Experimental and theoretical studies of the valence-shell dipole excitation spectrum and absolute photoabsorption cross section of hydrogen fluoride

Chemical Physics 88 (1984) 6 5 - 8 0 North-Holland, A m s t e r d a m -

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EXPERIMENTAL AND THEORETICAL STUDIES OF T H E VALENCE-SHELL D I P O L E EXCITATION S P E C T R U M AND ABSOLUTE P H O T O A B S O R P T I O N CROSS SECTION OF H Y D R O G E N FI.UORIDE A.P.

HITCHCOCK

Department of Chemistr); Mcl~Iaster University, Hamilton, Canada LSS 4M1

G.R.J. WILLIAMS

l

Department of Chemistry, Indiana Universit); Bloomington, IN 47405, USA

and C.E.

BRION and P.W. L A N G H O F F 2

Department of Chemist~, University of British Columbia, Vancouver, Canada V6T 1 Y6 Received 27 D e c e m b e r 1983

Absolute cross sectional measurements are reported o f the valence-shell dipole excitation spectrum o f H F obtained from suitably calibrated high impact energy, small m o m e n t u m transfer, electron energy-loss scattering intensities. Detailed assignments are provided o f all prominent features observed on the basis o f concomitant single- and coupled-channel R P A E calculations. The measured spectrum, obtained at an energy resolution o f = 0.06 eV (fwhm) in the = 9 to 21 eV interval, includes a dissociative feature centered at = 10.35 eV assigned as X 1~ + .._, ( l ~ r - t 4 o ) A t I'I, as well as numerous strong, sharp bands in t h e ~ 13 to 16 eV excitation energy region. These b a n d s are attributed o n basis o f the present calculations to Rydberg (1¢~- 1 n p ~ ) - v a l e n c e ( 3 0 - 1 4 a ) mixing in X 1~+ __~1~+ excitation symmetry, which gives rise to a long vibrational progression, and to strong l~r ~ n s o , moderate l'rr--~ n d o , and weak 1,n---*n p o g y d b e r g series in X l ~ + ~ tFI excitation symmetry. A weaker l~r --* nd~r Rydberg series also contributes to the spectrum in X aZ+ ---,~X + symmetry. The calculated a n d measured excitation energies and f numbers, particularly for the X l ~ ~ ( 1 ~ - 14o ) A l l'I, ~ ( 1 ~ - 13p~)B I ~..+ ~ (l~r- I 3 s o ) C I H , and ( 3 o - z 4 o ) D I X + transitions, are in good quantitative accord, suggesting that the overall nature of the H F spectrum is generally clarified on basis of the present studies. Finally, tentative assignments are provided o f weak features observed above the l'rr - t ionization threshold. As in previously reported j o i n t experimental and theoretical studies o f the valence-shell spectrum o f F2, high-resolution optical V U V measurements a n d calculated potential energy curves aid in the assignment and clarification o f the H F spectrum.

1. I n t r o d u c t i o n

The valence-shell dipole excitation spectrum of hydrogen fluoride has been the subject of continuing experimental [1-26] and theoretical [27-34] study. Early absorption [2,3] and emission [4] mea1 Present address: R.A.N. Research Laboratory, N e w Beach Road, Ruchcutter Bay 2011, N.S.W., Australia. 2 Visiting Professor, 1983. Permanent address: D e p a r t m e n t o f Chemistry, Indiana University, Bloomington, I N 47405, U S A .

surements have been refined with high-resolution VUV spectra [5-7], and both large-angle [8] and forward-scattering [9-11] electron energy-loss studies have been performed. Photoelectron spectra at selected VUV and X-ray photon energies [12-16], threshold photoelectron spectra [17], photoionization mass spectra [18-21], and ion-pair formation studies [22,23] have alsobeen reported. The experimental difficulties associated with_ this compound, are emphasized by the presence i n the literature of an apparently strongly-contaminated H F absorption spectrum k[24], as well as electron-

0301-0104/84/$03.00 © Elsevier Science Publishers B . V . (North-Holland Physics Publishing Division)

