Photodissociation processes in the HCl moleculeEwine F. van Dishoeck, Marc C. van Hemert, and A. Dalgarno Citation: J. Chem. Phys. 77, 3693 (1982); doi: 10.1063/1.444272 View online: http://dx.doi.org/10.1063/1.444272 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v77/i7 Published by the American Institute of Physics. Related ArticlesCommunication: Branching ratio measurements in the predissociation of 12C16O by time-slice velocity-map ionimaging in the vacuum ultraviolet region J. Chem. Phys. 135, 221101 (2011) Insights into mechanistic photodissociation of chloroacetone from a combination of electronic structurecalculation and molecular dynamics simulation J. Chem. Phys. 135, 194305 (2011) Photodissociation of N2O: Triplet states and triplet channel J. Chem. Phys. 135, 194303 (2011) Photodissociation of methyl iodide embedded in a host-guest complex: A full dimensional (189D) quantumdynamics study of CH3I@resorc[4]arene J. Chem. Phys. 135, 184102 (2011) Ab initio quantum dynamical study of the multi-state nonadiabatic photodissociation of pyrrole J. Chem. Phys. 135, 154310 (2011) Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Photodissociation processes in the HCI molecule Ewine F. van Dishoeck

Sterrewacht, Huygens Laboratorium, University of Leiden, P. O. Box 9513, 2300 RA Leiden, The Netherlands

Marc C. van Hemert

Department of Physical Chemistry, Gorlaeus Laboratories, University of Leiden, p.o. Box 9502, 2300 RA Leiden, The Netherlands

A. Dalgarno

Center for Astrophysics, Cambridge, Massachusetts, 02138 (Received 10 May 1982; accepted 14 June 1982)

Various ab initio methods have been employed for the study of photodissociation processes in the HCI molecule. Potential curves for selected singlet and triplet states and dipole transition moments between singlet states have been calculated. The transition moments vary significantly with internuclear distance for all states studied. The lifetime of the B 1,2' + state is predicted to be 3 ns. The calculations show that photodissociation of Hel occurs by absorption into the repulsive A III state and by absorption into the bound C III state, followed by predissociation. The theoretical photodissociation cross sections for the A III state and oscillator strengths for the C I II state are in good agreement with experimental data. The contributions from other excited states are investigated. The photodissociation rate of HCl in diffuse interstellar clouds is computed.

I. INTRODUCTION

There have been numerous experimental and theoret­ical studies of the photodissociation of neutral diatomic molecules and positive molecular ions but it appears that for no neutral species has a quantitative comparison of the measured cross sections with theoretical predic­tions been possible. Except for processes leading to the production of excited atoms which can be detected by the resulting emission, the end products of the photo­dissociation of neutral molecules are difficult to identify. Because many channels may contribute to the photodis­sociation process, the theoretical analysis often in­volves the study of many excited electronic states, both bound and repulsive, which must be described with com­parable accuracy and for which there occurs a com­petition between radiative decay and dissociation.

The hydrogen chloride molecule HCI is a simple sys­tem for which reliable absorption cross section data existl -3 and for which accurate calculations can be made. Theoretical studies of the excited electronic states·,5 have established that the observed absorption at 1400-1800 A occurs by transitions from the ground X 1~+ state into the repulsive A In state which dissociates directly into ground state products. The absorption spectra6,7 of the strong C In_x 1~+ transition at 1290 A show broadened lines, which indicate that the C In state undergoes predissociation. The absorption oscil­lator strength for the C In_x 1~+ system has recently been determined experimentally.7 Numerous other excited states are known to exist in the 1350-1050 A region, both from experiments2•6,8 and theoretical in­vestigations,5 but the assignments of the observed bands are often uncertain. No calculations of the transition moments, absorption oscillator strengths or photodis­sociation cross sections, which would assist in clarify­ing the interpretation, have been reported.

Hydrogen chloride is a constituent of the terrestrial atmosphere and the atmosphere of Venus. It is pre­dicted to exist in detectable amounts in interstellar

clouds9,10 but searches for it have been able only to place upper limits on its abundance. ll Photodissocia­tion of HCI is the principal destruction process in dif­fuse interstellar clouds and a better understanding of the details of the mechanism will help to locate the source of the discrepancy between the predicted abundances12

and the observed upper limits.

