- Top of page
- 1. Introduction
- 2. Results
- 3. Discussion
- 4. Conclusions
Ultrafast photodissociation of the 2 1A′ state of ClNO, which has an absorption spectrum peaking at 335 nm, is studied by computational and experimental methods. New potential-energy surfaces are calculated for the 1 and 2 1A′ states at the multireference configuration interaction (MRCI) level. Wavepacket dynamics simulations performed both exactly and by using the multiconfiguration time-dependent Hartree method yield essentially identical results. Transition dipole moments at a range of geometries are included in these calculations to correctly model the excitation. Vibrational and rotational state distributions of the NO product are obtained both computationally by analysing the quantum flux on the 2 1A′ surface and experimentally by use of 3D resonant multiphoton ionisation (REMPI), a variant of the velocity map imaging technique. The nascent NO is found to be only marginally vibrationally excited, with 91 % formed in v=0. The calculated NO rotational distribution peaks in the j=45–55 region, which compares favourably to experiment.
- Top of page
- 1. Introduction
- 2. Results
- 3. Discussion
- 4. Conclusions
The photodissociation of nitrosyl chloride (ClNO) has been studied as a prototypical example of bond rupture since the 1930s.1 In the UV/Vis region (2–7 eV) ClNO exhibits strong absorption and readily dissociates to give NO and Cl products in their ground electronic states. The NO can be formed in a variety of vibrational and rotational states depending on the photon energy and hence the excited electronic state accessed.2 With only 32 electrons it is amenable to computational study by ab initio methods. As an easily prepared, albeit highly corrosive, gas it is also convenient for detailed experimental investigation by techniques such as velocity map imaging. ClNO is also of interest to the atmospheric chemistry community, because it is a source of the Cl radical particularly in urbanised regions of the coast.3 A further motivation for revisiting the photochemistry of this molecule from a computational perspective is the possibility of using it as a target molecule for coherent control experiments through optical pulse shaping.4, 5
ClNO belongs to the Cs point group and hence its electronic states are of A′ or A′′ symmetry. Ignoring spin–orbit coupling, there are 12 states which correlate to the ground electronic states of NO and Cl (2Π and 2P, respectively) on dissociation: 3×1A′, 3×1A′′, 3×3A′ and 3×1A′′. All of these barring 1 1A′ are dissociative, but there is some variation in their lifetimes, with 1 1A′′ and 1 3A′′ in particular existing long enough to exhibit structured absorption bands.6–8 For the 2 1A′ state of interest here the dissociation process is over more quickly, but the topology of the potential-energy surface (PES) still has a marked influence upon the NO product state distribution.
The 2 1A′ state absorbs light between 280 and 400 nm (3 and 4.5 eV) with a peak at 335 nm (3.72 eV).9 It is commonly referred to in the literature as the B band following the nomenclature introduced by Goodeve and Katz.10 The exact identity of the state giving rise to this band was uncertain for some time, despite early calculations11 and experimental work showing that it was of A′ symmetry.12, 13 The problem was solved when Reisler and co-workers conducted photofragment yield spectroscopy experiments9, 13 which confirmed the symmetry and showed it gave rise to NO fragments primarily in the Π(A′′) Λ-doublet state. In a Hartree–Fock molecular orbital model, this implied that excitation was to an orbital perpendicular to the plane of the molecule. Combining this information with ab initio calculations showed clearly that the 2 1A’ state was responsible, with primary excitation occurring from the Cl pz orbital to a NO πz antibonding orbital. This assignment was further confirmed by later, more advanced calculations.14, 15
The experiments of Reisler et al. also revealed the NO (v=0) rotational distributions following photodissociation at 355 nm, which were found to be bell-shaped, peaking at j≈4613 or j≈43,9 where j is the rotational quantum number of the NO nuclear frame. More recent, detailed state-selected experiments carried out by Torres et al. found a similar narrow distribution peaking at j=46 for NO in its ground vibrational state.16 This high level of rotational excitation implies anisotropy on the excited-state surface, an observation borne out by previous calculations of the 2 1A′ surface.15
Herein, vibrational and rotational distributions in the NO fragment following dissociation on the 2 1A′ surface are calculated and compared to experimental distributions measured by using the 3D resonant multiphoton ionisation (REMPI) technique. The article also sets the foundation for forthcoming work on ClNO excited state surfaces including spin–orbit coupling, and on coherent control through optical pulse shaping.
