RAIR spectra of CO 2 /H 2 O ices: theoretical prediction and experimental results R. Escribano, V.J. Herrero, B. Maté, O. Gálvez and B. Martín-Llorente R. Escribano, V.J. Herrero, B. Maté, O. Gálvez and B. Martín-Llorente Instituto de Estructura de la Materia, CSIC, Madrid Emilio Artacho, Emilio Artacho, Department of Earth Sciences, University of Cambridge, UK

Outline: Continuation of previous talk Continuation of previous talk Ices of H 2 O/CO 2 : Ices of H 2 O/CO 2 : Experimental method: RAIR measurementsExperimental method: RAIR measurements Theoretical (solid state) calculations for pure CO 2 crystalsTheoretical (solid state) calculations for pure CO 2 crystals Summary of results Summary of results

Ices studied  H 2 O/CO 2 Composition of the mixtures  H 2 O/CO 2 : ~ 15:1 Preparation of the samples  Sequential deposition (first H 2 O, then CO 2 )  Co-deposition  Inverse sequential deposition (first CO 2, then H 2 O)  Sequential deposition over crystalline structures (first amorphous H 2 O, then annealed, then cooled to 80 K, then CO 2 )

Experimental setup RAIRS

RAIRS : reflexion-absorption infrared spectroscopy Polarization sPolarization pNon polarized

Transmission vs Reflection-Absorption Sequential deposition (H 2 O, CO 2 ) reflection-absorption 3 transmission S-polarization P-polarization

A little bit of LO/TO… Molecular vibrations of a single crystal of arbitrary shape: H = H(0) + H’ H(0) : molecular vibrations of uncoupled molecules H’ : long-range dipole-dipole interactions, H ij  e.g.: mol. 2 vibrating in mode  interacting with mol. 3 of all other cells vibrating in mode 

Use of D tensor: Use of D tensor: D depends only on the structure of the lattice and shape of the sample, but not on internal molecular properties or molecular orientation; when the shape is of ellipsoid of revolution, D can be calculated numerically H’ = Solving the equation of motion: Solving the equation of motion: H = H(0) + H’ H(0) : uncoupled molecules → ω 0 H’ : dipole-dipole interactions → ω n If dimensions of crystal (typically ~ nm) are much smaller than wavelength of incident radiation (1000 cm -1 <> 10 4 nm), then only factor that influences Ω α is shape of the crystal.

Usual experimental conditions: In most IR transmission measurements, incident radiation field lies in plane of substrate; if sample is thin film, then only TO vibrations can be seen (molecular vibrations in the plane of the film), never LO (perpendicular to that plane). Similarly, in RAIR experiments on thin films, only TO vibrations are seen in S polarization (no LO-TO splitting). In this case, the metal surface selection rule (MSSR) also applies. μ’→ω TO μ’→ω LO absorption at ω TO only for normal incidence transmission

absorption at ω TO and ω LO and many frequencies in between Polycrystalline sample with many crysytallite shapes If direction of propagation of incident radiation is not normal but tilted then LO and TO can be seen both in transmission and in P polarization RAIR spectra absorption at ω TO and ω LO Other experimental conditions:

Co-deposition (H 2 O+CO 2 ) Sequential crystalline S-polarization P-polarization

Summary of experimental results   RAIR spectra provide information on physical characteristics of sample   On all depositions (80K), CO 2 tends to form slabs, with two peaks on P-polarization spectra: ~2343 cm -1 (TO), 2380 cm -1 (LO), and only one on S-polarization spectra: ~2340 cm -1 for 3 band   After warming (105K), the CO 2 in slabs is fully desorbed, but a fraction remains with no crystalline structure: one peak at ~2340 cm -1 for both polarizations   This fraction is located inside the water ice and remains until heating up to the water phase change temperature (~165K), except for sequential crystalline deposition, for which all CO 2 is desorbed at 105K

Theoretical calculations of pure CO 2 crystals: SIESTA program “Spanish Initiative for Electronic Simulations of Thousands of Atoms” Brief description: Optimization of geometrical structures of periodic systems Calculation of force constants in the harmonic potential approximation Calculation of vibrational modes of the crystal Prediction of “stick” spectrum (frequency and intensity of each normal mode) Description of normal modes in terms of atomic Cartesian displacements Prediction of LO/TO splitting

CO 2 crystal Cubic, face centered, a=5.624Å Crystal with weak van der Waals forces among molecules Vibrational modes /cm -1 : Exp. Description 73,90,130 librational 655,660 2 bending sym stretch asym stretch

Calculated frequencies (LO/TO splittings in bracketts) 12 CO 2 (LO/TO)Int (0.4) < < (16.0) (29.4)1.04

