Molecular photodissociation
vvan Dishoeck & Visser: Molecular Photodissociation published as a chapter in Laboratory Astrochemistry
From Molecules through Nanoparticles to Grains eds. S. Schlemmer, T. Giesen, H. Mutschke, and C. Jäger2015, Weinheim: Wiley-VCH
Ewine F. van Dishoeck , & Ruud Visser , Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, theNetherlands Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse 1, 85748Garching, Germany Department of Astronomy, University of Michigan, 1085 S. University Ave, AnnArbor, MI 48109-1107, USA European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748, Garching,Germany
Photodissociation is the dominant process by which molecules are removed in anyregion exposed to intense ultraviolet (UV) radiation. Such clouds of gas and dust areindicated by astronomers with the generic title ‘photon-dominated region’, or PDR.Originally, the term PDR referred mostly to dense molecular clouds close to brightyoung stars such as found in the Orion nebula. There are many other regions inspace, however, in which photodissociation plays a crucial role in the chemistry: this includes diffuse and translucent interstellar clouds, high velocity shocks, the surfacelayers of protoplanetary disks, and cometary and exoplanetary atmospheres.In the simplest case, a molecule ABC absorbs a UV photon, which promotes it in-to an excited electronic state, and subsequently dissociates to AB + C. In reality, thesituation is much more complex because there are many electronic states that can beexcited, with only a fraction of the absorptions leading to dissociation. Also, thereare many possible photodissociation products, each of which can be produced in dif-ferent electronic, vibrational and rotational states depending on the wavelength of theincident photons. The rate of photodissociation depends not only on the cross sec-tions for all of these processes but also on the intensity and shape of the radiation fieldat each position in the cloud. Thus, an acccurate determination of the photodissocia- tion rate of even a simple molecule like water involves many detailed considerations, ranging from its electronic structure to its dissociation dynamics and to the specificsof the radiation field to which the molecule is exposed.In this chapter, each of these steps in determining photodissociation rates is system- a r X i v : . [ a s t r o - ph . I M ] F e b an Dishoeck & Visser: Molecular Photodissociation atically discussed. Section 4.2 reviews the basic processes through which small andlarge molecules can dissociate following UV absorption. Techniques for determiningabsorption and photodissociation cross sections through theoretical calculations andlaboratory experiments are summarized in Sec. 4.3. This section also mentions newexperimental developments that determine branching ratios of the different products.Various interstellar and circumstellar radiation fields are summarized in Sec. 4.4, in-cluding their attenuation due to dust and self-shielding deeper inside the cloud. Theformulas for computing photodissociation rates are contained in Sec. 4.5, togetherwith references to recent compilations of cross sections and rates. As a detailed ex- ample, recent developments in our understanding of the photodissociation of CO andits isotopologs are presented in Sec. 4.6. The chapter ends with a brief review ofthe photostability of polycyclic aromatic hydrocarbons (PAHs). Much of this chapterfollows earlier reviews by [1] and [2]. Small molecules
The processes by which photodissociation of simple molecules can occur have beenoutlined by [3] and [4]. A summary is presented in Fig. 4.1 for the case of diatomicmolecules. Similar processes can occur for small polyatomic molecules, especially ifthe potential surface is dissociative along one of the coordinates in the multidimen-sional space.The simplest process is direct photodissociation , in which a molecule absorbs aphoton into an excited electronic state that is repulsive with respect to the nuclearcoordinate. Since spontaneous emission back to the ground state is comparativelyslow (typical Einstein-A coefficients of s − compared with dissociation times of s − ), virtually all of the absorptions lead to dissociation of the molecule. Theresulting photodissociation cross section is continuous as a function of photon ener-gy, and peaks close to the vertical excitation energy according to the Franck-Condonprinciple. The width is determined by the steepness of the repulsive potential: thesteeper the curve, the broader the cross section. Its shape reflects that of the vibra-tional wavefunction of the ground state out of which the absorption occurs. Note thatthe cross section is usually very small at the threshold energy corresponding to thedissociation energy D e of the molecule; thus, taking D e as a proxy for the wavelengthrange at which dissociation occurs gives incorrect results.In the process of predissociation , the initial absorption occurs into a bound excitedelectronic state, which subsequently interacts non-radiatively with a nearby repul-sive electronic state. An example of such a type of interaction is spin-orbit couplingbetween states of different spin multiplicity. Another example is the non-adiabaticcoupling between two states of the same symmetry. The strength of the interactiondepends sensitively on the type of coupling and on the energy levels involved, butan Dishoeck & Visser: Molecular Photodissociation Figure 4.1
Photodissociation processes of diatomic molecules and corresponding crosssections. From top to bottom: direct photodissociation, predissociation and spontaneousradiative dissociation (based on [1]). predissociation rates are typically comparable to or larger than the rates for sponta- neous emission. The effective photodissociation cross section consists in this case ofa series of discrete peaks, which reflect the product of the oscillator strength of theinitial absorption and the dissociation efficiency of the level involved. The width iscontrolled by the sum of the radiative and predissociation rates and is generally large( s − , corresponding to 15 km s − or more in velocity units).If the excited bound states are not predissociated, spontaneous radiative dissocia-tion can still be effective through emission of photons into the continuum of a lower-lying repulsive state or the vibrational continuum of the ground electronic state. Theefficiency of this process is determined by the competition with spontaneous emissioninto lower-lying bound states. The photodissociation cross section again consists of aseries of discrete peaks, but the peaks are not broadened and have widths determinedby the total radiative lifetime (typically < − ).Because a molecule has many excited electronic states that can be populated by theambient radiation field, in general all of these processes will occur. As an example,Fig. 4.2 shows the potential energy curves of the lowest 16 electronic states of the OHan Dishoeck & Visser: Molecular Photodissociation Figure 4.2
Potential energy curves of the OH molecule (reproduced from [5]). radical: predissociation occurs through the lowest excited A Σ + electronic state,whereas direction dissociation can take place through the 1 Σ − , 1 ∆ and coupled Π electronic states. However, usually only one or two of these processesdominate the photodissociation of a molecule in interstellar clouds. In the case ofOH, these are the direct 1 Σ − and 1 ∆ channels. However, predissociation throughthe lower-lying A state is important in cometary atmospheres and disks around coolstars, where the radiation field lacks high-energy photons.The photodissociation of many simple hydrides like H +2 , OH, H O, CH, CH + , andNH proceeds mostly through the direct process. On the other hand, the photodisso-ciation of CO is controlled by predissociation processes, whereas that of H occursexclusively by spontaneous radiative dissociation for photon energies below 13.6 eV.Whether the photodissociation is dominated by continuous or line processes has im-portant consequences for the radiative transfer through the cloud (see Sec. 4.4.6).an Dishoeck & Visser: Molecular Photodissociation D Q0 11DIC IC ISC phosphorescenceabsorptionfluorescence