- Top of page
- 1. Introduction
- 2. Results
- 3. Discussion
- 4. Conclusions
Potential-Energy Surfaces: All electronic structure calculations were carried out by using the MOLPRO 2010 package.17 Firstly, PESs for the 1 and 2 1A′ states were constructed. 2464 ab initio points were calculated across the following binding coordinates:
rNO: every 0.2 bohr from 1.75 to 2.95 bohr.
rClN: every 0.25 bohr from 2.75 to 6.0 bohr and then every 0.5 bohr to 10.0 bohr.
Bond angle θ: every 10° from 20 to 170°.
The initial orbitals were obtained by using the CASSCF method18, 19 state-averaged over the first three states of 1A′ character. A full valence active space was used with the N and O 1s and Cl 1s, 2s and 2p orbitals kept doubly occupied but not frozen. For rClN values greater than 6.0 bohr the occupation of the molecular orbital corresponding to the Cl 3s atomic orbital had to be restricted to two to prevent erroneous orbital reordering.
The CASSCF orbitals were then used to calculate the 1 and 2 1A′ states by the multireference configuration interaction (MRCI) method (single and double excitations).20 The contribution of quadruple excitations to the overall energy was estimated by the Davidson correction with relaxed reference functions. All generated configuration state functions were included. For these calculations the Dunning augmented correlation consistent polarised valence quadruple zeta (aug-cc-pVQZ) basis set was used.
Although alternative fitting functions were investigated, the quality of the ab initio points was sufficiently good that the surfaces could be smoothly fitted by using 3D cubic splines. The resultant surfaces were used for dynamics calculations.
Wavepacket Dynamics Methods: The majority of the quantum dynamics calculations were performed by using the multiconfiguration time-dependent Hartree method (MCTDH)21, 22 as implemented in the Heidelberg software package.23 Although ClNO is a small molecule and can be treated by exact calculations with relative ease, the MCTDH method was chosen to allow many wavepacket propagations to be run rapidly with very little loss of accuracy, and also to allow the full functionality of the suite of analysis programs to be utilised. A full description of the MCTDH method is given in ref. 24.
Briefly, the MCTDH wavefunction is written as a sum of Hartree products, in which each degree of freedom is represented by single particle functions (SPFs). These SPFs are time-dependent basis functions, wherein lies the strength of the method: if the functions are allowed to adapt during a wavepacket propagation fewer are needed for an accurate description of the dynamics. The underlying equation of the MCTDH method is [Eq. (1)]:
where Q1,..,Qf are the nuclear coordinates, the expansion coefficients and the SPFs for each degree of freedom κ. When more than one PES is included in the calculation multiple, distinct sets of these SPFs can be used for each surface.
Each SPF comprises a linear combination of time-independent functions known as the primitive basis. The form of the primitive basis functions is dependent upon the nature of the corresponding degree of freedom. To improve computational efficiency the discrete variable representation (DVR) was used for these, allowing the wavefunction to be localised onto a grid.25 In this work, a Legendre DVR was chosen for the angular coordinate, with a sine DVR (using the particle-in-a-box functions as its basis) for the dissociative coordinate and a harmonic oscillator (HO) DVR for the bound coordinate.
Although the PESs were calculated with binding coordinates, in the dynamics calculations they were converted to the Jacobi scattering coordinates shown in Figure 1. The main advantage of this coordinate system is that it leads to a considerable simplification of the kinetic energy operator. For systems in which the total angular momentum is taken to be zero (an approximation used throughout in this work), the operator is [Eq. (2)]:
Figure 1. The Jacobi coordinates used in this work: r is the NO bond length, R the radial distance from the Cl atom to the centre of mass of the NO moiety and γ the angle between r and R, also known as the Jacobi scattering angle.
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where μR and μr are the reduced masses for the R and r coordinates respectively.
After the PESs have been fitted by splines they are transformed into MCTDH product form by using the POTFIT program from the Heidelberg MCTDH suite.26, 27 This allows the entire Hamiltonian to be written as a sum of products of SPFs and thus facilitates the calculation of the required integrals.
