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An ab Initio Calculation of the Valence Excitation Spectrum of H 2
O···Cl
2 : Comparison to
Condensed Phase Spectra
Ricardo Franklin-Mergarejo
Instituto Superior de Tecnologı´as y Ciencias Aplicadas, AVe. SalVador Allende y Luaces, Quinta de los
Molinos, Plaza, Habana 10600, Aptdo. Postal 6163, Ciudad Habana, Cuba, UniVersite´ de Toulouse, UPS,
Laboratoire Collisions Agre´gats Re´actiVite´, IRSAMC, F-31062 Toulouse, France, and CNRS, UMR 5589,
F-31062 Toulouse, France
Jesus Rubayo-Soneira
Instituto Superior de Tecnologı´as y Ciencias Aplicadas, AVe. SalVador Allende y Luaces, Quinta de los
Molinos, Plaza, Habana 10600, Aptdo. Postal 6163, Ciudad Habana, Cuba
Nadine Halberstadt*
UniVersite´ de Toulouse, UPS, Laboratoire Collisions Agre´gats Re´actiVite´, IRSAMC, F-31062 Toulouse, France,
and CNRS, UMR 5589, F-31062 Toulouse, France
Tahra Ayed
Centro de InVestigaciones Quı´micas, UAEM, CuernaVaca, Mor. 62210, Me´xico
Margarita I. Bernal Uruchurtu
Centro de InVestigaciones Quı´micas, UAEM, CuernaVaca, Mor. 62210, Me´xico
Ramo´n Herna´ndez-Lamoneda
Centro de InVestigaciones Quı´micas, UAEM, CuernaVaca, Mor. 62210, Me´xico
Kenneth C. Janda
Department of Chemistry, UniVersity of California, IrVine, IrVine, California 92697-2025 ReceiVed: February 14, 2009; ReVised Manuscript ReceiVed: April 8, 2009 Valence electronic excitation spectra are calculated for the H 2
O···Cl
2 dimer using state-of-the art ab initio
potentials for both the ground and the valence excited states, a basis set calculation of the ground state nuclear
wave funtion, and a wave packet analysis to simulate the dynamics on the excited state surface. The peak of
the H 2
O···Cl
2 dimer spectrum is blue-shifted by 1250 cm -1 from that of the free Cl 2 molecule. This is less
than the value previously estimated from vertical excitation energies but still significantly more than the blue
shift in aqueous solution and clathrate-hydrate solid. Seventy percent of the blue shift is attributed to ground
state stabilization, the rest to excited state repulsion. Spin-orbit effects are found to be small for this dimer.
Homogeneous broadening is found to be slightly smaller for the dimer than for the free Cl 2 . The reflection
principle and spectrator model approximations were tested and found to be quite satisfactory. This is promising
for an eventual simulation of the condensed phase spectra.
I. Introduction
The spectra of halogen molecules have long been known to be very sensitive to the local environment. 1,2
For instance, in
aqueous solution, the valence excitation spectrum of Cl 2 is shifted 550 cm -1 to the blue from the gas phase spectrum. 3 For Br 2 and I 2 the shifts are even more dramatic, 1750 and
2820 cm
-1 , respectively. 4,5
Although these spectral shifts have
received considerable attention, no satisfactory explanation hasbeen found. Part of the reason for this difficulty is that nearest
neighbor and bulk dielectric effects are probably both important and vary in importance depending on which halogen is being studied. 6,7 Recently, the sensitivity of the spectrum to the local environ- ment was studied for halogen in clathrate hydrate gas-solid solutions. Clathrate hydrates consist of a solid lattice in which the water molecules form different sized cages. For instance, a
28 water molecule cage that has 12 pentagonal faces and 4
hexagonal faces with an oxygen atom at each vertex and a hydrogen atom along each edge is referred to as a 5 12 6 4 clathrate hydrate cage. The spectrum of Cl 2 in a 24 water molecule 5 12 6 2 cage is unshifted from that in the gas phase. The spectrum of Part of the ÒRobert Benny Gerber FestschriftÓ. * Corresponding author, Nadine.Halberstadt@irsamc.ups-tlse.fr. Permanent address: Unite" de Recherche de Chimie The"orique et Re"activite", Institut Pre"paratoire aux Etudes dÕInge"nieur dÕEl Manar, Campus universitaire B.P.244, El Manar II, 2092 Tunis, Tunisia.