66

A.P. Hitchcock et aL / Spectrum a n d cross section o f H F

energy-loss spectra [25.26] shown recently to be f ro m molecular hydrogen, rather than hydr ogen fluoride [9]. Relevant theoretical studies, dating f ro m the early work of Pauling [27] a nd Mulliken [28]. include calculations of the ground-state potential curve in H a r t r e e - F o c k [29] and configuration-mJxing [30] approximations, as well as studies o f selected excited states [31-34]. Although continuing progress has been m a de in u n d e rs tan d in g the general nature and certain details o f dipole excitation processes in H F [1-34]. aspects o f the s p ectr um are as yet unsettled and require further clarification, and an absolute measurement o f the ab s or pt i on cross section in high resolution has a p p a r e n t l y not been reported to date. T h e r e are a p p a r e n t discrepancies between the high-resolution optical VUV studies [5-7] and the recent electron energy-loss measurements [9-11], and assignments based on the latter studies a n d plausible assumptions are not in accord with the most recent calculations [33,34]. T h e theoretical studies [31-34] differ with respect to excitation energies, f numbers, and configurational assignments of certain states, including the lowest-lying dipole-allowed excitation, and one o f them [34] p u rp o r ts to be in accord with earlier optical measurements [1-3], which are at variance with the recent energy-loss studies [8-11]. Quantitative c o m p a r is o n s between absolute cross.sectional measurements and corresponding calculations of excitation energies and f numbers should aid in clarifying these discrepancies, and should provide a basis for conclusive assignment of the spectrum. O f particular interest in this connection is the nature a n d location o f the strong intravalence 3o--, 4 0 ( 0 * ) or X --, Vo charge transfer excitation in the H F spectrum, which is expected to mix with R ydberg series [31-34], and, consequently, to contribute to the absorption cross section over a broad energy interval. A similar situation is observed in the spectrum o f F:, which has been the subject o f recent j o i n t e x p e r i m e n t a l - t h e o r e t i c a l study [35] closely related to the present development. Studies o f o t h er diatomic and polyatomic molecules indicate such o - - , o* contributions can also extend above threshold into ionization continua [36], in which cases they are generally referred to as shape resonances [37].

In the present study, previously repo rte d high-resolution electron energy-loss m easurem e n ts o f electronic excitation in H F [10] are placed o n an absolute cross sectional scale by suitable norrealization to lower-resolution absolute values [11]. Detailed quantitative comparisons are m a d e o f the resulting cross section with vertical-electronic single-channel static-exchange and coupled-channel R P A E calculations. Assignments are provided o f all p r o m i n e n t features in the measured cross section on basis of the calculations performed, and quantitative comparisons of absorpt i on intensities are made for the lowest few transitions. T h e calculated X~E+--*~H excitations are found to include a low-lying l~r ~ 4 o ( o * ) resonance transition, the position and intensity of which is in excellent accord with the measured cross section, confirming previous assignments of the dissociative (l~r-t4o)Atl-I state at 10.35 eV vertical as the lowest dipole-allowed excitation in H F [10]. Recent alternative theoretical assignments of the earlier optical VUV experimental data [1-6], which place the A~II state at = 8.9 eV [33] and at -- 7.7 eV [34] excitation energy, are reexamined. T h e calculated energies and integrated f num bers fro m these studies [33,34] are seen to be, in fact, in agreement with the present results. Strong 1,rr---, n s o , m o d e r a t e lxr ---, n d o . and weak l'rr ---, n p o R y d b e r g series in X l ~ + __. l i i s y m m e t r y are f o u n d to cont ri but e to the spectrum in the = 13 to 16 eV excitation energy interval, in good accord with features in the measured cross section. T h e r e are significant differences, however, between the present assignments and those report ed previously o n basis of the experimental spectrum a n d q u a n t u m defect analysis alone [10]. T h e calculated f n u m b e r of the resonance X l ~ + _~ (1,rr- 13so)C I i i m e m b e r o f the n s o series at 13.03 eV, tentatively assigned earlier on basis o f optical V U V studies as (1-rr-13po)C1H [7], is in satisfactory agreement with the measured value. Strong Rydberg-valence mixing occurs in X ~E+ __~lE+ excitation symmetry as a consequence o f an (30 ~ 4o)Vo intravalence interloper in the l~r --~ np~r R y d b e r g series. A weak Rydberg-like ( 1 ¢ r - ] 3 p c r / 3 o - 1 4 o ) B lS'-+ state is predicted at -----13.2 eV, with a stronger conj u g a t e ( 3 0 - 1 4 o / 1 ¢ r - 13p~r)D 1~ + intravalence state giving rise to a long vibrational progression in the