II. COMPUTATIONAL DETAILS

Two sets of calculations were performed, USing com­pletely different program packages. The calculations were of the type recently carried out for the OH mole­cule. 13 The first set of calculations, which we will call the "Gaussian calculation," was carried out USing a package of programs, consisting mainly of the IBMOL v SCF program, interfaced with the Wuppertal­Bonn multireference single- and double-excitation con­figuration interaction (MRD-CI) program series in­cluding configuration selection and energy extrapola­tion. 14,15 The Gaussian atomic orbital (AO) basis set employed for CI was the [78, 5p} basis of Dunning. 16 To this set were added one d function with exponent a = O. 6, one negative ion p function with a = 0.049, and two 8

diffuse functions with a = 0.025 and 0.015, one p with a = 0.020, and one d with a = 0.015. For hydrogen, the (58) primitive set of Huzinaga17 contracted to [38] by Dunning18 was chosen, augmented by one p function with a = 0.75 and one Rydberg 8 function with a = 0.03. In order to calculate the tranSition moments between the various states it was necessary to use a common set of molecular orbitals (MO's) in all subsequent CI's. Sever­al sets of MO's were investigated. CI calculations were carried out with a core conSisting of five MO's, cor­responding to the 1s, 28, and 2p orbitals of CI, which were kept doubly occupied in all configurations. Some test calculations were performed with a core of only one MO, corresponding to the 18 orbital of Cl, to confirm the unimportance of configurations formed by excita­tions out of the 2s and 2p orbitals. Depending on the symmetry, the configuration selection threshold was set

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3694 van Dishoeck, van Hernert, and Dalgarno: Photodissociation of Hel

at 15 or 30 JlH (1 JlH = 2.72 X 10-5 eV) in the calculations, choices which resulted in CI matrices of the order of 3000 configurations. The set of reference configura­tions, typically eight in number, consisted of all con-figurations with final CI coefficients greater than O. 1 12

in any of the states. The calculations were performed in C2v symmetry.

As an independent check on the reliability of the re­sults a second set of calculations was performed using the ALCHEMY package of programs. 18 These programs employ Slater-type AO's and we refer to the calcula-tions as the "Slater calculations." For CI, the [6s, 5p] basis set of Cade and Hu019 was taken with the addition of two 3d functions with exponents 2.0 and 1. 0, two more diffuse 4s and 4p functions with exponents 0.9 and 0.475, and one diffuse 4d function with exponent O. 45. For hydrogen, the basis used in the calculations on OH13 ,20

was employed. Again, several sets of MO's were ex-amined for use in the subsequent CI's. CI matrices consisting of 950 configurations for 1~+ states and 1273 configurations for 1n states were constructed by par­titioning the MO's into core (la, 2a, 3a, h), internal (4a-10a,21T-31T) and external (lla-20a, 41T-101T, 16-26) orbitals. For each symmetry, a reference set was then chosen which included most of the configurations with a CI coefficient greater than O. 1 in the Gaussian calculation for the lowest two states at any internuclear distance. The reference set for the 1~+ symmetry con­sists of

4J5J 21T4

4J5a6a 21T1

4J 6J 21T4

4J5if 21T3 31T

4J5a6a 211"3 311"

4J5a7a 21T4

and for the 1n symmetry of

4J5if6a 21T3

4J5i7a 21T3

4if5a28a 21T3

4J5if9a 2~

TABLE I. SCF and CI energies in hartrees of the ground state at the equilibrium internuclear distance R. = 2. 409 bohr.

Calculation

Gaussian

Slater

Ref. 4

Ref. 5

SCF

-460.0966

-460.1088

- 460. 2582a,c

-460. 1397c

-460.2179

-460.2259

aExtrapolated as described in the text. t>rn all CI calculations a core of five MO's was employed.

cIn the CI calculations the MO's resulting from an a 3n SCF calculation were used.

> ., w

10

8

6

4

2

o~ ______ ~~ ____ ~ ________ ~ __ ~ o 4 6

R(bohr)

FIG. 1. Calculated (extrapolated) MRD-CI potential energy curves for singlet states of HCl.

4if5J10a 2~

4if5a6a7a 21T3

Within the internal space, all single and double excita­tion configurations with respect to the reference con­figurations were taken into account and Single excitations into the external space were included. No configuration selection or energy extrapolation was performed and the calculation was carried out in C"v symmetry.

III. POTENTIAL CURVES

In the calculations, emphasiS was placed on the ac­curate determination of the transition moments. The SCF and CI energies for the ground X 1~+ state at the equilibrium internuclear distance R. = 2.409 bohr21 are presented in Table I. Because of the larger AO basis set the Gaussian calculation gives slightly lower ener­gies compared with other calculations. 4,5 The higher energy resulting from the Slater calculation is due mainly to the CI used.

