Electronic spectra of CH+ involving “long-range” states

Chemical Physics 124 ( 1988) 439-452 North-Holland, Amsterdam

ELECTRONIC

SPECTRA OF CH’ INVOLVING

“LONG-RANGE”

STATES

P.J. SARRE and C.J. WHITHAM Department of Chemistry, Received

8 February

University ofNottingham,

University Park, Nottingham NG7 2RD, UK

1988

Previously reported “near-threshold” laser photofragment spectra of CH+ near 540 nm are interpreted as arising from chargetransfer electronic transitions between levels lying just below the C+ (*P) +H(‘S) dissociation asymptote and a weakly bound long-range electronic state which correlates to the C (‘P) + H+ dissociation limit. The shallow well of the upper state is determined principally by the long-range attractive ion-induced-dipole and charge-quadrupole interactions between the carbon atom and the proton and shorter-range repulsive behaviour. In our interpretation, low-energy C+ ions are detected following radiative decay of laser-excited CH+ to continua just above the lowest dissociation limit. Experimental and theoretical evidence for this boundbound-free process is presented. The characteristics of long-range weakly bound states and the role of non-adiabatic interactions near to dissociation are discussed. The possibility that previously observed laser photofragment spectra near 350 nm arise from a similar origin is considered.

astrophysical molecules. Experimental attention has been focused recently on the photodissociation of fast beams of CH+ in the ultraviolet [2], visible [ 1,3,7,8] and infrared [ 4,6] regions of the spectrum. These studies have yielded information on near-threshold resonances in CH+ and have provided some insight into the nature of the dissociation of a diatomic molecule which has a number of electronic states which all correlate to the same dissociation limit, C+ (*P ) + H (*S ) . This experimental effort has been matched by a strong theoretical interest; near-threshold levels (resonances) have been described in terms of rotationally adiabatic potentials [ 6,9 1, resonance widths have been calculated [ 3,6,7,10,11] and fully coupled calculations have been performed which illustrate the importance of non-adiabatic interactions on near-threshold resonances and on a range of other dynamical aspects of the dissociation of CH+ [ 12,131. Of particular interest is the prediction of “multichannel scattering resonances” [ 12,13 ] which arise from strong non-adiabatic couplings between states near to the dissociation limit. These resonances are expected to be manifested experimentally as extra lines in laser photodissociation spectra of CH+ [ 12,131. In spectroscopic terminology, multichannel resonances are predissociated “quasibound” levels which are mixed with levels (resonances) of

1. Introduction Laser photofragment spectra of CH+ obtained using fast-ion beams have been described in a number of papers [ l-8 1. A substantial part of the visible photodissociation spectrum has been spectroscopically assigned to transitions between the X ‘C+ ground electronic state and quasibound levels of the A ‘II state [3,7]; additional lines near 350 [2] and 540 nm [ 3 ] have been reported but have not been defmitively assigned. In this paper we discuss the origin of the 540 nm lines and present evidence for our interpretation. We propose that they are due to electronic transitions involving a previously unobserved electronic state which possesses a long-range potential energy minimum. The shallow potential energy well of this state arises principally from the attractive longrange ion-induced-dipole and charge-quadrupole interactions between an ion and a neutral atom combined with shorter-range repulsive behaviour. We also suggest that at least some of the lines observed near 3 50 nm [ 2 ] have a similar origin. Interest in the CH+ molecular ion stems from many sources; it is a six-electron molecule which is amenable to high-quality ab initio calculations of its electronic structure, three electronic band systems have been identified and it is one of the most important 0301-0104/88/$ ( North-Holland

03.50 0 Elsevier Science Publishers Physics Publishing Division )

B.V.

440

P.J. Sarre, C.J. Whitham /Electronic spectra of CH’

other electronic states by non-adiabatic interactions. The large number of additional lines near 540 and 350 nm have been considered as possible examples of excitations to multichannel resonances [ 2,7,12, 13 1. In this paper we argue that this is not the case and describe a new interpretation for the spectra [ 8,141. However, we emphasize that optical transitions to multichannel resonances have been definitively identified in spectra of SiH+ [ 8,15,16 ] and in another region of the photodissociation spectrum of 13CH+ [ 161.

2. Experimental background All of the experimental work discussed here has been carried out with fast-ion-beam apparatus of very similar design. A brief outline is given in order to provide the necessary background to the theoretical aspects of this paper; further details are given in refs. [ 6,7,17,18]. In each experiment, a mass-selected beam of CH+ with a few keV energy is irradiated coaxially with a continuous wave laser. Resonant excitation of CH+ ions is achieved either by tuning the laser wavelength [ 3,7,8] or Doppler (velocity) tuning [ 1,2,4,6] the ion beam into resonance with fixed frequency laser lines. Photodissociation of CH+ results in the formation of C+ ions which are separated from the parent CH+ beam with a small electromagnet [ 7,18 ] or an electrostatic energy analyser [ 3,6,8 1. Measurement of the centre-of-mass translational energy release is achieved by scanning the electrostatic analyser. Important features of these experiments include the unambiguous identification of the parent molecule, the generation of extremely “hot” ions, the high spectroscopic resolution arising from the effect of kinematic compression in fast-ion beams and the “amplification” in the transformation from the centre-of-mass to laboratory frame which enables very small kinetic energy releases to be recorded. The sensitivity is exceedingly high because of the (almost) unit efficiency for detection of C+ fragment ions. In most cases fast-ion-beam instruments have been used in applications where laser excitation to predissociated levels is observed by detection of photoproduct ions. The interpretation given in this paper for the origin of the CH+ spectra near to 540 nm (and 350 nm) involves bound-bound laser excitation fol-

lowed by fluoresence and dissociation new possibilities for the fast-ion-beam

and opens up technique.