In the asymptotic region a complex absorbing potential (CAP)28, 29 is placed on the R coordinate in order to absorb the wavepacket. This function has the form [Eq. (3)]:
where Rcap is the start point, η is the strength (set here to 0.3), b is set to 3 and h(R−Rcap) is a Heaviside step function. Without a CAP there is a danger that the wavepacket would hit the edge of the grid and be reflected backwards or reappear at the opposite end of the PES. In addition, it is very useful, as the quantum flux which passes into it can be recorded and subsequently analysed.
A standard method for obtaining product state distributions following wavepacket propagations is to take the time-dependent wavefunction in the asymptotic region and then project it onto the eigenstates of the individual product species. This can also be done by using the combination of the flux operator and the CAP, as outlined in ref. 30. The flux operator F̂ measures the quantum flux passing into the asymptotic region of the surface along the Jacobi R coordinate [Eq. (4)]:
where Rcap is defined as before, and H̃=Ĥ−iW in order to include the CAP in the operator.
To calculate the scattering matrix from a ClNO photodissociation channel a into a NO product state b using this flux operator approach, the working equations are Equations (5) and (6):
where T is the final propagation time, Δ(E) the energy spread of the initial wavepacket and the projector onto the b state of NO. The form of the projector depends upon the state in question. It is also possible to apply multiple projectors, for example, to find out the amount of NO produced in a particular rotational state and a particular vibrational state.
In the exact calculations the wavepacket was propagated by using the short iterative Lanczos (SIL) method. In the MCTDH calculations the SIL method was used for propagating the expansion coefficients, and the Bulirsch–Stoer extrapolation integrator was used for the SPFs.24
Velocity Map Imaging: Velocity map imaging (VMI) is a well-established experimental methodology for recording quantum state selected product distributions following photodissociation.31 Usually a nanosecond UV laser pulse is used to dissociate the molecule of interest, and a second pulse subsequently probes the products by REMPI. The resultant ions are then detected on a position-sensitive detector which, by virtue of the electrostatic lens used to extract them, provides a velocity (speed and direction) map of the state-selected photoproducts. In favourable circumstances a single laser pulse can act both to dissociate the target molecules and to ionize the desired photoproduct, which is the approach used here.
The apparatus used has been described elsewhere.32, 33 Briefly, gaseous ClNO was prepared by mixing samples of Cl2 and NO in a stainless steel cylinder and backfilling with He carrier gas. Typical samples consisted of about 0.133 bar of Cl2 and about 0.266 bar of NO in 8.0 bar of He (≈5 %). The sample at a backing pressure of a few bar is expanded into a vacuum chamber through a pulsed valve (Parker, Iota one, series 9) and the resulting molecular beam is skimmed by a 1 mm-diameter skimmer (Molecular Beam Inc.) a few centimetres downstream of the valve through which it enters the ionization chamber. The velocity map electrostatic lens is configured on axis. Photodissociation was initiated by using a nanosecond laser pulse (Continuum Surelite II pumped Sirah Cobra-Stretch dye laser operating with Pyridine 2 or Styryl 8 and frequency-doubled) to a wavelength in the region of 350–380 nm.
To gain a rapid overview of the rotational state product distribution and to easily discriminate between NO that might be present in the molecular beam as a contaminant from incomplete reaction or as a photoproduct of NO2 dissociation (another potential contaminant species), the velocity-resolved or 3D REMPI technique recently introduced by Dick and co-workers has been used.34 In our version of the method, the voltages of the VMI lens are adjusted for direct-current slice-imaging,35 and the microchannel plate detector is gated with a short (<10 ns) high-voltage pulse to record only a thin slice through the centre of the Newton sphere of state-selected ions, as described in ref. 33.
Our image processing software (in-house code written in LabView) works by recording a series of controided images as a function of wavelength, which are subsequently post-processed. Recording only the centroid coordinates rather than the entire image at each wavelength considerably reduces the data-storage requirements, and typically a 2 nm-wavelength scan with images recorded every 0.005 nm requires about 300 kb of disc space, as opposed to the 1 Gb or more needed for a sequence of uncompressed images. Radial integration of each of these images yields a 1D data array of intensity against pixel number, which is directly proportional to the velocity of the detected photofragment. Combination of many of these processed images as a function of wavelength yields a 3D “map” of wavelength, velocity and intensity. A typical experimental scan involved accumulating data for 150 laser shots per wavelength step.