The potential energy curves are similar to those found in other calculations. 5 Those obtained from the Gauss­ian calculation are presented in Fig. 1 for the 1( X') 12:;+ , 2(B or V) 12:;., 1(A) 1n, 2(C) 1n and 11,6. Singlet states and in Fig. 2 for the 1(a)3rr, 2(b)3n, 1(t)32:;" 232:;+ and 1

3,6.

triplet states of HCI (see Ref. 5 for the nomenclature). The potential curves were obtained using the MO's re-

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van Dishoeck, van Hemert, and Dalgarno: Photodissociation of Hel 3695

> .. w

14

12

10

8

6

4

2

O,L-______ -L~ ____ ~L-______ ~ __ ~ o 2 4

R( bohr) 6

FIG. 2. Calculated (extrapolated) MRD-CI potential energy curves for triplet states of HCl.

sulting from the a 3n(lif2if3if4if5if6ah'21T3) SCF cal­

culation. The energies changed by less than 0.2 eV when the MO's resulting from the A 1n(lif2if3if4if5if 6ah'2~) or 3~+ (lif2if3if4if506ah'21T') SCF calcula­tion were employed. The character of the MO's is simi­lar to that found in earlier studies. '.5 The 5a MOchanges from a HCI bonding orbital at R. to a 3p orbital on CI at large R, while the 6a MO changes from a HCI antibond­ing orbital to a hydrogen s orbital. The 21T MO is mainly a CI 3p orbital, the 7a MO corresponds to a diffuse CI s orbital, while the 8a and 31T MO's have large diffuse CI p orbital contributions. The leading configurations for the singlet states at R" and the most important changes in configurations at larger internuclear dis­tances are shown in Table II. The A 1n and a 3n states can be described by a single configuration, with a CI coefficient greater than O. 97, at all bond lengths. The vertical excitation energies are within 0.2 eV of those obtained by Bettendorff et al. 5 except for the 2 3~+ state. Our calculations place the 2 3~+ state 0.2 eV below the experimental value of 10. 3 eV, ' while the calculations of Bettendorff et al. 5 place it 0.2 eV above the experi­mental value.

The potential curves for the 1~+ and 1n states resulting from the Slater calculation differ slightly from those obtained from the Gaussian calculation. Because of the smaller CI representation, the vertical excitation ener-

gies are too small. especially for states with diffuse character. Similar trends occurred in the computations of the excited states of OH. 13 The computed dissociation energy for the X 1~+ state is 4.2 eV for the Gaussian cal­culation and 3.9 eV for the Slater calculation. The dis­crepancies with the experimental value of 4.62 eV22 are in the expected range. 20 The equilibrium bond length of the X 1~+ state obtained from the Slater calculation is 2.50 bohr and from the Gaussian calculation 2.43 bohr. The measured value is 2.409 bohr. 21 The equilibrium bond length for the C 1n state resulting from the Slater calculation is 2.62 bohr and from the Gaussian calcula­tion 2.68 bohr. The experimental value is 2.55 bohr. 6

Similar discrepancies were found in other theoretical studies. 5

IV. TRANSITION DIPOLE MOMENTS

If rj=(xj,YpZj) denotes the pOSition vector of the ith electron with the Z axis along the line joining the nuclei, the dipole moment D(R) at R in atomic units for a transi­tion between ~ and n states is the matrix element <wI:I(-l/m~ixJ+iYJ)lwn), where wI: and 'itn are the electronic eigenfunctions at R of the ~ and n states, respectively and the summation is over all the electrons. For a ~-~ and a n-n transition, the dipole operator is - ~J Z J' The dipole moment jJ.(R) of a particular elec­tronic state is the expectation value of - ~J Z J at R, referred to the center of charge.

The molecular orbitals used in the CI representation are listed in Table m. These orbitals can be charac­terized by the dipole mom~nt jJ. of the electronic con­figuration involved. The corresponding SC F values for the a 3n, A ln, 2 3~+ and X l~+ states at 2.409 bohr

TABLE II. Principal configurations as functions of internuclear distance.

Leading configuration Leading configurations State at R ;2.409 bohr' at larger distances

X t2;+ .... 4;5; '" 2~ ~b

•••• 4;5(16(1 ••• 21f4

212;+ .... 4;5; ... 2,,331f1 ~ •••• 4;5(16(1 ••• 2~

hQ2 .... 4;5; ... 2~

Aln .... 4hif6(1 ••• 2,(1

Cln .... 4if5;7(1 ... 2,(1 4.75 •••• 4;5(16(17(1 ••• 2,,3

11/1. .... 4;5; ••• 2,(131ft

132;+ .... 4;5; ••• 2,,331f1 2.75 .... 4;5(16(1 ••• 2~

232;+ .... 4;5(16(1 ... 2~ 2.75 .... 4; 5if ••• 2,,3 31ft

a 3n .... 4;5;6(1 ••• 2,,3

b 3U' .... 4;5;7(1 ••• 2,,3

13/1. .... 4;5; ••• 2,(131f1 -

&A core of IJ2Ja¢11r' occurs in all configurations. ~he notation indicates that the change in configuration takes place around 4.0 bohr.