IR emission D2 Figure 4.3
Radiative and radiationless decay of large molecules, illustrating the processesof internal conversion (IC), intersystem crossing (ISC), fluorescence, phosphorescenceand infrared emission. This example is for a large ion such as PAH + with a ground statewith one unpaired electron (doublet spin symmetry) denoted as D , and doublet andquartet excited electronic states. Various vibrational levels within the electronic states areindicated. Large molecules
For large molecules, the same processes as illustrated in Fig. 4.1 can occur, but theybecome less and less likely as the size of the molecule increases. This is because thenumber of vibrational degrees of freedom of a non-linear molecule, N − , increas-es rapidly with the number of atoms N . Each of these modes has many associatedvibrational levels, with quantum numbers v increasing up to the dissociation energyof the potential. For sufficiently large N , the density of vibrational levels becomesso large that they form a quasi-continuum with which the excited states can couple non-radiatively (Fig. 4.3). Through this so-called process of internal conversion ,the molecule ends up in a highly excited vibrational level of a lower-lying electronicstate. The probability is small that the molecule will find its way across the multi-dimensional surface to a specific dissociative mode, so the most likely outcome is thatthe molecule ends up in an excited bound level and subsequently relaxes by emissionof infrared photons. Alternatively, the excited molecule can fluoresce down to theground state in a dipole-allowed electronic transition, or it can undergo so-called in-tersystem crossing to an electronic state with a different spin multiplicity from whichit can phosphoresce down in a spin-forbidden transition.Statistical arguments using (modified) Rice-Ramsperger-Kassel-Marcus (RRKM)theory suggest that N -atom molecules with N > ∼
25 are stable with respect to pho-todissociation, although this number depends on the structure and types of modesof the molecule involved [6]. Thus, long carbon chains may have a different pho-tostability than ring molecules. PAHs are a specific class of large molecules highlyrelevant for astrochemistry, and are discussed further in Sec. 4.7. Very few gas-phasean Dishoeck & Visser: Molecular Photodissociation experiments exist on such large molecules to test these theories.Ashfold et a. [7] have recently pointed out that many intermediate-sized moleculeswith N ≈ , including complex organic molecules such as alcohols, ethers, phenols,amines and N-containing heterocycles, have dissociative excited states that greatlyresemble those found in smaller molecules like H O and NH . Experiments showthat H-loss definitely occurs in these larger systems.The ionization potentials of large molecules lie typically around 7–8 eV. Most of theabsorptions of UV photons with larger energies are expected to lead to ionization buta small fraction can also result in dissociation through highly excited neutral states lying above the ionization threshold or through low-lying dissociative states of theion itself. These branching ratios are not well determined experimentally. Quantitative information on photodissociation cross sections comes from theory andexperiments. Theory is well suited for small molecules, in particular radicals andions that are not readily produced in the gas phase. Laboratory measurements ofabsorption spectra over a wide photon range exist primarily for chemically stablemolecules, both small and large. In the following, we first review the theoreticalmethods of computing potential energy surfaces and cross sections, and then discussthe experimental data.
Theory
All information about a molecule can be contained in a wave function Ψ , which isthe solution of the time-independent Schrödinger equation H Ψ( x, R ) = E Ψ( x, R ) (1) Here x stands for the spatial and spin coordinates of the n electrons in the moleculeand R denotes the positions of all N nuclei in the molecule. The total Hamiltonian H consists of the sum of the kinetic energy operators of the nuclei α and the electronsand of their potential energies due to mutual interactions. Equation (1) is a (3 n +3 N ) -dimensional second order partial differential equation that cannot be readily solved,even for small molecules. Born-Oppenheimer approximation
Because the mass of the nuclei is much larger than that of the electrons, the nuclei move slowly compared with the electrons. Most molecular dynamics studies therefore invoke the Born-Oppenheimer approximation for separating the nuclear and electron-ic coordinates: Ψ( x, R ) = Ψ el ( x ; R )Ψ nuc ( x, R ) (2) an Dishoeck & Visser: Molecular Photodissociation where the electronic energies E el ( R ) (also called the potential energy curves or sur-faces) are determined by solving the electronic eigenvalue equation with the nucleiheld fixed: H el Ψ el ( x ; R ) = E el ( R )Ψ el ( x ; R ) (3) Note that Ψ el now only depends parametrically on the nuclear positions R . Substi-tuting Equation (2) into (1) and using (3) gives (cid:2) − (cid:88) α ( 12 M α ) ∇ α + E el ( R ) − E (cid:3) Ψ nuc ( R ) = 0 (4) where the sum is over nuclei α with mass M α . In this equation, we use the assump-tion ∇ α Ψ el Ψ nuc = Ψ el ∇ α Ψ nuc , inherent in the Born-Oppenheimer approximation.Coupling terms involving ∇ α Ψ el are called non-adiabatic terms and their neglect isusually justified. Atomic units (a.u., not to be confused with astronomical units orarbitrary units) have been adopted, which have (cid:126) = m e = e = 1 . The unit of distanceis then 1 a.u. = 0.52918 Å (also called the Bohr radius or a ) and the unit of energyis 1 a.u. = 27.21 eV (or Hartree).Consider for simplicity a diatomic molecule with internuclear distance R . Theprobability of an electronic transition from state i to state f is governed by the mag-nitude of the electronic transition dipole moment D ( R ) , which can be computed from D ( R ) = < Ψ el f ( r ; R ) | d | Ψ el i ( r ; R ) > (5) where the integration is performed over the electron coordinate space and d is theelectric dipole moment operator in atomic units.The photodissociation cross section (in cm ) following absorption from a boundvibrational level v (cid:48)(cid:48) of the ground electronic state into the vibrational continuum k (cid:48) of an upper state at a transition energy ∆ E is then given by σ v (cid:48)(cid:48) (∆ E ) = 2 . × − g ∆ E | < Ψ nuc k (cid:48) ( R ) | D ( R ) | Ψ nuc v (cid:48)(cid:48) ( R ) > | (6) where the integration is over the nuclear coordinate R . Here g is a degeneracy factor(equal to 2 for Π ← Σ transitions, 1 otherwise) and all quantities are in atomic units.Similarly, the absorption oscillator strength between two bound states is f v (cid:48) v (cid:48)(cid:48) = 23 g ∆ E v (cid:48) v (cid:48)(cid:48) | < Ψ nuc k (cid:48) ( R ) | D ( R ) | Ψ nuc v (cid:48)(cid:48) ( R ) > | (7) Theoretical calculations of photodissociation cross sections thus consist of two steps:(1) calculation of the electronic potential curve or surfaces and (2) solution of thenuclear motion under the influence of the potentials.
