ensure their complete cooling and pumping of the buffer gas. All of the ionic fragments and remaining parent ions are extracted and accelerated for mass analysis in the linear TOF-MS and finally detected by microchannel plates (Z-Gap, Jordan TOF, Inc.). The resonant absorption of the UV laser is observed by monitoring the appearance of the ionic fragments at lower masses. In case of CytNa + , because of the low m/z cut-off of the Paul Trap, the photofragment sodium cation cannot be trapped in the QIT along with the parent ions, so the ions are immediately extracted from the trap (within 1 µs) after interaction with the laser. For CytK + , the potassium cation is stored, and we did not observe any other photofragment even at long fragmentation delays up to 30 ms after laser excitation. For CytAg + , the main photofragment at all excitation wavelengths is the cytosine cation Cyt + along with Ag + and loss of 43 Da (HNCO loss) from the CytAg + complex as minor fragments. Action spectra are recorded by scanning the laser frequency and monitoring the cationic alkali signal normalized by the intensity of laser and the parent ion signal.

The equilibrium geometries and the vibrational frequencies of the complexes in their ground and excited states were calculated with TURBOMOLE package (v6.6) [START_REF]TURBOMOLE V6.6. a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH[END_REF] at SCS-CC2 [START_REF] Grimme | Improved Second-Order Møller-Plesset Perturbation Theory by Separate Scaling of Parallel-and Antiparallel-Spin Pair Correlation Energies[END_REF] level of theory, making use of resolution of identity (RI) [START_REF] Ahlrichs | Efficient Evaluation of Three-Center Two-Electron Integrals over Gaussian Functions[END_REF] and Karlsruhe "def2" split valence polarization basis set with diffuse functions (Def2-SVPD). [START_REF] Weigend | Accurate Coulomb-Fitting Basis Sets for H to Rn[END_REF] In particular, the split-component scaled approach (SCS) was applied since it improves the accuracy of CC2 calculations for the charge transfer states. [START_REF] Hellweg | Benchmarking the Performance of Spin-Component Scaled CC2 in Ground and Electronically Excited States[END_REF] The calculated vibrationally-resolved electronic spectra were obtained with the PGOPHER spectra simulator package [START_REF] Western | A Program for Simulating Rotational, Vibrational and Electronic Spectra[END_REF] using the calculated frequencies of the ground and excited states. For sake of comparison, the simulation was performed at 0 K and using a convoluted with a gaussian function of 8 cm -1 (full-width at half-maximum FWHM).

RESULTS AND DISCUSSION

The UV photofragmentation of the CytNa + and CytK + complexes result in the formation of neutral cytosine and the corresponding alkali cation Na + and K + at m/z 23 and 39, respectively. It is worthy to note that Na + and K + are the only fragments obtained upon laser irradiation and no other ionic fragment, in particular the cytosine cation, was observed. This is at opposite to the result found for the CytAg + complex, in which the complex is excited to a charge transfer (CT) state from where it dissociates to Cyt + as the main ionic fragment. [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF] However, the present result is consistent with those reported by Rodgers and co-workers on the ground state fragmentation of the same alkali complexes induced by multiple photon dissociation (IRMPD). [START_REF] Yang | IRMPD Action Spectroscopy of Alkali Metal Cation--Cytosine Complexes: Effects of Alkali Metal Cation Size on Gas Phase Conformation[END_REF] This similarity strongly suggests that upon UV excitation, the complexes undergo internal conversion to the ground state followed by statistical fragmentation. The vibrationally-resolved UV photofragmentation spectra of both complexes shown in Figure 1 were recorded in the spectral range of 34500 to 36500 cm -1 . Above this excitation energy, the vibronic spectra are unresolved, exhibiting a broad absorption band decaying in intensity until 40 000 cm -1 . The 00 0 transition of CytNa + is detected at 35028 cm -1 (4.34 eV). The band origin (BO) has the largest intensity among the other vibronic transitions, revealing the good overlap between the vibrational wave functions of the ground and excited states, thus small geometry changes between the equilibrium structures of both states. For CytK + complex, the 0 0 0 band is found at 34707 cm -1 (4.30 eV) but at variance with CytNa + , the BO is not the most intense vibronic transition, suggesting a larger equilibrium geometry difference between the ground and excited states.