"The notation indicates that the configuration at infinite separa­tion is not yet attained and further changes in configurations take place.

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3696 van Dishoeck, van Hemert, and Dalgarno: Photodissociation of Hel

TABLE III. SCF molecular orbitals used and dipole moments. a

J1. ICF (R = 2. 409) State Configuration a.u.

a 3n 1; 2; 3; 4; 5; 6arrl2~ -1.01

Aln 5i 60"17T4 2rr3 -1.51

23~+ 50" 6 0"1 rr4 2 rr4 -0.47

XI~+ 5; 1hrr4 +0.47b

~he plus sign indicates H+CI- polarity. The values corre­spond to the Gaussian calculation. ~he measured value is + O. 4323 •

are presented in Table ill. The SCF result for the X 1~+ state lies close to the experimental value of + o. 4305 ± O. 0003 a. u. 23

The transition moment from the ground X 1~+ state to the A In state is presented in Fig. 3 as a function of internuclear distance R for the Gaussian and Slater cal­culations. It is a rapidly varying function of R in the Franck-Condon region. The Gaussian and Slater cal­culations agree well apart from a small shift similar to that observed in the ground state potential curves. The values of the transition moment at R. are com­pared in Table N. In the Gaussian calculation the transition moment depends somewhat on the choice of the MO's. The orbitals from the X 1~+ closed-shell configuration appear to be unsuitable, since more reference configurations are needed. The discrepancy between the transition moments resulting from the use of different MO's is reduced in the smaller Slater cal­culation, with the exception of the transition moments obtained using the X 1~+ MO's.

Similar conclusions apply to the transition moments between the X I~+ and C In states and between the A In and C In states, which are displayed in Figs. 4 and 5. The calculations are in satisfactory agreement and pro­duce transition moments which vary rapidly with inter­nuclear distance in the Franck-Condon region.

The transition moments are again sensitive to the choice of MO's in the CI calculations, as Table N demonstrates. Comparable differences between cal­culated transition moments occur for several other

TABLE IV. Transition moments at Rg = 2. 409 bohr.

MO's Size of CI

used Calculation in CI 1~+ states In states A In_x I~+

Gaussian a 3IT 2346 2395 0.3646 2346 3547 0.3714

A In 2242 3581 0.3942 23~+ 2414 3377 0.3483 Xl~+ 2512 3749 0.3903

Slater a 3n 950 1273 0.4217 A In 950 1273 0.4211 23~+ 950 1273 0.4136 Xl~+ 950 1273 0.3668

0.8

0.6

J

C

:::::: 0::

0 0.4

0.2

o.o~ ________ ~~ ______ ~ ______ ~~~~ o

R(bohr) FIG. 3. The calculated transition moment between the X I~+ state and the A In state as a function of internuclear separation. Full line: Gaussian calculation; dotted line: Slater calcula­tion. 0: Gaussian calculation, a 3n MO's; 0: Gaussian calcu­lation, A In MO's; ~: Slater calculation, a 3n MO's; 'V': Slater calculation, A In MO's.

small molecules, such as CO,24 C2, 25 and OH. 13,20 For the A In_x 1~+ transition in the CO molecule, 24 the canonical X 1~+ MO's were also found to be inappropriate for determining the transition moment and differences of up to 30% in the CO transition moment were found if X 1~+ or A In canonical MO's were used, even for CI wave functions containing 10000 configurations. A transformation of the X l:E+ canonical MO's to internally­consistent SCF orbitals brought the values much closer together. 24 For the Swan d 3n,._a 3ny system of C2 the transition moment depends strongly on the size of the CI employed. 25 For the OH molecule the transition mo-

Transition moments

C In_x I~+ C In_A In

0.4612 1.4952 0.5054 1. 2996 0.4765 1.4759 0.5094 1.3186 0.5602 1.3568

0.5408 1.4064 0.5687 1. 3176 0.5199 1. 2762 0.6018 1.1650

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van Dishoeck, van Hemert, and Dalgarno: Photodissociation of HCI 3697

08 c'n_ X'I+

0,6

~ --- -A-

c ::::: a:: 0

0.4

0,2

o,o~ ________ ~-= ________ ~ ________ ~ __ ~ 046

R(bohr)

FIG. 4. The calculated transition moment between the X I E+

state and the C In state as a function of internuclear separation. For explanation of the symbols see Fig. 3.

:3

::i 2 c

a:: o

• /\\

/A \

, I ,

O~--______ L-L-~~~~ ______ ~L-__ ~ o 4 6

R(bohr)

FIG. 5. The calculated transition moment between the A In state and the C In state as a function of internuclear separation. For explanation of the symbols see Fig. 3.