Electronic energies: method of configuration interaction
Step 1 is the calculation of the electronic potential energy surfaces E ( R ) and tran-sition dipole moments D ( R ) connecting the excited states with the ground state asfunctions of the nuclear coordinate R . It is important to realize that most aspects ofchemistry deal with small energy differences between large numbers. For example,an Dishoeck & Visser: Molecular Photodissociation the binding energy of a molecule or the excitation energy to the first excited state istypically only 0.5% of the total energy of the molecule. Thus, the difficulty in quan-tum chemistry is not only in dealing with a n + 3 N many-body problem, but also inreaching sufficient accuracy in the results. For example, the Hartree-Fock method, inwhich all electrons are treated as independent particles by expanding the molecularwave function in Equation (2) in a product of n one-electron wave functions, fails be-cause it neglects the ‘correlation energy’ between the electrons: when two electronscome close together, they repel each other. This correlation energy is again on theorder of a fraction of a percent of the total energy. Over the last decades, different quantum chemical techniques have been developedthat treat these correlations, and there are several publicly available programs. Mostof the standard packages, however, such as the popular GAUSSIAN package, or pack-ages based on density functional theory [8, 9], are only suitable and well-tested forthe ground electronic state and for closed-shell electronic structures. More sophisti-cated techniques based on the CASSCF (complete active space self-consistent field)or coupled cluster methods work well for the lowest few excited electronic states ofa molecule, but these states often still lie below the dissociation energy and do notcontribute to photodissociation. Accurate calculation of the higher-lying potentialsthrough which photodissociation can proceed requires multi-reference configurationinteraction (MR-CI) techniques [10, 11], for which only a few packages exist (e.g.,MOLPRO, [12]).In the CI method, the wave function is expanded into an orthonormal set of M symmetry-restricted configuration state functions (CSFs). Ψ el ( x ...x n ) = M (cid:88) c s Φ s ( x ...x n ) (8) The CSFs or ‘configurations’ are generally linear combinations of Slater determi-nants, each combination having the symmetry and multiplicity of the state underconsideration. The Slater determinants are constructed from an orthonormal set of one-electron molecular orbitals (MOs; obtained from an SCF solution to the Hartree-Fock equations), which in turn are expanded in an elementary set of atomic orbitals(AOs; called ‘the basis set’) centered on the atomic nuclei. The larger M is, the moreaccurate the results.In the multi-reference technique, a set of configurations is chosen to provide the ref-erence space. For example, the X Π ground state of OH has the main configuration σ σ σ π , where σ and π are the molecular orbitals. The reference space couldbe chosen to consist of all possible configurations of the same overall symmetry thathave a coefficient c s greater than some threshold in the final CI wave function. Forthe OH example, this includes configurations such as σ σ σ σ π in whichone electron is excited from the highest occupied MO (HOMO) to the lowest unoc-cupied MO (LUMO). Alternatively, an ‘active space’ of orbitals can be designated,e.g., the σ − σ and π − π MOs in the case of OH, within which all configurationsof a particular symmetry are considered. The CI method then generates all singleand double (and sometimes even higher) excitations with respect to this set of ref-an Dishoeck & Visser: Molecular Photodissociation erence configurations, several hundreds of thousands of configurations in total, anddiagonalizes the corresponding matrix. The resulting eigenvalues are the differentelectronic states of the molecule, with the lowest energy root corresponding to theground state.The quality of an MR-CI calculation is ultimately determined by the choice of theatomic orbital basis set, the choice of the reference space of configurations, and thenumber of configurations included in the final CI. The basis set needs to be at least of‘triple- ζ ’ quality (i.e., each occupied atomic orbital s, p, ... is represented by threefunctions with optimized exponents ζ ). Also, polarization and Rydberg functions (i.e., functions which have higher quantum numbers than the occupied orbitals, e.g., p for H, d and s for C) need to be added. The number of AOs chosen in thebasis set determines the number of MOs, which in turn determines the number ofconfigurations. For a typical high-quality AO basis set, the latter number is so large,of order , that some selection of configurations needs to be made in order to handlethem with a computer. For example, all configurations which lower the energy bymore than a threshold value (in an eigenvalue equation with the reference set) can bechosen to be included in the final CI matrix.Once the electronic wave functions Ψ el for the ground and excited electronic stateshave been obtained, the expectation values of other operators, such as the electricdipole moment or the spin-orbit coupling, can be readily calculated. Nuclear dynamics: oscillator strengths and cross sections
Step 2 in calculating photodissociation cross sections consists of solving Eq. (4) todetermine the nuclear wave functions using the electronic potential curves from Step1. Often the nuclear wave function is first separated into a radial and an angular part.If the angular part is treated as a rigid rotor, the radial part can be solved exactlyby one-dimensional numerical integration for a diatomic molecule so that no furtheruncertainties are introduced. Once the wave functions for ground and excited statesare obtained, the cross sections can be computed according to Eq. (6).For indirect photodissociation processes, the oscillator strengths into the discrete upper levels are computed according to Eq. (7) for each vibrational level v (cid:48) . If thecoupling between the upper bound level with the final dissociative continuum (ascomputed in Step 1) is weak, first order perturbation theory can be used to calculatethe predissociation rates k pr in s − . The predissociation probability η u of upper level u is then obtained by comparing k pr with the inverse radiative lifetime of the molecule A rad : η u = k pr / ( k pr + A rad ) . In our example of OH, this approximation works wellfor the calculation of the predissociation of the A Σ + state for v (cid:48) ≥ . If the couplingis strong, as is the case for the OH 2 and 3 Π states, the coupled equations for theexcited states (i.e., going beyond the Born-Oppenheimer approximation) have to besolved in order to compute the cross sections.For (light) triatomic molecules, the calculation of the full 3D potential surfacesand the subsequent dynamics on those surfaces is still feasible, albeit with signif-icantly more effort involved [13, 4, 14]. For multi-dimensional potential surfaces,often time-dependent wave packet propagation methods are preferred to solve the dy-an Dishoeck & Visser: Molecular Photodissociation Figure 4.4