3. Experimental observations In 1980, fast-ion-beam laser photofragment spectra of CH+ in the region near 350 nm were reported in a paper by Cosby et al. [ 21. Thirty-seven lines were recorded in ten spectral regions about 7- 10 cm- ’ in length by Doppler tuning CH+ absorption lines into resonance with the ultraviolet lines of argon and krypton ion lasers. Since that time a few of the lines have been assigned to transitions in the A ‘II-X ‘xc+ system involving shape resonances of the ‘l-l state [ 3 1, but the origin of the remaining lines has not been settled. The most striking aspects of the observations are the relatively high density of lines and the low translational energies of the C+ fragment ions which were measured to be less than 40 meV in the centre-of-mass frame. The results were tentatively interpreted in terms of laser excitation to predissociated levels of CH+ which lie just above the C’(‘P) +H(2S) dissociation limit, The unexpected line density was attributed to two near-threshold characteristics of CH+; it was noted that transitions to A ‘l-l energy levels lying between the C+(2P3/2)+H(2S) and C+(2P,,2) +H( 2S) dissociation limits would contribute to the photodissociation spectrum and secondly it was recognised that non-adiabatic interactions mix the electronic states substantially near to dissociation and so excitation to “dark” states would give rise to additional transitions [ 2 1. Alternative explanations were discussed in the same paper including laser excitation in the (0,O) band of the b 3Z--a 311system, followed by radiative decay into the continuum just above the C+ ( ‘P ) + H ( ‘S ) dissociation limit [ 2 1. An additional observation was described in a later publication [ 191; it was reported that the energy releases associated with laser excitation in some of the welldefined spectroscopic lines were not discrete, but rather kinetic energy release distributions of around 20 meV were found. This result is incompatible with an interpretation based on laser excitation from the ground state of CH+ to near-threshold quasibound levels which have spectroscopically determined energy widths of about 1 peV, but it lent support to the interpretation of the lines in terms of the bound-

P. J. Sarre, C. J. Whitham /Electronic spectra of CH +

bound b 3X--a 311 transition followed by radiative decay into continuum levels [ 19 1. The only study of the (0,O) band of the b ‘C--a 311 system was carried out at moderate spectroscopic resolution [ 201. While it is clear that there are rotational lines of the (0, 0) band in the same region as observed in the laser photofragment study, we have not been able to establish if there is a one-to-one matching between the lines from the two experiments. However, we have calculated the Franck-Condon factors for the bound-free emission transition and they are sufficiently low to cast some doubt on this being the origin of the lines. A high-resolution study of the (0, 0) emission band would answer this question definitively. An altemative explanation for their spectroscopic origin has been proposed [ 141 and is described in this paper. Further lines have been observed in the 350 nm region with corresponding kinetic energy releases of l2 eV [ 2,19 1. These are almost certainly due to transitions from the a 311 state to fairly high vibrational levels of the b ‘C- state [ 2,191 which are predissociated by the repulsive part of the c 3C+ state and are not relevant to the problem considered here. Photodissociation spectra discovered near 540 nm [ 3 ] possess many of the same characteristics as those just described for the 350 nm lines. The low ( w 1 cm-’ ) resolution (Doppler-doubled) spectrum consists of a very high density of lines extending from about 18350 cm-’ to at least 19600 cm-’ and the kinetic energy releases are predominantly less than 20 meV [ 3 1. In a high-resolution study of the region between 18350 cm-’ and 18708 cm- ’ using a singlemode laser, we were able to confirm the high density of lines and found that many of them exhibited proton nuclear hyperfine splittings of up to 600 MHz [ 7,8]. This splitting is a strong indication that at least one of the states involved in the transition has triplet character. We argued earlier [ 7 ] that the origin of the transitions near 540 nm was excitation from the ground electronic state to heavily mixed near-threshold levels with triplet character, as first discussed by Cosby et al. in connection with the lines near 350 nm [ 21. More recently, we found that lines of 13CH+ and CD+ also appear in the same region near 540 nm [ 81. This is a surprising result because isotopic substitution normally induces substantial shifts in the spectral lines. In a qualitative sense, the experimental data on the

441

lines in the 540 nm (and 350 nm) regions appear to have many of the characteristics of theoretically predicted near-threshold “multichannel resonance” spectra of CH+ [ 12,13 ] including a comparatively high line density, low kinetic energy releases and, in the case of the 540 nm lines, proton nuclear hyperfine splittings arising from triplet character in the electronic wavefunction [ 7 1. In this paper we argue that the transitions near 540 nm do not arise from excitation to multichannel resonances and propose that their origin lies in completely new electronic band systems. We also discuss the proposal [ 141 that at least some of the lines near 350 nm have a similar origin.