Scheme 1 Atom numbering of the Cyt-M + , cytosine in its keto-amino form.

The most stable form of the ground state geometries of all complexes is planar (Cs symmetry), containing the keto-amino tautomer of cytosine in which the metal cation simultaneously interacts with the carbonyl oxygen O7 and the nitrogen N3 atoms (see scheme 1) in agreement with a previous report by Rodgers and co-workers. [START_REF] Yang | IRMPD Action Spectroscopy of Alkali Metal Cation--Cytosine Complexes: Effects of Alkali Metal Cation Size on Gas Phase Conformation[END_REF][START_REF] Yang | Tautomerization in the Formation and Collision-Induced Dissociation of Alkali Metal Cation-Cytosine Complexes[END_REF] For the alkali complexes, geometry optimization of the first excited state which corresponds to a * transition also led to planar structure for both complexes. Nevertheless, they exhibited two imaginary frequencies indicating that they do not correspond to true minima of the excited state PES. The modes associated to the imaginary frequencies correspond to twist motion of the NH2 group and out-of-plane motion of the metal cation. A re-optimization of this structure starting with a small geometry distortion along the pyrimidinic out-of-plane motion finally lead, in both complexes, to true minima of the PES whose structures exhibit a slightly out-of-plane metal cation and small twist of the NH2 group. Figure 2 shows the optimized structures of the S1 * excited states for CytNa + and CytK + , the most relevant structural parameters (interatomic distances and dihedral angles) are reported in Table 1. As it was presumed from the photofragmentation spectra (Fig. 1), a larger geometry distortion from the planar Cs structure is found for CytK + than for CytNa + . The calculated vertical (Ev) and adiabatic (Ead) transition energies to the most relevant excited states for the photophysics of all complexes are shown in Table 2, together with the experimental energy for the 00 0 bands. In addition, the corresponding information for the CytAg + complex is also reported for comparison. In all cases, adiabatic energies were corrected by difference in the zero-point energy between the ground and excited states (ZPE), allowing a direct comparison with the experimental BOs. The calculated adiabatic energies of the first excited states are in very good agreement with the experimental values of the three complexes, been the difference between the calculated and the experimental values as small as 0.7% for CytNa + , 1.2% for CytK + and 1.3 % for CytAg +. Frequency calculations for the ground and excited states equilibrium geometries were used to simulate the vibronic spectra of both complexes. The comparison of the calculated and experimental photofragmentation spectra is shown in Figure 3. The active modes for both complexes are shown in Figure SI 1. For both complexes, the first two out-of-plane 1 and 2 modes which involve twist motion of the amino group have the strongest Franck-Condon activities, while a second set of vibronic progression is built from the in-plane 12 modes at 532 cm -1 and 528 cm -1 for CytNa + and CytK + , respectively. For the 2 mode, the alkali cation also shows an in-plane translation. The intensities of the two out-of-plane modes are stronger in CytK + than in CytNa + , in agreement with the larger structural deviation from the Cs structure in the former. In overall, the vibronic spectra are satisfyingly reproduced at this level of theory for both complexes, confirming that the locally excited * state has a slightly bent structure with the alkali atom out of the plane of cytosine. A close inspection to the spectra shows that each band is slightly broader than the bandwidth of the picosecond laser (full width at half maximum, FWHM = 8 cm -1 ). Thus, to get more information on the origin of this broadening the first 600-1000 cm -1 of each spectrum was also recorded with a nanosecond dye laser (FWHM = 0.2 cm -1 ) and a comparison of both is shown in Figure SI 2. The vibronic spectra recorded with the high-resolution UV laser exhibit similar transition widths for both complexes, revealing an homogeneous broadening in both complexes.

The bandwidth for each 00 0 band is larger than the broadening due to the rotational contour at 20 K (fitted with a Gaussian function of 2 cm -1 width) as expected and observed in systems with similar rotational constants. [START_REF] Nieuwjaer | Photodissociation Spectroscopy of Cold Protonated Synephrine: Surprising Differences between IR-UV Hole-Burning and IR Photodissociation Spectroscopy of the O-H and N-H Modes[END_REF] Besides, the vibronic transitions become even broader when the first out-of-plane modes (1 and 2) are excited (See Figure SI 1 for the vibrational modes assignment). The lifetime broadening (LTB), reported in Table 3 is estimated from the width of the Gaussian function used to fit the vibronic transitions, which is at least twice larger than the expected value (2 cm -1 ). These LTBs are used to obtain an estimation of the excited state lifetimes () of each vibronic state according to the following relationship:

𝐿𝑇𝐵 (𝑐𝑚 -1 ) > (2 𝜋 𝑐 𝜏) -1 = 5.3 𝑥 10 -12 𝜏(𝑠) ( 1
)
where c is the speed of the light in vacuum.