Absorption spectrum of gaseous H O illustrating the different electronic statesthrough which photodissociation can occur (reproduced from [15]). namics rather than the time-independent approach. Besides accurate overall crosssections, such studies give detailed insight into the photodissociation dynamics. Forexample, the structure seen in the photodissociation of H O through the first excited ˜ A state is found to be due to the symmetric stretch of the excited molecule just priorto dissociation.For larger polyatomic molecules, such fully flexible calculations are no longer pos-sible and one or more nuclear coordinates need to be frozen. In practice, often theentire nuclear dynamics calculations are skipped and only electronic energies and os-cillator strengths at the ground state equilibrium geometry are computed. Assumingthat all absorptions into excited states with vertical excitation energies larger than D e lead to dissociation (i.e., η u = 1 ), this method provides a rough estimate (upper lim-it) on the dissociation rate [16]. This method works because of the Franck-Condonprinciple, which states that the highest cross sections occur when the excitation ener-gies are vertical, that is, nuclear coordinates do not change between lower and upperstates (Fig. 4.1). Because only a single nuclear geometry has to be considered, theamount of work is orders of magnitude less than that of a full electronic and nuclearcalculation.The overall accuracy of the cross sections and oscillator strengths is typically 20–30% for small molecules in which the number of active electrons is at most ∼
30. Onthe order of 5–10 electronic states per molecular symmetry can be computed with reasonable accuracy. Transition energies to the lowest excited states are accurate to ∼ α at 10.2 eV. However, if it has an electronic state with a verticalan Dishoeck & Visser: Molecular Photodissociation energy close to 10 eV, and absorption into the state is continuous, theory can firmlystate that there is a significant cross section at Lyman α . An example is the 1 ∆ state of OH: even with ±
30 Å uncertainty in position, the cross section at 1215.6 Åis found to lie between 1 and × − cm .Virtually all molecules have more electronic states below 13.6 eV than can be com-puted accurately with quantum chemistry. Take our OH example: there is an infinitenumber of Rydberg states converging to the ionization potential at 13.0 eV. However,because the intensity of the radiation field usually decreases at shorter wavelengths,these higher states do not significantly affect the overall photodissociation rates. Their combined effect can often be taken into account through a single state with an oscil-lator strength of 0.1 lying around the ionization potential. Experiments
Laboratory measurements of absorption cross sections have been performed for manychemically stable species, including astrophysically relevant molecules such as H O,CO , NH , and CH . Most of these experiments have been performed at rather lowspectral resolution, where the individual ro-vibrational lines are not resolved. Fig-ure 4.4 shows an example of measurements for H O. A broad absorption continuumis observed between 1900 and 1200 Å, with discrete features superposed at shorterwavelengths. Note that the electronic states responsible for the absorptions at theshortest wavelengths have often not yet been identified spectroscopically.The absorption of a photon can result in re-emission of another photon, dissocia-tion, or ionization of the molecule, and most experiments do not distinguish betweenthese processes. If the photon energy is below the first ionization potential and if theabsorption is continuous, photodissociation is likely to be the dominant process. Ifnot, additional information is needed to infer the dissociation probabilities η u . Forthe H O example, the broad continuum at 1900–1400 Å corresponds to absorptioninto the ˜ A B state, which is fully dissociative. However, this is not necessarily true for the higher-lying discrete absorptions. An example is provided by the case of NOfor which fluorescence cross sections have been measured directly and found to varysignificantly from band to band, with η u significantly less than unity for some bands[17].Experiments typically quote error bars of about 20% in their cross sections if theabsorption is continuous. For discrete absorptions, high spectral resolution and lowpressures are essential to obtain reliable cross sections or oscillator strengths, sincesaturation effects can easily cause orders of magnitude errors.Most broad-band absorption spectra date from the 1950s-1980s and have been sum-marized in various papers and books [17, 18, 19]. An electronic compilation is pro-vided through the MPI-Mainz UV-VIS spectral atlas. Since about 1990, emphasishas shifted to experiments at single well-defined wavelengths using lasers, in par-ticular at 1930 and 1570 Å. The aim of these experiments is usually to study thedynamics of the photodissociation process at that wavelength, rather than obtainingcross sections. Such studies typically target the lower excited electronic states sincean Dishoeck & Visser: Molecular Photodissociation lasers or light sources at wavelengths < OH are being measured in the X-ray regime up to 100 eV [21]. High-resolution data in the FUV regime up to 13.6 eV are eagerly awaited.