A . P . Hitchcock et a L /

13.9 to 15.9 e V interval. T h e c a l c u l a t e d f n u m bers are in g o o d a c c o r d w i t h the c o r r e s p o n d i n g e x p e r i m e n t a l values. R e c e n t e x t e n s i v e c o n f i g u r a t i o n - m i x i n g studies d o not r e p o r t a w e a k e n e d R y d b e r g - l i k e B l ~ + s t a t e at the e q u i l i b r i u m i n t e r n u c l e a r s e p a r a t i o n in H F , a n a p p a r e n t c o n s e q u e n c e o f the use o f a restricted d i f f u s e basis set in the c a l c u l a t i o n s [34]. A w e a k 1-rr---, ndxr R y d b e r 8 series is also f o u n d to c o n t r i b u t e to the s p e c t r u m in X t I ~ + - - - - t ~ + s y m m e t r y in the = 13 to 16 e V interval. Finally, plausible a s s i g n m e n t s are p r o v i d e d o n basis o f the p r e s e n t c a l c u l a t i o n s o f w e a k f e a t u r e s o b s e r v e d a b o v e the 1~ -= t h r e s h o l d in b o t h e l e c t r o n energy-loss s p e c t r a a n d high-resolution V U V optical studies [7]. As in p r e v i o u s l y r e p o r t e d j o i n t e x p e r i m e n t a l - t h e o r e t i c a l studies o f the d i p o l e e x c i t a t i o n s p e c t r u m o f m o l e c u l a r fluorine [35], available optical studies [ 1 - 7 ] a n d calculated p o t e n t i a l c u r v e s in H F [ 3 1 - 3 4 ] c o m p l e m e n t a r y to the p r e s e n t m e a s u r e m e n t s a n d c a l c u l a t i o n s a r e helpful in assigning the s p e c t r u m . D e s c r i p t i o n s are given o f the e x p e r i m e n t a l a n d theoretical p r o c e d u r e s a d o p t e d in sections 2 a n d 3, respectively, results are r e p o r t e d in section 4, a n d c o n c l u d i n g r e m a r k s p r o v i d e d i n section 5.

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2. E x p e r i m e n t a l m e t h o d o l o g y H i g h - r e s o l u t i o n ( = 0.06 eV f w h m ) valence-shell e l e c t r o n energy-loss s p e c t r a in H F h a v e b e e n rep o r t e d p r e v i o u s l y e m p l o y i n g 2.5 keV i n c i d e n t energy electrons under small-momentum-transfer c o n d i t i o n s [9,10]. T h e a p p a r a t u s a n d d a t a collect i o n p r o c e d u r e e m p l o y e d are d e s c r i b e d in conside r a b l e detail elsewhere [38]. In the p r e s e n t study, these high-resol/ltion d a t a are p l a c e d o n a n a b s o lute cross sectional scale e m p l o y i n g c o r r e s p o n d i n g T R K - s u m - r u l e - n o r m a l i z e d d a t a ( = 0.9 eV f w h m ) r e c e n t l y o b t a i n e d [11] f r o m a d i p o l e (e, 2e) spect r o m e t e r [39,40] r u n in n o n - c o i n c i d e n c e f o r w a r d s c a t t e r i n g energy-loss m o d e . T h e c o n v e r s i o n p r o c e d u r e f r o m h i g h - r e s o l u t i o n e l e c t r o n energy-loss s c a t t e r i n g i n t e n s i t y to p h o t o a b s o r p t i o n cross sect i o n is d e s c r i b e d i m m e d i a t e l y below. U n d e r the s m a l l - m o m e n t u m - t r a n s f e r c o n d i t i o n s o f the e l e c t r o n energy-loss e x p e r i m e n t [9-11], the electric-dipole ( p h o t o a b s o r p t i o n ) limit o f the Be-