J. Phys. Chem. A2009,113,7563-75697563
10.1021/jp901488x CCC: $40.75?2009 American Chemical SocietyPublished on Web 05/06/2009
Br 2 in the same cages is shifted by 880 cm -1 , only half of the shift in aqueous solution. In the larger, 28 water molecule 5 12 6 4 cage, the shift of the Br 2 spectrum is even smaller, 360 cm -1
The shift of the I
2 spectrum in the 28 water molecule cage is
1440 cm
-1 , about half of the shift between the gas phase and aqueous solution. The large difference between the spectra of the halogens in aqueous solution and in the hydrate clathrates, as well as the very different shifts for the three halogens in each environment, is an interesting problem worthy of detailed investigation. We have started a program of study in which the spectra in dimers, clusters, and eventually aqueous solution will be investigated.
A recent paper
8 reported a study of the two-dimensional potential energy surfaces for the ground states and singlet and triplet valence excited states of H 2
O···Cl
2 and H 2
O···Br
2 . The details of the dimer potentials were found to be quite sensitive to the basis set and degree of electron correlation. Another interesting result of this study is that the calculated vertical valence excitation energies for the two dimers are even larger than those observed in aqueous solution. These results have convinced us to investigate both the effects of spin-orbit coupling and coupling between the halogen stretch and the intermolecular stretch on the spectra. The results of this study for H 2
O···Cl
2 are reported in this paper.
II. Method
Given that Cl
2 is the chromophore, and that photodissociation leads to a repulsive H 2
O···Cl
2 interaction, a 2-D model is the minimum required for a meaningful calculation of the valence excitation spectrum. In addition, a previous study 8 showed that the Cl-Cl and O-Cl coordinates are strongly coupled in both the ground and valence excited states. Here we explore the effects of this coupling on the dimer spectrum within the 2-D model using the wave packet dynamical method and testing the reflection principle and spectator model approximations. A. Spin-Orbit Addition to PES.A detailed study of the spectroscopic properties of the chlorine molecule must include spin-orbit effects. Among other things the proper description of the dissociation limits for the relevant spectroscopic states (A, B, C) depends crucially on their inclusion. The methodology we have followed has been described in detail in a related study of the Ne···Cl 2 system 9 where the spin-orbit effects play a significant role. Here we summarize the main ingredients. We use the relativistic effective core potential (RECP) of chlorine developed by the Stuttgart group 10,11 which provides an efficient way for including spin-orbit effects. The original valence basis set has been extended with polarization and diffuse functions to yield the final set 3s3p3d2f1g. For the water molecule we use the AVTZ (augmented correlation consistent triple-zeta) basis set. The relevant spin-orbit states are obtained by diagonalizing the total Hamiltonian which consists of the usual electronic term plus the spin-orbit interaction term. The basis set for diagonalization is obtained by first optimizing the orbitals in a complete active space (CAS) defined by the valence electrons and orbitals of chlorine, together with a state-averaging of nine electronic states close in energy to the states involved in the spectroscopy. We then perform multireference configu- ration interaction (MRCI) calculations to include dynamic electron correlation including the valence electrons of the water molecule. The total number of spin-orbit states obtained is 36. All calculations were performed with the MOLPRO2006.1 package. 12 B. Principle of the Absorption Spectrum Calculation.In this work we determine the H 2
O···Cl
2 absorption spectrumusing a two-dimension model. The coordinates, as described in our previous publication, 8 are the intramolecular Cl-Cl coor- dinaterand the intermolecular coordinateR(from the center of mass of the water molecule to the center of mass of Cl 2 The other geometrical parameters are fixed at their equilibrium values, with O-Cl-Cl collinear and the hydrogen atoms symmetrically bent off the O-Cl-Cl axis. AtT)0 K the
Hamiltonian is then
H )-p 2
2μ∂
2 ∂r 2 -p 2
2m∂
2 ∂R 2 +V (r,R)(1) whereμ)m Cl /2 andm)m Cl m H 2 O /(m Cl +m H 2 O ) are the reduced masses associated withrandR, respectively, and V (r,R) is the two-dimensional potential energy surface in state ?with?denoting the X, B, or C electronic state.V (r,R)is obtained by two-dimension interpolation 13 of the ab initio points of ref 8.