Photodissociation products
Inclusion of photodissociation reactions in chemical networks requires knowledgenot only of the rate of removal of species ABC, but also of the branching ratios tothe various products, AB + C, A + BC or AC + B. Each of these species can beproduced with different amounts of electronic, vibrational and/or rotational energy,with the absolute and relative amounts depending on wavelength. None of this detailis captured in the standard tabulations, which, at best, give branching ratios betweenproducts integrated over all wavelengths or at a single wavelength, and neglect anyvibrational or rotational excitation.A great number of very elegant modern experiments are now available to explorethe fragments, based on a range of photofragment translational spectroscopy andtime-resolved photon-electron spectroscopy methods [7]. Product imaging tech-niques date back to the 1980s and characterize both the velocities, internal energiesand angular distributions of the photodissociation products [22].Velocity map imaging is a recent example of such a technique well suited for prob-ing photodissociation (Fig. 4.5) [23, 24]. In this method, a molecular beam containingthe molecule of interest is created by a pulsed supersonic expansion, which ensures in- ternal state cooling. After passing through a skimmer and a small hole in the repellerplate lens of an ion lens assembly the beam is crossed by a dissociation laser beam toform neutral fragments, which are immediately state-selectively ionized by a probelaser beam using resonance enhanced multi-photon ionization (REMPI). The ionsretain the velocity information of the nascent photofragments. Velocity map imag-ing uses a special configuration of an electrostatic immersion ion lens (combinationof repeller, extractor, and ground electrodes) to ensure mapping of the ion veloci-ty independent of its position of formation. After acceleration through the ion lens,the particles are mass-selected by time of flight upon reaching the surface of a two-dimensional imaging detector, which converts ion impacts to light flashes recordedby a CCD camera. The two-dimensional image can then be converted to its desired 3-D counterpart by using an inverse Abel transformation. The lens effectively reducesthe ‘blurring’ of the images.Another variant on this technique is Rydberg H-atom time of flight spectroscopy.Here the nascent H atoms produced by photodissociation in the ground n = 1 statean Dishoeck & Visser: Molecular Photodissociation Figure 4.5
Experimental setup for velocity map imaging of photodissociation products(based on [23]). are excited into the n = 2 state using a Lyman α laser at 1216 Å and subsequentlyto a high Rydberg state with n = 30 –80 using longer wavelength (e.g., 3650 Å)radiation. The neutral Rydberg H atoms then reach a microchannel plate where theyare field-ionized and detected. A completely different set of experiments has been applied to study the branchingratios of large carbon chain molecules. Here, high velocity collisions combined withan inverse kinematics scheme have shown that the most favorable channels are Hproduction from C n H and C production from C n [25]. Otherwise the fragmentationbehavior is largely statistical.An example of the complexity of the situation is provided by the OH and H Ocases. For OH, the potential curves in Fig. 4.2 show that absorption into the 1 Σ − state results in ground-state O( P) + H, but absorption into the higher lying ∆ , Π and Σ + states in excited O( D) and O( S). The cross sections into these states aresuch that about equal amounts of O( P) and O( D) are produced in the general in-terstellar radiation field, but only 5% of O( S) [5]. An astrophysical confirmation ofthis prediction is the detection of the red line of atomic O ( D → P) at 6300 Å fromprotoplanetary disks [26, 27]. On the other hand, for radiation fields dominated bylower photon energies such as in comets exposed to solar radiation, the main productis ground-state O( P).an Dishoeck & Visser: Molecular Photodissociation H O is one of the few polyatomic molecules for which the product distribution hasbeen well characterized as a function of energy. Both theory and experiment haveshown that absorption at 6–8 eV into the first ˜ A electronic state produces OH in theground electronic Π state with some vibrational excitation but little rotational exci-tation. In contrast, absorption at 9–11 eV into the second ˜ B electronic state producesOH in highly excited rotational levels of the A Σ + excited electronic state, but withlow vibrational excitation. Absorption into even higher excited states results in O +H or O + H + H products, rather than OH + H. For other polyatomic molecules, ex-perimental information is spotty at best. Early experiments were often performed at high pressures, where the observed products could result from subsequent chemicalreactions in the gas that would not occur at the low densities in space [19].Some guess of the most likely products can be made on the basis of product energies(when does a product channel open up?) and correlation diagrams [7], but thesetechniques are usually limited to the lowest-lying channels that may not dominate theoverall dissociation. Often, the astrochemical databases simply assume a statisticaldistribution over the various products averaged over all photon energies. Note that theinformation on the product distribution of species like CH OH is relevant not onlyfor gas-phase chemistry but even more so for ice chemistry [28].