4. Origin of the lines in the 540 nm (and 350 nm) regions The heart of this paper is concerned with a new interpretation of the unassigned laser photofragment data on CH+. The principal observations requiring rationalisation are: high densities of lines which appear only in these two regions of the spectrum, low C+ kinetic energy release distributions associated with excitation in these lines and proton nuclear hyperflne splittings of up to 600 MHz in the 540 nm lines. The key to our interpretation of the origin of the 540 nm spectra is recognition that the 540 nm wavelength corresponds closely to the energy separation between the C+ (*P) + H( ‘S) dissociation limit and the higherlying C( 3P) +H+ limit as shown in fig. 1. Laser excitation from energy levels just below the C+ (‘P) + H (*S) dissociation threshold to bound levels just below the higher-lying limit necessarily lies in the observed wavelength region. Part of the spectrum near 540 nm recorded at high resolution in our laboratory is shown in fig. 2. Considering the origin of the 540 nm transitions first, fig. 1 shows that the d 311 and b 3C- states correlate with C ( 3P ) and a proton. At short internuclear separation the d 311 state is repulsive while the b 3Estate is strongly bound and forms the upper state of the b-a system [ 201. However, at long range the form of the potential energy for the d 311 and b 3Z- states is dominated by the ion-induced-dipole and chargequadrupole terms which may be written:

P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

442

C(3P)+ H+

_

C+(z~) + H&S)

; Internuclear separation /A

Fig. 1. Potential energy curves for CH+ correlating to the first three dissociation limits (reproduced with permission from ref. [14].Thecurvesarefrom:X,A[12],B,CandD[21],a[12], b [22], c [23] and d [22]. the c, d, Band D states all have shallow wells with minima at about 3.5 A. The electronic transitions near 540 nm (and proposed near 350 nm) are shown.

V(r)=-C4/r4+C3/r3. The first term is attractive for both states, while the sign of C, (which involves the carbon atom quadrupole moment) is positive for the b 3E- state and negative for the d 311 state [ 221. Consequently, the d 311

state possesses a small potential energy minimum at long range while the b 3C- state has a maximum (see fig. 1). The d 311 state is repulsive at shorter internuclear separation due to an avoided crossing with the lower-lying a ‘II state which would correlate to the C (‘P) -l-H+ dissociation limit if its dominant electronic configuration at the equilibrium bond length were maintained at all values of the internuclear separation. Just below the C+ (2P) + H ( 2S) limit, there are high vibrational levels ofthe X ‘2+, A ‘II and a 311 states and also a few vibrational levels of the c 3C+ minimum (which also arises from the long-range attractive ion-induced-dipole form of the potential). Laser excitation from the near-threshold triplet levels to the bound levels of the d 311 state is fully allowed according to electric dipole selection rules and has good Franck-Condon factors (see section 5). However, the electronic transition moments have not been calculated and may have a strong effect on the spectrum. The relative importance of excitation from the a 311 and c 3Z+ states is addressed in section 5. Radiative decay from the d 311 state occurs to the bound triplet levels just below the lower limit and also to the continua of the triplet states. The latter decay route results in fragmentation of the molecule into C+ and a hydrogen atom. Detection of the C+ ions then allows the bound-bound spectrum to be recorded. It is only those energy levels near to the dissociation limits which can contribute to the spectrum because of the necessity for good Franck-Condon factors for both the excitation (bound-bound) and emission (bound-free) steps. The origin of the low kinetic energy release distributions is examined in

18595

18585

18575

Wavenumher I cm.’ Fig. 2. Part of the spectrum

near 540 nm recorded

at high resolution.

The spectrum

is notable for the high density of rotational

lines.

P.J. Save, C.J. Whitham /Electronic spectra of CH +

detail in the following section; in general terms the energy release is low because it is necessary to conserve nuclear position and momentum in the electronic transition to the lower state continua and a small distribution of energies is observed because the lower state is not discrete. The nuclear hyperfine interaction which gives rise to the splittings in many of the 540 nm lines is a reflection of the electron spin density at the proton. The origin and magnitude of this effect in the high levels of the a % state have already been described in detail [ 6,7 ] and the effect on the spectrum is shown in fig. 8 of ref. [ 8 1. In qualitative terms, the hypertine splittings in the rotational lines arise because there is a large Fermi contact interaction in the lower triplet states and a negligible interaction in the excited d 311 state which approximates to a carbon atom loosely bound to a bare proton. Following this discussion on the 540 nm lines, we propose that at least some of the lines near 350 nm arise from excitation from the singlet states just below the C+ + H limit to weakly bound long-range singlet electronic states which correlate to the C( ‘D) + H+ dissociation asymptote. Recent ab initio calculations [ 2 1 ] show that the C ‘C+ and D ‘l-J states possess long-range minima with well depths of z 1200 cm-’ while the B ‘A state does not (see fig. 1) . If the separation between the C+ (‘P ) + H ( 2S ) and C( ‘D) +H+ limits is taken to be 29050 cm-‘, then for a vibrational level of an excited singlet state which lies 1000 cm-’ below the C( ‘D) +H+ limit and excitation from a vibrational level lying 400 cm-’ below the lowest dissociation limit, transitions near to 28450 cm-’ are predicted. This is exactly the region in which lines are found in the experiment [ 2 1. Four overlapping electronic band systems are expected, namely C ‘x+-X ‘Z+, C ‘x+-A ‘II, D ‘II-X ‘C+ and D ‘II-A ‘l-I so the line density is expected to be quite high. However, not all of the transitions have high transition moments in the region of internuclear separation of interest. The C ‘x+-X ‘Z+ transition is calculated to have a very high oscillator strength, while the D ‘II-X ‘C+ transition is predicted to be very weak at large internuclear separation [ 241. The contribution of excitation from the A ‘II state is dependent on the fluorescence lifetimes for A ‘II-X ‘C+ decay from high-lying vibrational levels. These have not been measured but they are probably sufficiently