The bound statesΦ
xn (r,R) in the X electronic surface are determined by diagonalizing the Hamiltonian matrix in a direct product DVR (discrete variable representation 14-16 ) basis set. Each DVR basis set was obtained by diagonalizing the corre- sponding position operator in an adapted harmonic oscillator basis set (corresponding to the harmonic approximation of the potential minimum). For the sake of comparison with experi- ment, the vibrationally averaged values of the Cl-Cl distance r 0 and H 2 O-Cl 2 center of mass distanceR 0 are deduced from the average values of 1/r 2 and 1/R 2 over the ground level wave function, respectively. The vibrational frequencies and anhar- monicities are obtained from solving the following equation E V r ,V R )-D e +pω r (V r +1/2)+pω R (V R +1/2)- pω r r (V r +1/2) 2 -pω R R (V R +1/2) 2 p(ω?) rR (V r +1/2)(V R +1/2)(2) for the five energy levels E 00 (≡E 0 ), E 10 ,E 01 ,E 11 ,E 02 , adding the minimum energy value of the interpolated surfaceD e -920.64398 cm -1 (r e )2.0266 Å,R e )3.9018 Å) since no V r )2 level was found. Since both coordinates are dissociative in the excited state and dissociation is fast, we chose the time-dependent formulation to obtain the absorption spectrum. In this formulation, the absorption spectrum is given by the Fourier transform of the autocorrelation function of a wave packet propagating on the excited state surface. This wave packet is initially determined as the bound state wave function (determined in the previous step) multiplied by the transition dipole moment (r,R,t)0))μ ?X (r,R)Φ X 0 (r,R)(3) We used the split-operator technique with a time step of 1.0 au (2.4×10 -2 fs) and propagation times of 16000 au (384 fs). Thergrid consisted in 256 points from 1.8 to 2.6 Å, the one in
Rhad 256 points running from 3.6 to 16 Å.
One-dimensional absorption spectra were also determined for comparison with gas phase results or for analysis. These were determined as follows. The one-dimensional Hamiltonian reduces to h )-p 2
2μ∂
2 ∂r 2 +V (r)(4) with7564J. Phys. Chem. A, Vol. 113, No. 26, 2009Franklin-Mergarejo et al. V (r))V (r,R 0 whereR 0 is a fixed value of the intermolecular coordinate. The
X-state bound wave functions?
V (r) were obtained by finite difference 17 followed by Numerov-Cooley 18 integration. The absorption spectra were determined using the time-dependent formulation as described above, or the energy-resolved formula- tion (coupled channel integration using the De Vogelaere's algorithm 19,20 ) for a check. Cl 2 gas phase absorption spectra were obtained forR 0
16 Å, the largest intermolecular distance for which potential
energy surfaces were determined. They were compared to spectra obtained from empirical curves fitted to the experimental spectra as a test of the ab initio surfaces. C. The Spectator Model.The basic assumption of this model is that the water molecule does not have time to move much during the Cl-Cl dissociation. In this case, the sole effect of dimer formation is to modify the potential energy curves of Cl 2 . Hence the spectrum can be calculated in one dimension, with the intermolecular distanceRfixed atR 0 )3.92 Å (the maximum of the 2-D H 2
O···Cl
2 wave function) in eq 4. If the predictions of this model are in good agreement with the accurate two-dimension wave packet result, it will prove extremely useful to predict the spectra of Cl 2 in different water environments (clusters, clathrate cages, ice, aqueous solution): the calculation will then reduce to the isolated molecule spectrum but with potential energy curves modified by the environment. D. The Reflection Principle Method.In analyzing the resulting spectra, we will make reference to the reflection principle. This is an approximation to the absorption cross section that gives very useful physical insight in the case of a dissociative excited state potential. In one dimension the continuum wave function of the excited state?at energyEis simply replaced by a delta function at the classical turning point E,r 0 (r)=δ(r-r 0 |(∂V /∂r)(r 0 1/2 (5) with E)V (r 0 The usual reflection principle formulation for the absorption spectrum is the following ?rX (E ph E,r 0 ?X x0 2 (6) whereE ph )E-E 0 is the photon energy, equal to the energy of the continuum wave functionEminus the X bound state energyE 0quotesdbs_dbs5.pdfusesText_10
An ab Initio Calculation of the Valence Excitation Spectrum