General interstellar radiation field
Determinations of the average intensity of the interstellar radiation field (ISRF) fallinto two main categories (see [29] and [30] for critical reviews). The first method isto estimate the number and distribution of hot stars (O, B, A, ... type) in the Galaxy,use a model for the dust distribution and properties to determine the absorption and scattering of the stellar radiation, and then sum their fluxes to determine the energydensity at a typical interstellar location. This method dates back to [31] and [32],and has most recently been revisited by [33]. The stellar fluxes used in these modelsare a combination of observed fluxes of early-type stars and extrapolations to shorterwavelengths using model atmospheres.The second method is to use direct measurements of the UV radiation from thesky at specific wavelengths [36]. Also in this method, model stellar atmospheres areused to provide information at wavelengths not directly observed. In both methods,direct starlight from early B stars is found to dominate the measured interstellar flux.Specifically, most of the flux at a given point in space comes from the sum of discretesources within 500 pc distance from that point.The various estimates of the local ISRF in the solar neighborhood agree remarkablywell, within a factor of two. The median value found by [33] is within 10% of themean energy density of U = 8 × − erg cm − Å − of [32], averaged over the912–2070 Å FUV band ( ∆ FUV ). The strength of the one-dimensional interstellaran Dishoeck & Visser: Molecular Photodissociation Figure 4.6
Comparison of the general interstellar radiation field of Draine (1978)(extended for λ >
Å using the representation of [34]) with various stellar radiationfields scaled to have the same integrated intensity from 912–2050 Å. The scaledNEXTGEN model radiation field of a B9.5 star [35] is included as well (dash-dotted). Thewavelength ranges where the photodissociation of some important interstellar moleculesoccurs are indicated (reproduced from [2]). radiation field is often indicated by a scaling factor G with respect to the flux F inthe Habing field ( F FUV = cU FUV ∆ FUV ) of . × − erg cm − s − , which is afactor of 1.7 below that of [32]. Thus, the standard Draine field implies G = 1 . .Care should be taken that photodissociation rates used in astrochemical models referto the same radiation field.If a cloud is located close to a young, hot star, the intensity incident on the cloud boundary may be enhanced by orders of magnitude compared with the average ISRF.A well-known example is the Orion Bar, where the intensity is enhanced by a factorof . × with respect to the Draine field. In contrast, at high latitudes where fewearly-type stars are located, the intensity may be factors of 5–10 lower in the FUVband than that of the standard ISRF field. Throughout the galactic plane and overtime scales of a few Gyr, variations in the local energy density by factors of 2–3 areexpected due to the birth and demise of associations containing high-mass O and Bstars within about 30 Myr. Moreover, the ratio of the highest-energy photons capableof dissociating H and CO and those in the more general FUV range may vary by afactor of 2 in time and place [33].an Dishoeck & Visser: Molecular Photodissociation Stellar radiation fields
The surface layers of disks around young stars are another example of gas in which thechemistry is controlled by photodissociation. The illuminating stars range from lateB- and early A-type stars (the so-called Herbig Ae/Be stars) to K- and M-type stars(the T Tauri stars). For the latter, if the stellar atmosphere dominates the flux, ordersof magnitude fewer high-energy photons are available to dissociate the moleculesthan in the ISRF scaled to the same integrated intensity (Fig. 4.6). In particular, the number of photons capable of dissociating H and CO and ionizing carbon is greatlyreduced [2, 37]. However, if accretion onto the star is still taking place, the hot gas inthe accreting column produces high-energy photons, including Lyman α , which candominate the FUV flux [38]. Lyman α radiation Fast shocks (velocities >
50 km s − ) produce intense Lyman α radiation due to col-lisional excitation of atomic hydrogen in the hot gas or recombination of ionizedhydrogen [39, 40]. Another prominent line in shocks is the C III resonance line at977 Å. Fast shocks can be caused by supernovae expanding into the interstellar medi-um, or by fast jets from protostars interacting with the surrounding cloud. Accretionshocks onto the young star mentioned above are another example, as are exoplanetaryatmospheres. Some molecules, in particular H , CO and N , cannot be dissociatedby Lyman α . Other simple molecules such as OH, H O and HCN can. A recentsummary of cross sections at Lyman α is given by [2]. Cosmic-ray induced photons
A dilute flux of UV photons can be maintained deep inside dense clouds through theinteraction of cosmic rays with hydrogen in the following process:
H or H + CR → H + or H +2 + e ∗ (9)e ∗ + H → H ∗ + eH ∗ → H + h ν The energetic electrons e ∗ produced by the cosmic rays excite H into the B Σ + u and C Π u electronic states, so that the FUV emission is dominated by Lyman- andWerner-band UV photons. Higher-lying electronic states contribute at the shortest wavelengths. As a result, the UV spectrum produced inside dense clouds resembles strongly that of a standard hydrogen lamp in the laboratory. Figure 4.7 shows theUV spectrum computed following [41, 42] for e ∗ at 30 eV and either all H in J =0or distributed over J =1 and J =0 in a 3:1 ratio. Note that the precise spectrum doesan Dishoeck & Visser: Molecular Photodissociation Figure 4.7
Cosmic-ray induced spectrum of H assuming that all H is in J =0 (left) ordistributed over J =1 and J =0 in a 3:1 ratio (left). The spectrum shows the number ofphotons per 1 Å bin for initial 30 eV electrons and are normalized to the total number ofionizations (figure by Gredel, updated from [41, 42]). depend on the H level populations and the ortho/para ratio. Because of the highlystructured FUV field and the lack of high-resolution cross sections for most species,the resulting photodissociation rates may be quite uncertain. On the other hand, thelarge number of lines has a mitigating effect. Dust attenuation
The depth to which ultraviolet photons can penetrate in the cloud and affect the chem-istry depends on (i) the amount of photons at the boundary of the cloud; (ii) thescattering properties of the grains as functions of wavelength; (iii) the competitionbetween the atoms and molecules with the grains for the available photons, which,in turn, depends on the density of the cloud; and (iv) possible self-shielding of themolecules.The absorption and scattering parameters of the grains determine the penetration depths of photons. The ultraviolet extinction curve shows substantial variations fromplace to place, especially at the shortest wavelengths in the 912–1100 Å region, whichcan greatly affect the CO and CN photodissociation rates [43, 44]. Similar variationsare expected to occur for the albedo (cid:36) and the asymmetry parameter g as functions ofwavelength, but little is still known about these parameters at the shortest wavelengths[45].There is considerable observational evidence that dust grains in the surface layersof protoplanetary disks have grown from the typical interstellar size of 0.1 µ m to atleast a few µ m in size or more. These large grains extinguish the UV radiation muchless, allowing photodissociation to penetrate deeper into the disk [2, 46].an Dishoeck & Visser: Molecular Photodissociation Self-shielding