443

long that these levels are populated in the laser interaction region. The kinetic energy release distributions will be very similar to those for the triplet transitions but in this case radiative decay will occur to the continua of the A ‘II and X ‘C+ states. NO observation of hyperfine splittings in the 350 nm lines has been reported [ 2 ] and would not be expected to be observed in singlet electronic band systems. We conclude this section with three general comments. First, in qualitative terms the high density of lines arises from the relatively small rotational constants for the vibrational levels involved in the ground and excited states. The energy level structure of the triplet levels has been calculated and is described in detail in the next section. Secondly, both of the transitons involve charge transfer between the two atoms and so in principle the oscillator strength is expected to be fairly high - at least for those excitations which involve electron transfer along the bond. A calculation of the r-dependent electronic transition moments for all of the electronic transitions would be of considerable interest. Finally, in order to observe the 540 nm (or 350 nm) spectra, it is necessary to generate CH+ ions with population in vibrational levels which lie about 4 eV above the potential energy minimum of the ground state. In fact the formation of “hot” ions in the electron-impact ionisation/fragmentation process of larger precursors is well known. Additional evidence for high rovibronic excitation in the case of the near-threshold levels of CH+ is provided by the study of the infrared photodissociation spectrum of CH+ [ 6 1. In this work it was found that infrared laser excitation occurred from levels within about 1000 cm-’ of the C+ (‘P) +H ( 2S) dissociation limit and almost certainly covering the range of levels from v= 7 to 12 and J=20 to 40 in the a ‘IT state. As the apparatus used in ref. [ 61 is very similar to that employed in the visible/ultraviolet photodissociation studies, there can be little doubt that highlying rovibrational levels are also populated in the experiments discussed here. We have not yet accomplished a vibrational and rotational assignment of the lines in either the 350 nm or 540 nm spectral regions. It is extremely unlikely that this will be possible for the data in the 350 nm region without observation of more lines. As part of our effort to assign the spectra in the 540 nm region, we have undertaken a number of calculations

444

P.J. Sarre, C.J. Whitham /Electronic spectra of CH’

which support our explanation for the origin of the spectra and reveal some of the interesting features of transitions which occur between electronic states at very large internuclear separation. These are now described.

5. Theory relating to the triplet transitions near 540 nm In this section we describe calculations of the energy levels of the a 311, c 3C+ and d 311 states, the vibrational band intensities and the translational energy releases which provide support for our interpretation of the origin of the spectrum. The approach is based on the information on the potential energy curves obtained from ab initio calculations. 5.1. Calculation of energy levels of the triplet states

close to their dissociation limits Near to the threshold for dissociation of a molecule into fragments possessing electronic angular momentum, it is important to take the effect of nonadiabatic interactions such as spin-orbit coupling into account. This applies to the problem considered here because both the carbon atom and the carbon ion carry electronic angular momentum. There are two lower (2P,,2 and 2P3,2) and three higher (3P2, ‘P1 and 3P0) fine structure dissociation limits when spinorbit coupling is included. By contrast, this asymptotic behaviour is of little interest when considering electronic transitions involving the inner parts of deep wells because the electronic angular momentum is usually quantised in the molecule-fixed frame. In these new CH+ electronic spectra at least some of the vibrational bands are expected to involve energy levels which lie in the recoupling region between the atomic and molecular limits. Considering first the well-isolated bound states such as the X ‘C+, A ‘II and a 311 states near to their potential energy minima and neglecting magnetic interactions, the r-dependent rovibronic wavefunction can be written:

(1)

where Jo is the total angular momentum of CH+, MO is its projection in the space-fixed frame, Q is its projection in the molecule-fixed frame, xvoJ,,(r) is the rovibrational wavefunction and IASZ) is the electronic wavefunction in a Hund’s case (a) basis and the notation of ref. [ 12 ] is employed. The wavefunction v. is an eigenfunction of the Hamiltonian, Ho(r)=&,,(r)

+ rnuc(r)

(2)

,

where in the adiabatic Born-Oppenheimer (ABO) approximation, the case (a) functions are eigenfunctions of Helec with eigenvalues V,,,(r). The rovibrational wavefunctions are then solutions to

fi2 1 a2

(

r+

2~ r ar2

8

-+ 2,ar2 b30(r) >xU,,Ar)

=ExDo,dr) .