Table 3 shows that the excited state lifetimes at the band origin is 1.2 and 1.3 ± 0.2 ps for CytNa + and CytK + , respectively and it is significantly reduced upon excitation of the 1 and 2 out-of-plane modes. It is noteworthy that no further broadening as compared to the band origin is observed following excitation of the 12 in-plane mode at about 530 cm -1 in both complexes.

The short excited state lifetimes estimated for these complexes together with the specificity on the out-of-plane modes strongly suggests that the main deactivation process is the internal conversion to the ground state and that the out-of-plane motion couples both states, as it has been already observed in other related systems. [START_REF] Broquier | Excited State Dynamics of Cold Protonated Cytosine Tautomers: Characterization of Charge Transfer, Intersystem Crossing, and Internal Conversion Processes[END_REF][START_REF] Blancafort | Singlet Excited-State Dynamics of 5-Fluorocytosine and Cytosine: An Experimental and Computational Study[END_REF][START_REF] Sobolewski | Photophysics of Malonaldehyde: An Ab Initio Study[END_REF][START_REF] Sobolewski | On the Mechanism of Rapid Non-Radiative Decay in Intramolecularly Hydrogen-Bonded π Systems[END_REF][START_REF] Zgierski | Ab Initio Study of a Biradical Radiationless Decay Channel of the Lowest Excited Electronic State of Cytosine and Its Derivatives[END_REF][START_REF] Merchán | Ultrafast Internal Conversion of Excited Cytosine via the Lowest ππ* Electronic Singlet State[END_REF] The previous UV photofragmentation spectrum of the CytAg + complex was recorded in a MS2 scheme, the CytAg + complex being issued from the photodissociation of the Cyt2Ag + complex at 273 nm. [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF] In this work, the CytAg + is directly produced in the ESI source and is thus transferred in the cold QIT where cold ion spectroscopy is performed. (Figure SI 3). Interestingly, the two spectra do not significantly differ from each other. The onset of the photofragmentation for cold CytAg + complex is found at 31665 cm -1 (3.92 eV), [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF] which is ~ 0.4 eV lower than the 00 0 bands of the first excited states of CytNa + and CytK + complexes. The adiabatic * transition of CytAg + lies in the range of 4.25-4.32 eV, i.e. in the same spectral region that the first excited * state of CytNa + and CytK + . This also suggests that the first excited states of the CytNa + and CytK + complexes studied in this work considerably differs from the first excited state of CytAg + .

A close inspection to Table 2 shows that the first excited state for the later complex is a CT (nO*) state, in which one electron from a lone pair orbital nO of the O7 atom of Cyt is promoted to the * orbital localized on the Ag + moiety. On the contrary, the first excited state of CytNa + and CytK + is a * state, consequently the electron remains on the Cyt moiety. In these latter cases, the first CT involving the transfer of the electron from Cyt to Na + / K + is the forth excited state (*) located 1.5 eV higher than the bright * state. The other CT states with nO* or nN* electronic configurations lie even higher in energy.

Also related to this fact, the other main difference between CytNa + , CytK + and CytAg + complexes is the fragmentation pattern upon UV excitation. From the BO (4.3 eV) to the shortest excitation wavelength used in this work (210 nm, 5.9 eV, spectrum not shown), CytNa + and CytK + dissociate to Cyt and Na + or K + , respectively, while the CytAg + complex fragments to the CT dissociation channel Cyt + and Ag even at low excitation energy of 3.9 eV.