67

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energy resolution: (-- - - --) previously reported TRK normalized ----0.9 eV resolution cross section obtained on an (e. 2e) spectrometer run in forward-scattering energy-loss mode [11]. The present results are normalized to the absolute TRK cross section in the -----25 to 45 eV energy interval employing a fitting function of the form aE b, as discussed in the text. Indicated spectral assignments made on basis of static-exchange and R P A E calculations described in sections 3 a n d 4. Ionization potentials adopted from previously reported studies [12-18].

t h e - B o r n inelastic scattering t h e o r y c o r r e c t l y describes the s c a t t e r e d e l e c t r o n i n t e n s i t y [41]. In a c c o r d a n c e with this f o r m a l i s m , the e l e c t r o n energy-loss s p e c t r u m is c o n v e r t e d to cross sectional d a t a b y m u l t i p l i c a t i o n with the c o n v e r s i o n f u n c tion a E b, w h e r e E is e n e r g y loss a n d a a n d b a r e c o n s t a n t s that d e p e n d o n the i m p a c t e n e r g y a n d the a n g u l a r a c c e p t a n c e o f the s p e c t r o m e t e r [42]. B e c a u s e o f the l o w e r r e s o l u t i o n (-----0.9 e V f w h m ) o f the a b s o l u t e cross section [11] used in the n o r m a l i z a t i o n p r o c e d u r e , the h i g h - r e s o l u t i o n spect r u m is p l a c e d o n a n a b s o l u t e scale in a c c o r d a n c e w i t h the B e t h e - B o r n t h e o r y in a s e q u e n t i a l m a n n e r . First, a m o d e s t r e s o l u t i o n ( = 0.5 eV f w h m ) elect r o n energy-loss s p e c t r u m in the = 7 to 45 e V energy-loss i n t e r v a l [10] is c o n v e r t e d to cross sec-

68

A . P . Hitchcock et aL / Spectrum a n d cross section o f H F 70i

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Fig. 2. Valence-shell photoabsorption cross section in H F obtained as in fig, I, v,-ith an energy resolution of = 0.06 eV (fwhm). employing the normalization procedures discussed in the text. Indicated spectral assignments made on basis of static-exchange and R P A E calculations described in sections 3 and 4. Detailed quantitative comparisons between previous studies and the present theoretical and experimental values o f excitation energies a n d f n u m b e r s for the transitions assigned in the figure are presented in table 4. The X--+ A and B state assignments are seen to refer to broad spectral features, the latter coincidently underlying the sharper X--+ C excitation. Vibrational spacings in the X ~ C and D state progressions correspond approximately to that ( - - 0 . 3 6 eV) in the ( l ~ - t ) x Z I I ionic state [17.181. As indicated, the B and D states correspond to a mixed Rydberg-valence conjugate pair b o t h involving l ~ - t 3 p . - : and 3 o - [ 4 o ( o * ) configurations.

tional data using the similar resolution ( = 0.9 eV fwhm) absolute cross section [11]. This normalization is accomplished by least-squares fitting the product o f a conversion function ( a E b) with the measured relative scattering intensities (above a linear background) to the generally smooth absolute data [11] in the --- 25 to 45 eV interval, where the small differences in resolution ( = 0.5 versus = 0.9 eV) do not affect the spectral shape. The background subtracted prior to the a E b conversion is chosen to insure that the integrated cross section of the lowest-lying broad feature in the 8 - 1 2 eV region of the converted spectrum, assigned as the dissociate X--+ A t l I transition [10].