(3)

This approach will fail for the determination of energy levels near to a dissociation threshold where more than one Born-Oppenheimer potential surface correlates to the same dissociation limit such as the dissociation asymptotes of CH +. We have used the methods employed by Freed and co-workers [ 12,13,25-271 in order to determine rotationally adiabatic (relativistic) potentials in the near-threshold region. The use of rotationally adiabatic potentials in this type of problem has been discussed in earlier work on CH+ [ 6,9]. Spin-orbit and Coriolis interactions are incorporated naturally and the correct asymptotic behaviour of the potentials is reproduced. The formalism draws heavily on theory developed for the calculation of scattering resonances and highlights the strong relationship between near-threshold bound levels and quasibound levels. The Hamiltonian for the problem is taken to be, G(r)

= T(r) +K,,,(r)

+&Jr)

,

(4)

where the spin-orbit Hamiltonian H,, is explicitly included but smaller terms such as the spin-spin and nuclear hyperfine interactions are omitted. The Coriolis term emerges when the nuclear kinetic energy operator is separated into radial and angular parts. Rather than solving the full Schriidinger equation for the problem, our aim is to determine diagonalised rdependent potential energy curves and to use these to determine the approximate eigenvalues for the

445

P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

rovibronic levels. In outline, the first step is to introduce a parity-defined basis )JMASZp) formed from a linear combination of molecule-fixed Hund’s case (a) basis functions,

x [Dk2(% +(-I)

A Y) IASG

p+J-sD$

_&a,

A y) 1-AS-C)

1.

(5)

These functions diagonalise Helec( r) for all values of r. For the C+ (‘P) + H (‘S) limit there are twelve basis functions which fall into two parity blocks, one containing X ‘E+, A ‘II, a 3112,1,. and c %:, the other containing A ‘II, a 3TI2,,,0 and c 3C[0. Similarly, the states correlating to the C ( 3P) + H+ limit are separable into two blocks containing d 3112,1,o, b 3Zi- and d 3112,1,o,b 3CI,~ respectively. A second basis is introduced which is termed an “atomic” or “asymptotic molecular” basis,

IJWtic+_h>

(6)

r+oc, .

We note that the electronic angular momenta of the separated atoms form part of this representation in which j=jc+ + jH,the quantum number 1 describes the rotation of the nuclei about their centre-of-mass, p is the component of I in the space-fixed frame and Y,,(i) are spherical harmonics. The heart of the theory relies on recognising that for r-+cc the case (a) wavefunctions are related to the asymptotic electronic wavefunctions through ]/iSZ) = I Ic+&+

) I I”AH ) ISC) .

(7)

Substitution of (7) into (5) and comparison of (5) with (6) for large r yields the elements of the transformation matrix T, (JMj&+ j, IJMASCp)

,

(8)

which are given explicitly in ref. [26]. The total Hamiltonian may be written in either an “atomic” or a “molecular” basis, and the full solutions to the Schrijdinger equation in the asymptotic basis are obtained from

2

-LILr+T 2~ r ar*

=E(rMr)

V,,,(r)

,

Tt+ (9)

where r,u(r) is either a multichannel continuum wavefunction for unbound states [ 121 or a wavefunction for a bound level in this case. The diagonal matrix &,, contains the elements of the spin-orbit operator in the asymptotic basis and E is defined to be zero at the barycentre of the fine structure atomic states. In preference to solving this equation, we have taken the following terms, TV,,,(r)

Tt+-

I2 +d 2,ur2 So

(10)

and evaluated the r-dependent diagonalised (adiabatic-rotational-electronic) potentials for each value of J and parity. For the C+ (‘P) + H (*S) limit each parity and J involve a 6 x 6 matrix and for the C( 3P) + H+ limit the parity blocks have dimensions of 4 x 4 and 5 x 5. The eigenvalues for nuclear motion on these surfaces are then determined by solving the radial Schriidinger equation using a program of LeRoy [ 28 1. This procedure is very much quicker than solving eq. (9), but it neglects the coupling between states induced by the radial nuclear kinetic energy operator. Also, it should be noted that the matrix elements of the spin-orbit and Coriolis operators are treated as constant though in reality they have some dependence on internuclear separation [ 13 1. This approximation is widely used in scattering calculations and is not likely to be too serious a problem for energy levels which lie close to the dissociation asymptote. In spite of these reservations, the calculated rovibronic energy levels will be a good approximation to those obtained from a complete solution to the Schriidinger equation and will only be poor when there is near-degeneracy of levels of the same J and parity which are strongly coupled by the radial kinetic energy operator. For the ABO potential of the a ‘II state we used the potential described in ref. [ 121. Up to u= 15, which lies 600 cm-’ below the dissociation asymptote, the vibrational energy levels obtained including the spinorbit and Coriolis coupling are in reasonable agreement with those obtaining using the ABO potential alone. Beyond this point the vibrational levels from

P.J. Sarre, C.J. Whitham /Electronic spectra of CH’

446

the two calculations disagree markedly. For example, two additional bound vibrational levels, v= 18 and 19, are supported on the 311; surface following the diagonalisation (see fig. 3 ). (The labelling of the ‘II components is the asymptotic labelling given in fig. 4 of ref. [ 29 ] and is discussed in ref. [ 121. ) It is emphasised that the uncertainty in the potential is large enough to change the energies of the calculated levels significantly and even the total number of vibrational levels cannot be stated with confidence. Nevertheless, it is valuable to conduct these calculations as a guide to the near-threshold behaviour of CH+. The calculated rotational energy levels for v= 15 and v= 17 are given in figs. 4a and 4b. The levels of v= 17 clearly show the onset of “atomic” character in which the spin-orbit splitting of 63.4 cm-’ in C+ has a pronounced effect on the energy level structure. In particular the 31%,and ‘IIf, components correlate to different fine-structure limits. The lambda-doublet splitting in the 311, stack is strongly influenced by an avoided crossing between the 311E and 311; components. The effect of spin-orbit coupling on the potential energy curves in the nearthreshold region has also recently been examined by calculation of the spin-orbit matrix elements between the states [ 2 11. The rotational levels of v= 15