2,0

2II+_XI}; +

1,6

1,2

~

0 ~

a:: 0

0,8

0.4

0,0

° 4 6 8 R(bohr)

FIG. 6. The calculated transition moment between the X I E+

state and the 21E+ state as a function of internuclear separa­tion. For explanation of the symbols see Fig. 3.

ments for the 2~+ states, 20 and other excited states, 13

resulting from three separate calculations agreed within 20%, even though the MO's and the sizes of the CI used were quite different. Increasing the size of the CI in the present Gaussian calculation on HCl for the In states (see Table m) improves the results but still larger CI's are needed to remove the discrepancies resulting from the use of different MO's.

The transition moment connecting the X 1~+ and 2 1~+ states is presented in Fig. 6. Small differences occur between the moments calculated using the A In and a 3n molecular orbitals. The transition moment is small in the Franck-Condon region of the X l~+ state but it in­creases to a large value in the region of the minimum in the outer well near 4. 75 bohr where an avoided crossing of the states occurs. The 2 1~+ state of HCl resembles the C 2~+ and 3 2n states of OH where at large distances a minimum in the potential and a peak in the transition moment coincide at an avoided crossing with a lower­lying state. 13,20

The transition moment between the excited 2 1~+ state and the excited A In state is shown in Fig. 7 as a func­tion of R. The moment is very large in the Franck­Condon region of the ground state but decreases sharply for R greater than about 2. 7 bohr.

We do not have reliable estimates of the transition mo­ments to higher-lying excited states. Preliminary studies suggest that the transition moments from the

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3698 van Dishoeck. van Hemert. and Dalgarno: Photodissociation of Hel

2.0

0.4

't. \

'A.. -6- - -6_ - -t:.- - _ -6-

ooL __ ---.LL_~t:::==::::'...---.L_.__~ o 4 6 8

R(bohr)

FIG. 7. The calculated transition moment between the A I rr state and the 2 I~+ state as a function of internuclear separa­tion. For explanation of the symbols see Fig. 3.

state to the A In state is given by the expression

uu .. (E) = 1. 225 X 10-23 gE I [x •• (R) I D(R) I Xu .. (R)j2 cm2 ,

where g is a degeneracy factor equal to unity for 6 - 6 transitions and to two for 6 - n transitions and Xk' (R) is the final continuum wave function normalized to the asymptotic form

( 2Jl )1/2. ,

X.·(R)- . 1T1i 2k' sm(k R+1)) ,

in which k' = (2JlE)I/2 is the wave number, Jl is the re­duced mass of HCl measured in units of the electron mass, and 1) is a scattering phase.

We obtained Xu" and X.' by numerical integration of the vibrational wave equations20 with several versions of the potential functions. In the evaluation of the ma­trix element [X.' I DI Xu"]' Gaussian and Slater dipole mo­ments D(R) were used. The photodissociation cross sections calculated from Gaussian potential energies and transition moments obtained with a 3n and A In MO's and from Slater potential energies and transition mo­ments obtained with a 3n or A In MO's are presented in Fig. 8. The cross sections differ by not more than 20%. They pass through a maximum value of 4x 10-16

cm2 at a photon energy of 8 eV or a photon wavelength of 1550 A and decrease rapidly at higher energies.

X 16+ state to the 3 16+ and 4 16+ states are quite large 4

in the Franck-Condon region of the ground state and vary rapidly with R. The transition moments to higher In states we find not to be very large but the inclusion of higher Rydberg functions in the basis set may modify this conclusion.

In spectroscopic studies, Douglas and GreeningB have identified three very strong absorption bands comparable in intensity to the C-X band, about 11 eV above the ground state, which they label as the J-X, N-X, and P-X bands. According to Ginter and Ginter6 and Betten-dorff et al. ,5 the J bands are attributable to transitions into the 3 16+' or H 16+ state and the Nand P bands to transitions into higher excited n states, also called K In and M In. Our calculations support the tentative assignment of the J band, and do not exclude those of the N and P bands.

V. PHOTODISSOCIATION OF HCI

The threshold for the photodissociation of HCl occurs at an energy of 4.62 eV or at a wavelength of 2683 A. It is clear from Fig. 1 that photodissociation will occur following absorption into the low-lying repulsive A In state which is accessible at wavelengths shorter than 2683 A by an electric dipole transition from the ground state.