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E n e r g y (eV) Fig. 3. Valence-shell p h o t o a b s o q a t i o n cross section in H I : o b tained as in figs. 1 and 2, with an energy resolution o f = 0.06 eV (fwhm), sho~Sng further detail in the 12-17 eV interval. The small tic marks below the measured spectrum indicate the positions of prominent features tabulated in table 5. Indicated spectral assignments m a d e on basis o f static-exchange and R P A E calculations described in sections 3 and 4. The dashed curve centered at = 13.2 eV underh'ing the h r --* 3so excitation provides an estimate o f the X ~ B ]-~-+ contribution to the cross section. D o m i n a n t confighrations are indicated in each case, with principal q u a n t u m numbers given above each state designation and vibrational q u a n t u m numbers shown below these. Note that the mixed Rydberg-valence n p ~ / o * series includes two terms with n = 3, corresponding to the conjugate B and D t ~ + states, the latter exhibiting a long and strong vibrational progression overlapping higher members o f the series. Specifically, the 0 ---*3 and 0 ---*5 members o f the X ---, (3p . - , / o ' ) D state excitation are seen to coincide with the 0 --* 0 m e m b e r of the X---* (4p.'rr/o*) and (Sp'tr/o*) excitations, respectively.

matches that of the absolute data [11]. The cross section obtained from this procedure is shown in comparison with the absolute data [11] in fig. 1, and is discussed further below. Next, the previously reported high-resolution electron energy-loss spectrum taken over the = 8 to 23 eV interval [10] is placed on an absolute scale by matching it to the now normalized = 0.5 eV resolution spectrum of fig. 1. This normaliTa-

A.P. Hitchcock et ai. / Spectrum and cross section o f H F

tion is accomplished byL backg~rotmd subtraction a n d least-squares fitting in the -----18 to 23 eV interval, which is an essentially non-structured region where again resolution differences are inconsequential. The b a c k g r o u n d subtracted prior to the conversion is chosen to insure that the spectral shapes of 0.5 eV and 0.06 eV resolution cross sections match in the 8-12 eV region after the a E b conversion. The resulting high-resolution cross section in the --- 8 to 21 eV interval is shown in fig. 2 a n d discussed further below. Finally, a normalized high-resolution cross section on an expanded energy scale is constructed in the ~ 12 to 17 eV interval by least-squares fitting the previously reported d a t a [10] in the largely unstructured ---16 to 17 eV interval to the cross section of fig. 2. In this case, agreement between the value of the integrated cross section or f number corresponding to the -----12.8 to 13.5 eV excitation energy interval obtained from the cross section of fig. 2 and from the expanded-scale result is the criterion used to select the linear background subtracted from the intensity d a t a prior to conversion. The resulting cross section in the - 12 to 17 eV interval is reported in fig. 3 and discussed further below. The three least-squares fitting procedures indicated above give conversion functions of the form a E b, with b = 1.74, 1.40 and 1.40 in the three cases, respectively. These values are smaller than the theoretical exponent o f b = 3 [41,42], largely as a consequence of the non-zero angular acceptance of the spectrometer [38]. Since the voltage ratios on the retarding lenses increase significantly under operating conditions pertaining to high resolution [38], the angular acceptance of the spectrometer is somewhat larger at higher energy resolution, accounting for the differing b values obtained under low (b = 1.74) a n d high (b-----1.40) resolution conditions. T h e quality of the d a t a derived by these conversion procedures is indicated b o t h by the overall comparison with the --".0.9 eV resolution absolute d a t a shown in fig. 1, and by the internal consistency of the f numbers obtained from the three spectra b y integrating over various energy intervals. The integrated f numbers so obtained from figs. 2 and 3 for sharp features generally agree to