Because the physical and chemical structure of cloud edges is controlled by the pho-todissociation of H and CO and photoionization of C, it is important to pay partic-ular attention to the details for these molecules. CO is discussed in Sec. 4.6. Thephotodissociation of H occurs by absorptions into the Lyman and Werner bands at912–1100 Å followed by spontaneous emission back to the vibrational continuum ofthe ground state [47, see also Fig. 4.1]. The absorption lines have typical oscillator strengths f ≈ . –0.03, and on average about 10% of the absorptions lead todissociation. The strongest lines become optically thick at H column densities of – cm − for a Doppler broadening parameter b of 3 km s − , implying thatmolecules lying deeper within the cloud are shielded from dissociating radiation be-cause all relevant photons have been absorbed at the cloud edge (‘self-shielding’).The photodissociation rate of H is about . × − s − in the unattenuated inter-stellar radiation field, corresponding to a lifetime of about 700 yr. Inside the cloud, thelifetime becomes longer by several orders of magnitude because of the self-shieldingprocess. The remaing 90% of the absorptions are followed by UV fluorescence backinto the bound vibrational levels of the H ground state.Photoionization of atomic carbon has a continuous cross section of about − cm over the 912–1100 Å region. Thus, for column densities N (C) > cm − ,carbon starts to self-shield [48]. Moreover, the saturated absorption bands of H andH over the same wavelength range remove a considerable fraction of the ionizingradiation (‘mutual shielding’). The photodissociation rate k pd of a molecule by continuous absorption is given by k contpd = (cid:90) σ ( λ ) I ( λ ) dλ s − , (10) where σ is the cross section for photodissociation in cm and I is the mean intensity ofthe radiation in photons cm − s − Å − as a function of wavelength λ in Å (Fig. 4.6).For the indirect processes of predissociation and spontaneous radiative dissociation,the rate of dissociation by absorption into a specific level of a bound upper state u from lower level (cid:96) is k linepd = πe mc λ u(cid:96) f u(cid:96) η u x (cid:96) I ( λ u(cid:96) ) s − , (11) where f u(cid:96) is the oscillator strength, η u is the dissociation efficiency of the upper level(between 0 and 1), and x (cid:96) is the fractional population in level (cid:96) .The determination of the cross sections and oscillator strengths from theory andexperiments has been discussed in Sec. 4.3. Cross section databases are avail-able from [2] at ∼ ewine/photo and from [49]an Dishoeck & Visser: Molecular Photodissociation at amop.space.swri.edu for cometary species. For more complex speciesalso of atmospheric interest, a large compilation is available through the MPI-Mainz UV-VIS spectral atlas at and .Photodissociation rates as functions of depth into a cloud using the standard inter-stellar radiation field [32] have been presented for a variety of molecules [1, 45], andmost recently by [2]. The latter paper and associated website also summarize rates incooler radiation fields such as appropriate for late-type stars. The depth dependencedue to continuum extinction can be represented by a simple exponential function, with exponents that vary with grain scattering properties and that depend paramet-rically on cloud thickness. A list of cosmic-ray induced rates for use in dense cloudmodels has been given by [42]. CO is the most commonly observed molecule in interstellar space and used as a tracerof molecular gas throughout the universe, from local diffuse clouds to dense gas atthe highest redshifts. Additional impetus for a good understanding of its photodisso-ciation processes comes from recent interpretations of oxygen isotope fractionationin primitive meteorites, which are thought to originate from isotope selective pho-todissociation of CO in the upper layers of the disk out of which our solar systemformed [50]. To model these processes, information on the electronic structure of allthe CO isotopologs, including those with O, is needed.CO is an extremely stable molecule with a dissociation energy of 11.09 eV, corre-sponding to a threshold of 1118 Å. It took until the late 1980s to establish that nocontinuum absorption occurs longward of 912 Å, but that CO photodissociation isdominated by line absorptions, most of which are strongly predissociated [51, 52].These early laboratory data were used to build a detailed model of the CO photodis- sociation rate in an interstellar cloud [53, 54]. The depth dependence of the COphotodissociation is affected not only by self-shielding, but also by mutual shieldingby H and H because these species absorb in the same wavelength region. CO, inturn, can shield the less abundant CO, C O and C O species, with the amountof shielding depending on the wavelength shifts in the absorption spectrum. Thus, acomplete numerical simulation of the entire spectrum of CO, its isotopologs, H and H is required to correctly compute the attenuation at each depth into a cloud[55, 56].In the 20 years since these first models, a steady stream of new laboratory data hasbecome available on this key process. In the late 1980s, many of the bands recorded inthe laboratory were for CO only and had no electronic or vibrational designations,so that simulation of the isotopolog spectra involved much guesswork. In particular,the magnitude of the isotopolog shifts depends sensitively on whether v (cid:48) in the upperstate is zero or not. Moreover, predissociation rates were generally not known andwere simply assumed to be unity. High-resolution spectra for many important bandsan Dishoeck & Visser: Molecular Photodissociation of CO, CO, C O and C O were subsequently measured with synchrotronlight sources [57, 58, 59, 52]. The fact that the experimental oscillator strengths havenow been reconciled with values inferred from astronomical measurements leaveslittle doubt about their accuracy [60]. Ultra-high-resolution spectra of selected stateshave been obtained with VUV lasers [20]. These exquisite data provide not onlypositions down to 0.003 cm − accuracy, but also measure directly the line widthsand thus the predissociation probabilities. This is especially important for the C Σ + and E Π states responsible for most of the isotope-selective effects [61, 62, 63, 64].Visser et al. [65] used the recent laboratory data to develop a new model for the CO isotope-selective photodissociation including the O isotopologs, and appliedit to interstellar clouds and disks around young stars. They also computed shieldingfunctions for a much larger range of CO excitation temperatures and Doppler broad-enings. Although the overall rate has changed by only 30%, from . to . × − s − for the standard interstellar radiation field [32], the modeled depth dependencediffers significantly from earlier work. In particular, the isotope selective effects arediminished by a factor of three or more at temperatures above 100 K. Note, however,that even this new study [65] still had to make many assumptions on line positions,oscillator strengths and predissociation rates for the minor isotopologs, since high-resolution spectra of these minor species have not yet been measured or published.Unexpected differences of up to an order of magnitude have been found between os-cillator strengths of CO and CO for the same bands, complicating extrapolationsfrom the main isotopologs. These differences likely arise from mixing between var-ious electronic states that depend sensitively on the relative location of the energylevels and may thus differ for a specific ro-vibronic v (cid:48) , J (cid:48) level of a particular iso-topologue, as found for the case of N [66].Another set of experiments on the CO isotopolog photodissociation has been car-ried out using the Berkeley synchrotron source [67] . In contrast with the Paris andAmsterdam results, these data are at comparatively low spectral resolution and wereanalyzed much more indirectly by following a set of subsequently occurringchem-ical reactions. The data were interpreted to imply different predissociation proba- bilities for individual levels of isotopologs caused by near-resonance accidental pre-dissociation processes. In this interpretation, the isotope-selective effects found inmeteorites would not require self- or mutual shielding processes. While accidentalpre-dissociation is not excluded, these experiments and their conclusions have beenchallenged on many grounds and are not supported by the higher resolution data citedabove [65, 68, 69, 70]. This episode demonstrates that there is no substitute for high-quality molecular physics data in which individual unsaturated lines are recorded, inorder to draw astrophysical conclusions.Another very stable molecule for which the photodissociation occurs primarily byline absorptions is N . Thanks to decades of laboratory experiments, the line oscilla-tor strengths and predissociation probabilities of the excited ro-vibrational states arenow known with very high accuracy. The N and N N data have recently beensummarized and applied to interstellar chemistry [71, 72].an Dishoeck & Visser: Molecular Photodissociation Figure 4.8
Photodissociation and photoionization rates of PAHs as functions of number ofcarbon atoms for the general interstellar radiation field. Solid: loss of C, dotted: loss of H;dash-dotted: ionization. Note the stability of the larger PAHs against dissociation. Figuremade using data from [73] following [74].