The cross section for the photodissociation of HCl by the absorption of radiation of energy E in hartrees in a transition from the v" vibrational level of the X 16+

3

'" E u

CD

'Q b 2

O~~ ____ -L ________ ~ ______ ~~~~~

6 7 8 10

E(eV)

FIG. 8. Calculated photodissociation cross sections as func­tions of incident photon energy for the A I rr state starting from the X I~+ (v" =0) state. -: calculated using the Gaussian po­tential curves and the Gaussian a 3 rr MO's transition moment function: - -: calculated using the Gaussian potential curves and the Gaussian A Irr MO's transition moment function; - --: calculated usi~ the Slater potential curves and the Slater a 3rr MO's or A rr MO's transition moment function; 0: experi­ment3 • The theoretical cross sections have been sUghtly shifted in energy so as to give equal positions of maxima.

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van Dishoeck, van Hemert, and Dalgarno: Photodissociation of Hel 3699

4

2

I' n \ I,' \ \

V"=I/' \\ , I

I ' I I \ IV"=2

I , \ \ , \ \ \', , \ \ \ .. \\ \\ , \ \\ , \ .. \ \ \\ /-'" , \\

,,"- ..... ")t( ", OLL~~~ __ ~';~_'~'~'~' __ -L~~ __ ~~ ______ ~ __ ~~~'~ 5 6 7 8 9 10

E(eV)

FIG. 9. Calculated photodissociation cross sections as func­tions of incident photon energy for absorption Into the A I IT state. starting from various vibrational levels v " of the X 12;+ state. -: vU=O; --; v"::::l; ---: v ll =2"

Figure 8 includes absorption cross sections measured by Inn3 which are claimed to be more reliable than the earlier data of Romand1 and Myel' and Samson. 2 Satis­factory agreement is obtained between the different theoretical calculations and the measured values below a photon energy of 8.5 eV. Thus, the measured absorp­tion can be definitely identified with a transition to the repulsive A In state which dissociates to ground state hydrogen and chlorine atoms.

A discrepancy between theory and the experiment of Inn3 appears above a photon energy of about 8.5 eV or 1460 A. The repulsive a 3n and 1 3~+ states are located. in the appropriate energy region but absorption into them involves a change in spin multiplicity and cannot be large enough to resolve the discrepancy. We have carried out a careful study of the uncertainties in the calculated po­tential energy curves and they can not explain the dif­ference. It may arise from measurement error. There

TABLE V. Oscillator strengths for the (0-0) band of the C In -X 12;+ system.

X 12;+ potential C 1 n potential Transition curve ~Urve moments

Gaussian Gaussian Gaussian a 3n MO's

Gaussian Gaussian Gaussian A In MO's

Slater Slater Slater a 3n MO's

Slater Slater Slater A In MO's

foo

0.10

0.09

0.13

0.14

Experiment {Ref. 7) (0.185 ± 0.037)

TABLE VI. Calculated oscillator strengths& for the (O-v') bands of the C In...,x 1~+ sys­tem.

v' fD~' A (A)

0 1. 5(-]) 1290.3 2.4(-2) 1247.1

2 2.4(-3) 1209.6 3 6.0(-5) 1175.2

"The values correspond to an RKR potential for the C I n state. an empirical potential26

for the ground state and a dipole moment calculated using A In stater MO's, shifted by - O. lao (see the text).

is a scatter of 35% in the various experiments above 8. 5 eV.

Figure 9 presents the theoretical photodissociation cross sections for absorption from the v" =0, 1, and 2 vibrational levels of the X l~+ state, calculated with the Gaussian potential energies and the transition moment ob­tained from the a 3n MO's. The different shapes re-flect the structure of the initial eigenfunctions.

At higher energies, absorption bands of Hel have been observed. 2,6,8,27 Price"'I observed a sharp absorption band at 1330 A, seen also by Myer and Samson2 and Tilford et al. 6 It has been attributed to a discrete tran­sition into the lowest vibrational level of the b 3n state, which obtains its intensity via spin-orbit coupling with the nearby C In state. We discuss first the allowed absorp­tions into the C In state. The very strong absorption bands from the lowest vibrational level of the X 1~. state into the C In state are located in a progression beginning with the 0-0 band at 1291 A. Their intensities may be characterized by the band absorption oscillator strengths

fov' = ~ gAB 1 [xo(m I D(R) I x." (R)] \2 , where I1E is the transition energy, all quantities are measured in atomic units and g is a degeneracy fac-tor equal to two in this case. We have calculatedfo~' using the various ab initio potential energy curves and dipole moments and the resulting values of foo are pre­sented in Table V. They cluster in the range O. 12 ± O. 03 and are all smaller than the experimental value 0; 185 ± O. 037. 7 The C In_x 1~+ dipole moment is changing rapidly with R and the calculated oscillator strength is sensitive to small shifts of the potential energy curves and transition moment. The slightly large equilibrium bond length of the computed C 1n Gaussian curve may well be the cause of the low calculated oscillator strengths. Nevertheless the discrepancy with the value O. 185 is larger than expected and the theoretical results support a value nearer the lower limit of the experi­mental range.