52

j

4

j

i

i

i

!i

lb

Internuclear separation I A Fig. 3. Potential energy curves of the a ‘II and c ‘X+ states near to the two dissociation asymptotes, C’ (2P,,2) +H(‘S) and C+ ( ‘Pj,z) + H (*S). The rotationally adiabatic potential energy curves and vibrational energy levels of only two components of the a ‘II state are shown, ‘H; (upper) and ‘LI; (lower). The effect of spin-orbit coupling on the c %+ curve is not included.

show the more usual pattern of components in a 311 state. Laser excitation may also occur from the bound levels of the c 3C+ state to the d 311 state. The c 3C+ well is calculated [23] to be about 200 cm-’ deep with an equilibrium internuclear separation of 3.5 A. As all of the components of this state correlate to the upper C+ (‘P3/2) limit, the rovibrational energy levels are not particularly unusual and are not reported here. In order for excitation from the c 3Z+ state to contribute to the 540 nm spectrum, it must be populated in the ion source. It is not clear how this could occur but the possibility cannot be ruled out. It is unfortunate that the analysis of the spectra may be further complicated by the overlapping of d 3II-a 311and d 3II-c ‘C+ electronic transitions. The potential for the d 311state has been calculated by Levy et al. [ 22 ] and has a potential energy minimum at 3.44 8, of 710 cm-‘. The vibrational and rotational levels of the d 311 state were calculated in a similar manner and those for v= 1 are shown in fig. 5. The energy levels are consistent with those of a normal 311energy level pattern. The rotational branch structure of the electronic transitions has been calculated from these energy levels. For excitation from v= 17, 18 and 19 of the a 311 state, the pattern is predicted to be markedly different from a transition between ‘II states near to the bottom of their potential energy wells but we reserve futher comment on this aspect of the spectrum until a rotational analysis has been accomplished. Finally, we suggest that a calculation the electronic transition moments would be of interest. If the situation for the singlet-singlet transitions [ 241 is mirrored for the triplet systems, the II-E transition will be very weak. However it should be noted that nonadiabatic mixing of the states at an internuclear separation as large as 3.5 8, is substantial and would have to be taken into account in the transition moment calculation. 5.2. Vibrational band intensities and kinetic energy releases The intensities of the vibrational bands of the d 311a 311and d 311-c 3X+ transitions depend on the vibrational populations in the lower levels, the r-dependent electronic transition moments and the product

447

P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

0

87

7-

6

6= I

s-

6-

8_

-50

7

5-

48-

g .

4-

5-77

l..

I 76-

4-

5=

4-6_

2 5-

2-

6_ 3-

3-

4B

3-

4

5

-100

2-55-

4-

2-

3E

44-

2-

3-

3 322-

‘n,

‘HI a

‘4

‘i$

‘% b

v=

1.5

‘l-4

‘3

Y = 17

Fig. 4. Calculated rotational energy levels for (a) U= 15and (b) u= 17 levels of the a ‘II state for J> I. The influence of the atomic spinorbit splitting of 63.4 cm-’ is clear for v= 17 which lies in the region of angular momentum recoupling, while the U= 15 level has an energy level pattern corresponding to the “molecular” limit.

of the Franck-Condon factors for laser excitation and emission to the lower-state continua. At present we have no information on the first two of these, although the parallel transition wiil probably be substantially stronger than the pe~endicular excitation. However, the Franck-Condon factors are readily evaluated. For the d ‘l&a 311transition, we chose to calculate the Franck-Condon factors for excitation from vibrational levels of the a “TIg rotationally adiabatic potential. For the c 31c+ state, the non-adiabatic effects are less impo~ant and the ABO c-state potential was used. The vibrational bands lie close to the wavelength corresponding to the separation between the two lowest dissociation limits. (For completeness the b3C--a 3TI band intensities for excitation to near-threshold vibrational levels of the

b 32- state were also evaluated and found to be negligibly small. ) Emission from the d jlT state can occur to the continua of both the c 3P and a ‘II states even though the a 3fJ state does not have a repulsive potential energy curve in the region vertically below the d 31Tstate. The probabilities (Franck-Condon factors) for emission from vibrational levels of d 3fI to both of the lower continua are given in table 1. These were determined by calculating the Franck-Condon factors between a given upper vibrational level and all of the bound levels of a given lower electronic state, and recognising that the sum of all the Franck-Condon factors is unity when the continuum contribution is included. The Franck-Condon factors are quite sensitive to the form of the potential in the near-

P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

448

-300 I-

6-

7-

-350 -

7 5

’

5-

6-

7= 4-

sg

6B

2-

S-

3-

2 3

3-

4;

1 5

_4@j

-

2-

43Y 2-

-450

3n2

3n1

3bl

-

V=l

Fig. 5. Rotational energy levels for v= I (J> 1) of the d ‘TTstate calculated from the diagonalised potentials.