69

within = 10%, and usually to:within less t h a n 5%. Moroever, when _integrations over broad energy intervals are performed, the three Cross sections o f figs. 1~3 provide results in excellent quantitative accord, and in good agreement with values obtained from the previously reported low-resolution absolute cross section [11]. The total integrated f numbers over the entire discrete interval, for example, obtained from figs. 1-3 are 0.518, 0.538 a n d 0.536, respectively, whereas that obtained from the previously reported absolute cross section [11] is 0.561. Since the present results exhibit a satisfactory degree of internal consistency, they are thought to be free from systematic errors in the conversion of energy-loss intensities to absolute cross sections. However, as a consequence of other possible systematic error [42], conservative error bars of 20% are adopted for purposes of comparisons with theoretical and other experimental studies. Although some structures are evident in the cross sections of fig. 1, and have been assigned there on basis of the theoretical studies, these data should be used primarily for purity confirmation a n d for energy calibration in subsequent higher resolution studies. The absolute cross sections o f figs. 2 and 3 exhibit m a n y well-resolved structures, which provide a useful basis for spectral assignment. The assignments indicated in the figures are made employing the present calculations, a n d are discussed in considerable detail in section 4 below. Finally, it should be noted that the present absolute cross sections of figs. 2 a n d 3 are largely complemeirtary to previously reported high-resolution optical VUV studies [5-7]. Whereas the highresolution optical studies provide precise line positions, even for relatively weak bands, the lack of a suitably calibrated intensity scale precludes estimates of b a n d strengths from the data. Moreover, although weak sharp features can be easily discerned in high-resolution optical spectra a n d state assignments provided, broad-features of considerable intensity are easily overlooked in such data. W h e n taken together, however, the previous optical studies a n d the present electron energy-loss measurements provide a useful basis for clarifying the absorption spectrmn of H F .

70

A.P. Hitchcock et a L /

Spectrum and cross section o f H F

3. Theoreticalmethodology The computations performed in the present study follow closely previously reported procedures [43]. A (lo22o23o21~4)iZ+ ground-state H a r t r e e - F o c k function is constructed at the experimental H F equilibrium nuclear separation (R e = 1.733 ao) [1] employing a standard [4s, 2p, l d ; 3s. lp] cartesian gaussian basis set [44]. This compact basis is then supplemented with a large number o f additional gaussian functions having exponents that form approximate even tempered series. In table 1 are shown the specific basis functions employed, chosen in accordance with the s, p. and d Rydberg series expected. As in earlier studies [35], canonical orthogonalization procedures are used to test for and eliminate near linear dependence in the basis set. The Fock matrix is then constructed and diagonalized in the expanded basis, and a total of 8g occupied a n d virtual orbitals obtained employing standard computational procedures. In table 2 are shown the resulting o, -rr, and 8 canonical orbital energies, which are seen to span sensibly the lower valence portion of the spectrum. These Fock orbitals provide the oneelectron basis of particle and hole states in which

Table 1 Supplemental cartesian gaussian basis set employed in H F calculations a) Type b)

Exponent

F (s-Lvpe)

1.7355 O.4968

F (p-type)

1.691 0,790 0,369 0.100 0.050 0.09_5 0.0125 0.00625

Type b) F (d-type)

Exponent 0.5631 0.3251 0.1877 0.1084 0.0063

(s-type)

0.010

H (p-type)

0.410 0.180 0.080

H

~) Functions employed in H F calculations in addition to a (9s, 5p, l d ; 4s, l p ) / [ 4 s , 2p, l d ; 3s, lp] valence basis adopted from Dunning and Hay [44], b) The p-type basis includes p.~, p>., p_. functions, and the d-type includes d~z, dyz, d . z , dxy , dx. , d.v-. functions. As a consequence, the supplemental d-type functions also contribute to s-type Rydberg series.

static-exchange a n d R P A E calculations are performed. It should be noted in this connection that self-consistency of the ground-state wavefunction is not obtained in the extended basis set, thereby avoiding calculation and transformation of a very large number of two-electron integrals, as discussed in detail in a previous publication [43]. The occupied (lo, 20, 30, 1~) and virtual Fock orbitals obtained from such a single-pass diagonalization provide an orthonormal set in the full expanded basis, and, consequently, are conveniently employed in the subsequent spectral calculations. Static-exchange or single-excitation configuration-mixing calculations for electrons moving in the fields of individual hole states provide an overview of the X lZ + ~ l y + and ~II excitation