For absorption in the 1-0 band, we obtain a value of fOl in the range 0.02-0.03 which is consistent with the measured value of O. 022 within the experimental Wlcer­tainty of a factor of two. Table VI lists the values of fa". for v' ::5 3 calculated with an RKR potential for the C In state, an empirical representation of the ground­state potentia126 and the dipole moment obtained with

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3700 van Dishoeck, van Hemert, and Dalgarno: Photodissociation of Hel

the Slater A In MO's, shifted towards smaller R by O. lao because of the difference in the empirical and Slater calculations of the equilibrium internuclear dis­tance of the ground state. If the Slater potential energy curves and the Slater dipole moment are used without any empirical modifications, there results foo = 0.14, fOl = 0.022, f02 =2. 8x 10-3, andf03 =2. Ox 10-4

•

We estimate now the absorption oscillator strength of the forbidden transition into the b 3n state. It is related to the allowed transition by the approximate formula28

where z is a measure of the interaction strength be­tween the b 3n and C In states. The spectroscopic analysis of Tilford and Ginter6 yields a value of about 56 for Z2 so that with an oscillator strength of O. 17 for the transition into the C In state, f(X lE'_b 3II)- 3xlO-3.

Photodissociation occurs following absorption into the C In state. Superposing Fig. 1 and 2 shows that the C In state is crossed by the repulSive 1 3E' state and it will undergo predissociation through spin-orbit coupling. Other triplet states may participate in the process. Experiments indicate that the predissociation of the C In state is very effiCient, the observed linewidths ex­ceeding the radiative-damping widths. 7 A theoretical estimate of the rate for predissociation by the 1 3E' state can be made from the Fermi Golden Rule. USing the calculated potential curves and an estimated spin­orbit interaction of O. 1 eV. a predissociation rate of 1015 S-l is obtained. The C In state may also radiate into the lower lying repulsive A In state. The prob­ability for spontaneous emission into this continuum is calculated20 to be approximately 5 x 106 S_l with the theoretical potentials and transition moments, so the process contributes negligibly to dissociation of the C In state. The b 3n state may decay similarly by predissociations and by radiative transitions to the lower lying repulsive 1 3E' and a 3n states.

Absorption bands at 1236 A and at shorter wave­lengths have been detected by Tilford and Ginter6 and by Douglas and Greening8 and identified by them as a pro­gression in the 2 IE' state. As Fig. 1 shows the 2 IE' state can be regarded as a Single state with a double minimum or as two interacting states. 5 The inner state is the spectroscopic E IE' state and the outer state the spectroscopic V or B IE' state. The E IE' state has a progression of absorption bands beginning at 1194 A. Absorption into the V(B) IE' state has been observed in a very weak progression beginning at 1236 A corresponding to vibrational level v' = 6.8 The computed absorption oscil­lator strengths for the 0-0 band of the X IE' -E IE' transition range from 0.001-0.003. They are con­siderably smaller than the C-X (0-0) band oscillator strength and photodissociation by absorption into the E IE' state is unimportant. Because of the large dif­ferences between the equilibrium separation of the ground state and the location of the minimum of the B IE' state, the absorption oscillator strengths into the vibra­tional levels of the BIZ;' state occupying the outer well of the 2 lZ;' state are extremely small and the bandS with v' :s: 5 have not been detected in absorption.

Many other excited states are observed in experimen­tal studies of absorption by Hel. 6,8 They are mainly Rydberg in character, except for the lower lE+ members where considerable Rydberg-valence mixing occurs. 5

The Rydberg states include the C In state which can be described approximately as the result of the excitation from the 21T orbital to a 4s orbital, 5 though to fit it into the Rydberg series a large quantum defect is needed. An estimate of the absorption oscillator strengths for pure Rydberg states can be derived from the photoioniza­tion cross section. The Hartree-Fock calculations of Faegri and Kelly29 give a cross section at the threshold energy of 12.8 eV30 of about 2.5x10-17 cm2

• Ifn is the principal quantum number of the Rydberg state, the dis­crete oscillator strength is approximately 6. 2/n3

, divided between the accessible Rydberg type lZ;' and In excited states.

The total oscillator strength of the states lying above the C In state may thus be as much as 0.2. The absorp­tion, though strong, may not contribute significantly to the dissociation of the molecule. The excited states are bound and are not crossed by repulsive triplet states. They may decay predominantly in radiative transitions to discrete levels of low-lying electronic states.