PAH molecules are a class of large molecules that are very stable against photodis-sociation in the general interstellar medium, explaining their ubiquitous presence ingalaxies [75]. However, in clouds exposed to very intense radiation, such as the innerregions of protoplanetary disks and the immediate environments of active galacticnuclei, the smaller PAHs can be destroyed within the lifetime of the source. As dis-cussed in Sec. 4.2.2, the dissociation process of a large molecule involves a multistepprocess, in which the molecule first absorbs a photon and is promoted to an excitedelectronic state, then decays non-radiatively to high vibrational levels of the ground state, and finally finds a path to dissociation. The rate of this process thus dependsnot only on the initial absorption rate, but also on the competition with other process-es during these steps. In the first step, the absorption of the photon can also lead toemission of an electron through ionization or photodetachment with probability η em .In the final step, there is competition between dissociation and cooling by infraredemission. The PAH photodissociation rate thus becomes [76, 74, 77, 78, 73]: k pd = (cid:90) (1 − η em ) η diss σ abs I λ dλ where η diss is the yield of a single dissociation process given by η diss = (cid:80) X k diss , X ( k diss + k IR ) . Here k diss , X is the rate for a particular loss channel X (e.g., H removal), k diss isthe sum over all such channels, and k IR is the infrared emission rate. Possible lossan Dishoeck & Visser: Molecular Photodissociation Figure 4.9
Overview of the PIRENEA experiment to study the photostability andfragmentation pattern of PAHs exposed to UV radiation [79]. channels are H, H , C, C and C [76], with the rates determined by the RRKMquasi-equilibrium theory according to k diss ,X = A X ρ ( E int − E ,X ) ρ ( E int ) where A X is the pre-exponential Arrhenius factor for channel X and ρ ( E ) is thedensity of vibrational states at energy E . Dissociation only occurs if the internalenergy of the molecule E int exceeds the critical energy E for a particular loss chan- nel. Values for E ,X were summarized by [73]. The above formulation needs to bemodified for clouds exposed to very intense radiation fields ( G > ), when mul-tiphoton events start to become significant, i.e., the PAH molecule absorbs anotherUV photon before it has cooled down completely. This can significantly increase thedissociation rate.To compute the dissociation rates, values of σ abs as a function of wavelength areessential. The data used in astrophysical models largely come from models developedby [80], based on experiments by [81]. There is also limited experimental informationon the loss channels, as summarized by [77]. For example, [82, 83] have measuredthe photostability of small PAHs of various sizes and shapes against H-loss. Fig-ure 4.8 compares the H-loss channel quantitatively with that of other loss channelsand illustrates the competition with ionization.In a novel experiment, called PIRENEA, the spectroscopy and photodissociation ofPAHs into various fragments can be studied [79, 84, 85]. Specifically, gas-phase PAHcations are produced by laser irradiation of a solid target and then guided into an ionan Dishoeck & Visser: Molecular Photodissociation cyclotron resonance cell, where they are trapped in a combined magnetic and electricfield. The stored ions are irradiated by a xenon lamp (2000–8000 Å) and the productsare analyzed by Fourier-transform mass spectrometry. Ions of interest can be selectedand isolated by selective ejection of other species. Initial results show that irradiationleads predominantly to atomic hydrogen atom loss, consistent with the work of [82],but loss of C H and perhaps even C H is also seen from dehydrogenated PAHs[86]. This chapter has summarized our understanding of basic photodissociation processesand the theoretical and experimental approaches to determine cross sections, productbranching ratios and rates for astrophysically relevant species. The demand for accu-rate photorates is likely to increase in the coming years as new infrared and submil-limeter facilities widen the study of molecules in the surfaces of protoplanetary disksand exoplanetary atmospheres. Critical evaluation of the photodissociation data forthese different environments are needed, since rates or cross sections determined forinterstellar clouds cannot be simply transposed to other regions.
The authors are grateful to Marc van Hemert and Geert-Jan Kroes for many fruitfulcollaborations on theoretical studies of photodissociation processes, and to RolandGredel, Christine Joblin and Dave Parker for providing figures. Support from aSpinoza grant and grant 648.000.002 by the Netherlands Organization of ScientificResearch (NWO) and from the Netherlands Research School for Astronomy (NOVA) is gratefully acknowledged.an Dishoeck & Visser: Molecular Photodissociation an Dishoeck & Visser: Molecular Photodissociation References E. F. van Dishoeck.
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