The dissociation energy threshold (Eth) for the CT dissociation channel can be estimated by Equation 2:

𝐸 𝑡ℎ ≥ 𝐼𝑃 𝐶𝑦𝑡 -𝐼𝑃 𝑀 + 𝐸 𝑏 (𝑆 0 ) (2)
where IPCyt corresponds to the ionization potential of Cyt (8.73 eV), [START_REF] Lobsiger | The Adiabatic Ionization Energy and Triplet T1 Energy of Jet-Cooled Keto-Amino Cytosine[END_REF] IPM is the ionization potentials of the metal atoms and Eb(S0) stands for the ground state binding energy of the complexes. [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF][START_REF] Yang | IRMPD Action Spectroscopy of Alkali Metal Cation--Cytosine Complexes: Effects of Alkali Metal Cation Size on Gas Phase Conformation[END_REF] All values are reported in Table 4 together with the calculated value of Eth. The energy threshold Eth leading the Cyt + ionic fragment in CytAg + (4.01 eV) is predicted in the same energy range yet slightly higher than the adiabatic excitation energy of the S1 (nO*) calculated at 3.98 eV. The onset of the fragmentation spectrum of CytAg + is observed at 3.93 eV, with a long and bell-shape vibronic progression, which precludes the accurate determination of the 00 0 transition (see Fig SI4). The simulated Franck-Condon spectrum of the S1 nO* state of CytAg + is reported in Figure SI 4. Since the complex keeps the Cs planar structure in the optimized nO* excited state, only the in-plane vibrational modes in combination with even quanta of out-of-plane bending modes are active. Such symmetry restriction leads to a rather simple vibronic spectrum in the first 500 cm -1 above the band origin, at odds with the experimental spectrum. A dense manifold of close lying vibronic transition as experimentally observed can be found at higher excitation energy, from 1000-1500 cm -1 above the band origin.

As shown in

This suggests that the band origin of the nO* state might be located slightly below the energy Eth, impeding the dissociation of the complex near the band origin. Finally, the binding energy of the complex is calculated at 2.86 eV, [START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF] but as already mentioned in ref 25, the ionic Ag + fragment is barely detected even through excitation of the strong -* transition. This implies that internal conversion from both n* and * excited states to the ground state has a very low quantum yield, otherwise silver cation would have been detected as photofragment.

CONCLUSIONS

The UV photofragmentation spectra of cold CytNa + and CytK + complexes were recorded and compared to the one of CytAg + . Both the spectroscopy and the photofragmentation channels differ for the alkali complexes, the only fragmentation channel being the alkali cation Na + /K + without involvement of charge transfer from the cytosine to the metal cation. The first excited state for these alkali complexes is a * state. Ground and excited state optimizations at the SCS-CC2 level of theory were performed. The calculations show that in the first excited state of both complexes, the alkali cation lies out-of-plane of the cytosine which has the NH2 group slightly twisted. Both the simulated Franck-Condon spectra and the adiabatic transition energies to the first excited state (ππ*) are in good agreement with the experimental values. Unlike CytAg + , the energy of the CT states involving the transfer of an electron from the Cyt moiety to M + for both CytK + and CytNa + complexes were not experimentally observed, putting a lower limit of 5.9 eV for the first CT state. Therefore, unlike what happens with Ag + , the interaction of Cyt with these alkali metal cations (Na + and K + ) does not lead to the Cyt radical cation following photoexcitation at low energy UV photons. It is thus suggested that the alkali cations do not induce any photo damage process in DNA.

AUTHOR INFORMATION

Corresponding Author

Figure 1 .

 1 Figure 1. UV photodissociation spectra of CytNa + (top) and CytK + (bottom) recorded with a mid-resolution (8 cm -1 ) ps OPO laser.

Figure 2 .

 2 Figure 2. S1 optimized structures and molecular orbitals involved in excited states of CytNa + , CytK + and CytAg + .

Figure 3 :

 3 Figure 3: Comparison of the experimental and simulated vibronic spectra of (a) CytNa + and (b) CytK + .

Table 1 :

 1 interatomic distance (Å) and dihedral angle (deg) of the optimized structures of Cyt-M + (M: Na, K, Ag) in the ground and excited electronic states.

		Na + …Cyt	K + …Cyt		Ag + …Cyt
		S0 (Cs)	*	S0 (Cs)	*	S0 (Cs)	n* (Cs)	*
	N3…M	2.466	2.351	2.874	2.738	2.287	2.259	2.195
	O7…M	2.234	2.374	2.558	2.74	2.394	2.170	2.514
	O7C2N3M	0	-4	0	-7.4	0	0	1
	H1N8C4N3	0	36	0	41	0	0	18
	H2N8C4N3	0	15	0	15	0	0	12

Table 2 .