Above 12.8 eV photoionization occurs and it is then the principal photodestruction process.

VI. THE RADIATIVE LIFETIME OF THE 2(8) l~+ STATE

Absorptions into low-lying vibrational levels of the outer well of the 2 10+ state, or equivalently the Vor B lZ;+ state, from the v" = 0 level are improbable but emissions from them to high vibrational levels of the X lZ;+ state are not and they have been recorded31 in ex­periments with discharges through hydrogen chlorine vapour.

The excited vibrational levels probably decay pref­erentially by radiating to the XIZ;+ and A In states. Because of the rapid decrease in the 2 IE' -A In dipole moment,' shown in Fig. 7, the probabilities of transition to the A In state will be small and their lifetimes are determined by radiation to the X I Z;+ state.

If Xv,(R) is the vibrational wave function in the B IE+ state and Xv .. (R) is the vibrational wave function in the X l~. state, both normalized to unity, the transition probability A v' v" is given by

Av'v" = 2.03 X 10-6 v!. v" 1 [Xv.(R) 1 D(R) 1 Xv .. (R)] 12 S-l,

where vv'v" is the transition frequency in cm-l• The

lifetime of level v' is given by the expression

where the sum over v" includes an integration over the continuum vibrational levels of the final electronic state. 20

We have calculated the radiative lifetime of the t! = 0 level of the BIZ;' state using both ab initio potential energy curves in the nuclear wave equations. The 2 IZ;+_ X IZ;' dipole moments, which are shown in Fig. 6, are very large in the region of the outer minimum of the

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van Dishoeck, van Hemert, and Dalgarno: Photodissociation of HCI 3701

T ABLE VII. Interstellar HCI photodissocia­tion and photoionization rates in S-I for an optically thin cloud.

Transition

Aln cln b 3n Higher lying states

Ionization

2.1 5.3 0.1

2.3 0.9

2 l'E+ state so the calculated lifetimes To are short, ranging from 2-4 ns. The calculated lifetimes of those higher vibrational levels which are not greatly per­turbed by interaction with the E 1'6+ levels are slightly longer. The contributions to the radiative lifetimes from transitions into the vibrational continuum of the X 1~+ state are less than 1% for Vi =0, but as much as 20% for v' = 5.

VII. PHOTODESTRUCTION OF ATMOSPHERIC AND INTERSTELLAR HCI

Chlorine compounds playa central role in the chemis­tries of the stratospheres of the planets Earth3! and Venus33 and photodissociation of HCl is a critical pro­cess in the chemical sequences. Recent calculations32,33

assumed that photodissociation occurs only by absorption into the A In state of HCI and adopted the cross sections measured by Inn. 3 Additional contributions to the pho­todissociation rate come from absorptions into the C In, b 3n and possibly the Rydberg states, though the wave­lengths of the transitions lie in a region where molecular oxygen is an effective absorber.

The calculated photodissociation rates in interstellar clouds34 also have assumed only transitions into the A In state. We present in Table VII the contributions to the photodissociation rate in optically thin interstellar clouds arising from the continuous absorption into the A In state and the discrete absorptions into the C In and b 3n states. For oscillator strengths for the C In state we employed the values listed in Table VI and for the b sn state we employed an oscillator strength of 3 x 10-3•

We assumed that all absorptions into these states lead to dissociation. Absorption into the discrete higher lying states may contribute to the dissociation process. To obtain an upper limit to the possible rate, we adopted an effective oscillator strength of 0.2 for these states, and assumed a dissociation efficiency of unity. The photo­ionization rate corresponding to the cross sections of Faegri and KelltS is included in the table. In calculating the photodestruction rates we adopted the mean inter­stellar radiation field of Roberge et al. 34

The photodissociation rate is 7. 5 X 10-10 S_l if the ab­sorption into the higher lying states is excluded and is 9.8 X 10.10

S·l if the maximum possible contribution from the higher lying states is included. Previous studies of interstellar hydrogen chlorideS

- l ! used a rate in the op­tically thin limit of 2.4 x 10-10 S·l. The enhanced photo­destruction rate obtained here diminishes substantially the discrepancy between observation and theory and in

conjunction with other modifications to the chemistry may remove it. 35

ACKNOWLEDGMENTS

The authors are very grateful to Dr. J. H. Black and Dr. K. Yoshino for many helpful discussions. Theyal­so wish to thank Professors R. J. Buenker and S. D. Peyerimhoff for making available their set of programs, and for communicating their results prior to publica­tion. This work was supported by the Netherlands Organization for the Advancement of Pure Research (ZWO) and by the National Science Foundation under Grant AST-81-14718.

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3702 van Dishoeck, van Hemert, and Dalgarno: Photodissociation of Hel

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