threshold region because this determines the number and the energies of bound levels. The results in table 1 show that, in favourable cases, the probability of a transition to the continuum can be over 50%. This helps to explain why the spectrum can be observed; the populations of vibration-rotation levels which lie just below the dissociation limit are certainly very low, but laser excitation in a rotational line results in the production of a fragment C+ ion with a relatively high probability of up to 0.7, the value depending on the vibrational level of the excited state. This assumes that the fluoresence lifetime of the d 311state is short compared with the flight time in the apparatus. This is likely to be so because the transition is of the charge-

transfer type but it is not possible to be definitive on this point. The overall band intensities for both d-a and d-c excitation followed by emission to the C+ + H continuum are given in figs. 6a and 6b respectively. The relative importance of the two lower-state continua is critically dependent on the electronic transition moments which may differ markedly as indicated earlier. Comparison of the predicted band structures in fig. 6 with the stick spectrum of our recorded data given in fig. 7 shows that the wavelength range of the predicted spectrum is approximately correct. It is known that the spectrum extends to at least 19600 cm-’ [ 3 ] but we have not yet recorded this region at high resolution. It is clear from fig. 6 that the lines which are reported to occur at wavenumbers above 19000 cm- ’ (up to 19600 cm-’ [ 31) must be due to excitation from vibrational levels of the a 3Tl state. Within our overall interpretation, this provides evidence that excitation from the a 311 state occurs and forms part of the spectrum. Fig. 6 shows that the predicted intensity beyond about 18900 cm- ’ is very low in comparison with that in the 18500- 18900 cm- ’ region in apparent contradiction with the reported observation that the spectrum extends to above 19600 cm- ’ with comparable intensity [ 31. We suggest that this is due to the likely increase in the vibrational level populations with decrease in vibrational quantum number which is not included in fig. 6. It is difficult to assess if excitation from the c 3C+ state is important and it is quite possible that its contribution to the spectrum is negligible. A lower limit to the low-frequency cut-off in the spectrum is determined by the depth of the d 311well and should be near to the value of IP(C)-IP(H)-&(d

311)=18250cm-‘.

This is close to the value observed in our work and in the low-resolution study [ 3 1. The high-frequency cut-

Table I Calculated Franck-Condon factors for emission from different vibrational levels of the d ‘II state to the continua of the a ‘II; and c ‘IX+ states. The values were obtained by calculating the Franck-Condon factors for emission to all bound vibrational levels of the two lower states and using the fact that the sum of all Franck-Condon factors must be unity

aW CG

u’ =o

v’ = 1

v’ =2

V’=3

VP=4

u) = 5

0.02 0.02

0.05 0.29

0.28 0.66

0.50 0.59

0.66 0.60

0.60 0.60

449

P.J. Sarre. C.J. Whitham /Electronic spectra of CH+

j

wavelength dependence of the bound-free emission probability. Using a computer program of LeRoy [ 301, we have computed the emission profiles (C+ energy releases) for fluorescent decay from the vibrational levels of the d 311 state to the c 3E+ and a ‘II continua. The results are shown in fig. 8. It is found that the mean centre-of-mass energy releases are low and that the centre-of-mass peak shapes are characteristic of a distribution of energy releases, although the exact form is critically dependent on the shape of the potential in the near-threshold region. It is of interest to note that the fwhm of the energy release profile depends on the vibrational quantum number of the excited state. This should be of value in achieving

Wavenumber /cm-l

Fig. 6. Calculated vibrational band structure for the laser photofragment C+ detection of (a) the d ‘lI-a ‘TI& and (b) the d ac ‘X+ bound-bound-free transitions. Radiative decay to the continua of both a ‘TI; and c ‘X+ states is included. The separation between the dissociation limits of 18858 cm-’ is marked with a dotted line.

is not likely to be as sharp and the intensity to shorter wavelengths will be determined by a combination of the poorer Franck-Condon factors but higher vibrational populations for excitation from vibrational levels of the a 311 state which lie progressively deeper into the a ‘II well. The calculation of the kinetic energy release into the C+ fragments is equivalent to evaluation of the off

18300

18400

185CO

18700

Fig. 7. Stick diagram of the rotational lines recorded in our laboratory at high resolution in the 18350-18730 cm-’ region.

0

7

loo

200

300 C+ ‘energy’

400

500

floe

700

/ cm“

Fig. 8. Calculated kinetic energy release profiles in the mass frame for C+ resulting from radiative decay of and 2 levels of the d ‘TI state to the continua of the (a) (b) c ‘Z+ states. In each case a distribution of kinetic leases is obtained.

centre-ofthe v’ = 1 a ‘II; and energy re-

450

P.J. Sarre, C.J. Whitham /Electronic spectra of CH’

a vibrational and rotational assignment of the spectrum. The results of these calculations provide strong support for our interpretation of the origin of the 540 nm lines. We propose that at least some of the lines near 350 nm [2] are very similar in origin but involve excitation from levels of the X ‘Z+ and A ‘II states to levels just below the C( ID) +H+ Iimit. Radiative decay will occur to the continua of the singlet states from which the molecule was initially excited, but again only to the region just above the C+ (2P) + H ( 2S) dissociation threshold.