 2 Vertical (Ev) and adiabatic (Ead) transition energies for the most relevant electronic excited states with the corresponding oscillator strengths (Osc. Str.) for CytNa+, CytK+ and CytAg+ complexes calculated at the SCS-CC2/Def2-SVPD level of theory. The experimental values (bold) are in parenthesis.

	Complex	State	Ev	Ead	Osc. Str.
		S1 (*)	4.95	4.31	0.0940
				(4.34)
		S4 (*)	6.45	-	0.0025
	CytNa +
		S11 (nO*)	7.36	-	0.0529
		S12 (nN*)	7.81	-	0.1296
		S1 (*)	4.93	4.25	0.0859
				(4.30)
		S4 (*)	6.46	-	0.0019
	CytK +
		S11 (nN*)	7.28	-	0.0578
		S12 (nO*)	7.70	-	0.0784
		S1 (nO*)	4.15	3.98	0.0077
				(3.93)
		S2 (nN*)	4.84	-	0.0079
	CytAg +
		S3 (*)	4.89	4.39	0.0909
				(4.32)
		S7 (*)	5.56	-	3.7 10 -5

Ead are corrected by the zero point energy difference (ZPE) between the two states. Ev and Ead are given in eV.

Table 3 :

 3 Lifetime broadening (LTB in cm -1 ) of different transition of the Cyt-Na + and Cyt-K + complexes and minimum excited state lifetimes (minin ps) for each transition.

		Cyt-Na +			Cyt-K + 
	mode	LBT (cm -1 )	min (ps)	mode	LTB (cm -1 )	min (ps)
	0 0 0	4.5 ± 0.25	1.2	0 0 0	4 ± 0.25	1.3
	1 (49 cm -1 )	11.9 ± 1	0.45	1 (39 cm -1 )	6.1 ± 0.25	0.8
	2 (122 cm -1 )	6.8 ± 0.25	0.8	2 (85 cm -1 )	5.7 ± 0.25	0.8
	 2	6.7 ± 0.25	0.8	 2	9 ± 0.5	0.6
	12 (532 cm -1 )	4.9 ± 0.25	1.1	12 (528 cm -1 )	4.1 ± 0.25	1.3
	1 + 12	6.5 ± 2	0.8	1 + 12	6.5 ± 0.25	0.8

Table 4 ,

 4 Eth for CytNa + and CytK + are approximately 2 eV larger than the corresponding value for CytAg + as a consequence of the lower IP of Na and K as compared to the IP of Ag. Then, the CT state is pushed up in the former complexes above the * state, to energies higher than the excitation energy region explored in this work. Therefore, not only the first excited state of CytNa + and CytK + are not the same than in CytAg + , but also the excitation of the complexes in the 4.3 -5.8 eV range is below the dissociation threshold for leading to Cyt + and M.[START_REF] Taccone | Communication: UV Photoionization of Cytosine Catalyzed by Ag +[END_REF]

Table 4 .

 4 Energy threshold for the CT fragmentation channel (Eth) for the CytM + (M = Ag, Na and K) complexes, calculated according to Eq. 2. The ionization potential of the M atoms (IPM) and ground state binding energy Eb(S0) of the complexes are also shown.

	Complex	IPM (eV)	Eb(S0) (eV)	Eth (eV)
	CytAg +	7.58 a	2.86 b	4.01
	CytNa +	5.14 a	2.23 c	5.82
	CytK +	4.34 a	1.67 c	6.07

a Ref.49 b Ref.25 c Ref.32

*E-mail: gpino@fcq.unc.edu.ar; Tel: +54-351-5353866 ext. 53529 *E-mail: gilles.gregoire@u-psud.fr ; Tel: +33 169153103 ACKNOWLEDGMENTS This work has been conducted within the International Associated Laboratory LEMIR (CNRS/CONICET) and was supported by CONICET, FONCyT, SeCyT-UNC and the ANR Research Grant (ANR2010BLANC040501-ESPEM). GAP thanks the Labex PALM (ANR-10-LABX-0039-PALM) for the invited Professor grant in 2019. We also acknowledge the use of the computing facilities Méso-LUM of the LUMAT federation (LUMAT FR 2764) and MAGI of University Paris 13.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.