Summary of theoretical results  Theoretical DFT calculations on pure CO 2 ice reproduce observed crystal symmetry and structure and predict vibrational frequencies with ~6% red-shift in worst case  LO-TO splitting is also predicted slightly smaller than observed

Future plans  Studies of other binary mixtures: H 2 O/CH 3 OH, H 2 O/NH 3, H 2 O/N 2 O,…  Studies of ternary systems: H 2 O/CH 3 OH/CO 2  Ab initio or DFT calculation of amorphous solids

Funding agencies: CAM, FSE for studentship CAM, FSE for studentship CSIC: studentship for UA with University of Jaén, Juan de la Cierva Program, PIF F0051 “Hielocris” CSIC: studentship for UA with University of Jaén, Juan de la Cierva Program, PIF F0051 “Hielocris” Spanish Ministry of Education, Project FIS , Sabbatical grant Spanish Ministry of Education, Project FIS , Sabbatical grant

The Madrid group Molecular Physics of Atmospheres and Plasmas Miguel Angel Moreno Belén Maté Kenty Ortega Oscar Galvez Verónica Verdejo Isabel Tanarro Beatriz Martín Isabel Méndez Víctor Herrero

Parameter Ω α assuming normalized n α (r 1 ) functions such as:

CO 2 spectra Cube (8x8x8) Needle (32x4x4) Slab (16x16x2) Calculated spectra Signorell, JCP 2003

Transmission vs Reflection-Absorption Sequential deposition (H 2 O, CO 2 ) (1) transmission 3

S-polarizationP-polarization (2) Reflection-absorption 3 3 Sequential deposition (H 2 O, CO 2 )

Solving the equation of motion ω n also called ω LO, ω 0 = ω TO Ω α (varies between 0 and 1) ω LO ≥ ω TO (almost) always H = H(0) + H’ H(0) : uncoupled molecules → ω 0 H’ : dipole-dipole interactions → ω n If dimensions of crystal (typically ~ nm) are much smaller than wavelength of incident radiation (1000 cm -1 <> 10 4 nm), then only factor that influences Ω α is shape of the crystal: Spherical crystals: Ω x = Ω y = Ω z = 1/3 and all vibrations ω n = 1/3 (ω LO +2 ω TO ) Thin films: Ω x = Ω y = 0 (for polarization parallel to surface of film), Ω z = 1 (for polarization perpendicular to surface of film); and then two absorptions are seen at exactly ω TO and ω LO.

Tensors R and S: For spectroscopic activity, k~0 and summation for D becomes: For spectroscopic activity, k~0 and summation for D becomes: where R depends on crystal structure (cubic, orthorrombic, …) but not on wavevector k, and S conveys the contribution from the sample surface polarization charge, and depends on the shape (slab, needle,…) of the sample but not on the structure of the crystal. For ellipsoids of revolution: with g=0 for sphere, -8π/3 for slab, 4π/3 for long needle

Oblate or prolate crystals: μ’→ω TO μ’→ω LO absorption at ω TO only for normal incidence transmission absorption at ω TO and (ω LO + ω TO )/2

SIESTA (cont’d.) Technical details of the method: Energy optimization algorithm: conjugate gradient DFT: Perdew-Burke-Ernzenhof generalized gradient Pseudopotentials: Troullier-Martins with partial core Basis Set: variationally optimized (MV Fernández-Serra) double-zeta with polarization Grid mesh cutoff: 300 Ry fineness K-sampling: 6 Å Force constants calculated numerically, 0.01 Å step Born charges: 5 x 2 x 2 sampling in reciprocal space … fairly strict relaxation parameters required to achieve high symmetry of the crystal

CO 2 crystal Cubic, face centered, a=5.624Å Crystal with weak van der Waals forces among molecules Vibrational modes /cm -1 : Exp. Calc. Description 52-90(9) translational 73,90, (8) librational 655, ,608(8) 2 bending (4) 1 sym stretch (1) 3 asym stretch 2306(3)

Dispersion curves Dispersion curves 3

Results

Summary  RAIR spectra provide information on physical characteristics of sample  On all depositions (80K), CO 2 tends to form slabs, with two peaks on P-polarization spectra: ~2343 cm -1 (TO), 2380 cm -1 (LO), and only one on S-polarization spectra: ~2340 cm -1 for 3 band  After warming (105K), the CO 2 in slabs is fully desorbed, but a fraction remains with no crystalline structure: one peak at ~2340 cm -1 for both polarizations  This fraction is located inside the water ice and remains until heating up to the water phase change temperature (~165K), except for sequential crystalline deposition, for which all CO 2 is desorbed at 105K  Theoretical DFT calculations on pure CO 2 ice reproduce observed crystal symmetry and structure and predict vibrational frequencies with ~6% red-shift  LO-TO splitting is also predicted slightly smaller than observed