6. Conclusion The interpretation of the CH+ photofragment spectra presented here can account for all of the experimental data. One experimental point which remains is the reported observation of variations in linewidth [2,7]. It is unlikely that the fluorescence lifetime is sufficiently short to cause lifetime broadening of up to 700 MHz [ 2,7 ] and we now attribute this effect to power and apparatus-induced broadening in both experiments. The asymmetric line profiles and broad underlying features detected in some of the lines [ 7 ] have now also been observed in transitions between bound and predissociated levels in a number of ions when high laser power is used and must also be considered an instrumental or powerbroadening effect. The long-range minima identified in this paper have much in common with the characteristics of van der Waals molecules while the high vibrational levels of the lower electronic states are of the type discussed by Stwalley [ 311 although modified in this case by non-adiabatic effects (see fig. 3 ). Few examples of weakly bound electronic states have been found spectroscopically in molecular ions although the importance of long-range attractive potentials is widely recognised in ion-molecule reaction chemistry. The closest examples are the electronic emission [ 32-351 and laser photofmgment spectra [ 361 of the mixed rare gas diatomic cations such as HeNe+. In parallel with this work, the weakly bound upper state of the HeNe+ emission spectrum arises from a combination of the long-range ion-atom attraction and shorter-range avoided crossings. The attractive part

of the ab initio potential energy surface for the d 311 state of CH+ has been shown to be well described in terms of the known atomic polarizability and quadrupole moments of the carbon atom [ 221. The repulsive behaviour at shorter range arises from an avoided crossing with the 311state which correlates to the lower Cf (2P) + H ( 2S) dissociation limit. Similar considerations hold for the singlet states which correlate to theC(‘D)+H+limit. The nature of “long-range” vibrational levels near to the top of a deep potential well of a diatomic molecule has been discussed by Stwalley [ 3 1] who also described the probabilities of transitions involving the highest vibrational levels of two electronic states. The strength of the transition in such a case is normally derived from the near-atomic character of the excitation, for example in a system like LiH [ 3 1 ] the excitation is principally an electronic transition on the Li atom. In the case of CH+ the oscillator strength is derived from the charge-transfer nature of the transition. Stwalley also considered the emission probability from a long-range level into the continuum of a lower electronic state [ 311. The vibrational wavefunctions of the weakly bound states of CH+ are similar to those of long-range vibrational levels in that their amplitude is concentrated at large internuclear separation. In order to have a significant transition probability into the continuum, the positions and momenta of the nuclei must be essentially unchanged in the electronic transition. This restriction is satisfied in the bound-free emission from the weakly bound states to the continuum immediately above the dissociation threshold. The possibility of radiative emission in CH+ at “‘long range” has been discussed as a possible process following absorption in the C ‘Z+-X ‘Z+ transition [ 371. The laser-induced bound-bound-fry mechanism (with fragment detection ) , which is invoked here to explain the origin of the spectra, has previously been shown to occur in a study of neutral Hz [ 38-4 11. In this work, neutralisation of a fast ion beam of H,+ leads to formation of H2 in its c ‘II; state. Excitation to higher electronic states is induced with a tunable laser. One of the processes observed is subsequent decay of excited state levels to the continuum of the b 3I;: state and the formation of product hydrogen atoms which are detected. The experiment has revealed a wealth of information on the states of Hz. A

P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

report of the determination of an excited state vibrational wavefunction through measurement of the energy release spectrum of H2 has appeared [ 421. This has a close parallel with the energy release calculations described in this paper although in our case the releases are extremely small compared with the releases of up to 4 eV in the Hz experiment. In conclusion we have discussed evidence that the spectra of CH+ observed in the laser photofragment spectrum close to 540 nm arise from charge-transfer electronic transitions between levels of electronic states which lie just below two of the dissociation limits of CH+. The interpretation we have presented can account for all of the spectroscopic and other experimental data although a spectroscopic assignment of the lines remains to be achieved. The interpretation relies heavily on the existence of a long-range minimum in the d 311electronic state of CH+ as predicted by ab initio calculations. Our explanation of the origin of these new transitions strongly suggests that the lines in the 540 nm region (and possibly also near 350 nm) are not due to laser excitation to “multichannel” resonances just above the C+ (2P) + H (‘S) limit as previously proposed. We are engaged in a rotational analysis of the spectrum in the 540 nm region and aim to record a more substantial part of the spectrum than achieved to date. The work has implications in a variety of fields including molecular spectroscopy, ion-atom collisions and the study of angular momentum recoupling and chemical bond formation. It remains to be seen if these new transitions or potentials of CH+ are also of importance in astrophysics.

Acknowledgement We have benefitted greatly from the interest and guidance of Dr. C.J. Williams and Professor K.F. Freed on the theoretical aspects of the energy level calculations. We thank Dr. H. Helm and Dr. P.C. Cosby for helpful discussions on their experiments and for providing information on the shapes of the 540 nm kinetic energy release peaks, Dr. M. Carre for sending us the data on the triplet band system and Professor R.J. LeRoy for sending us copies of the programs LEVEL and ABSCFT. We thank the SERC, the Research Corporation Trust and the Nuffield

451

Foundation for research grants. PJS thanks the Nuffield Foundation for a Science Research Fellowship and CJW thanks the SERC and the National Westminster Bank for research studentships.

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P.J. Sarre, C.J. Whitham /Electronic spectra of CH+

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