Table 2 Canonical Fock orbital cnersies in HI: ~) o orbitals --

715.65 42.06 -- 20.74 0.12 0.33 0.60 0.7l 1.17 2.48 3.63 5.51 6.04 9.70 11.17 13.40 15.33 20.41 25.02 28.80 33.25 --

o orbitals

~ orbitals b)

8 orbitals b)

38.54 49.95 57.09 61.65 74.04 82.99 106.79 109.82 138.88 148.39 167.61 174.49 285.60 372.26 456.34 993.23

-- 17.58 0.32 0.60 1.13 2.79 5.65 6.37 10.81 14.31 17.37 25.02 32.54 40.57 50.35 69.59 82.50 106.06 145.31 149.74 365.57

0.61 7.79 20.85 42.41 82.52 144.86

a) Energies in eV obtained from S C F calculations o f the ground X t~: + state in H F at the experimental equilibrium internuclear separation ( R e =1.733 ao) [1] employing the basis set o f table 1. As is discussed further in the text, self consistency is obtained in the valence portion o f the basis set only, with the spectrum reported here constructed from a subsequent s i n ~ e - p a s s diagonalization in the full gaussian basis. b) Two ~-type and two 8-type orbitals are obtained, respectively, for each ,a a n d 8 energy indicated.

A.P. Hitchcock et al. / Spectr~n and cross section o f H F

spectra in H F at an uncoupled level o f approximation. The resulting o, ~r a n d 8 i m p r o v e d virtualorbital (IVO) one-particle states,, represented in the Fock basis of 360, 40¢:, a n d 128 states, respectively, correspond to V tzv-a) potentifils, and, consequent ly, give rise to appropriate R y d b e r g series a n d associated C o u l o m b accumulation points [45]. By contrast, the canonical-Fock spectrum o f t a b l e 2 corresponds more closely to an N + 1 electron system, and, consequently, does not include b o u n d (discrete) virtual orbitals. Configuration mixing a m o n g the various uncoupled IVO channels is studied by performing random-phase-approximation-with-exchange (RPAE), or time-dependent H a r t r e e - F o c k [46], calculations in the full Fock basis. These calculations give X 1~+ ~ l ~ + and III spectra, involving 124 hole-particle and 124 particle-hole states or configurations, obtained from diagonalization of R P A E matrices of dimensionality 248. Inspection of the R P A E vectors obtained, and comparison with the single-channel IVO calculations, indicates the extent of configuration mixing present among the various single-excitation series. O f course, it should be noted that two h o l e - t w o particle and higher-order configurations are not included in the present R P A E calculations. Although double and higher-order excitations can contribute to dipole-allowed states in certain diatomic molecules, particularly at larger internuclear separation, previously reported valencebasis-set configuration-mixing calculations [31] indicate single-particle excitations dominate the dipole spectrum in H F at the equilibrium internuclear separation. Finally, discrete excitation energies and dipole f numbers for X l ~ + __~l ~ + and aFI excitations in H F in the vertical-electronic approximation are constructed from b o t h IVO and R P A E vectors. As in previously reported dipoleexcitation studies [35,43], it is convenient to reference the calculated term values to experimental [11-18], rather than H a r t r e e - F o c k [29], ionization potentials in order to facilitate comparisons between theory and experiment. The pre.sently reported large-basis-set, vertical electronic, dipole excitation calculations in H F are largely complementary to previously reported configuration-mixing studies [31-34]. Whereas the earlier calculations include the multiple-excitation

71

configurations required to provide reliable potentia!-energy curves for the lowest few electronic states; t h e ielativd~r small basis sets used, in these studies preclude-the prediction of RYdberg series and reliable transition intensities. Correspondingly, the present large-basis-set singie excitation studies are n o t suitable for potential curve calculations, but, rather, provide reliable vertical electronic transition oscillator strengths, which are of particular importance in regions of Rydberg-valence mixing. As in previous studies [35], when taken together, the two sets of complementary calculations provide a reliable basis for spectral assignment of measured excitation profiles. Finally, in connection with the spectral assignments reported below, it should be noted that so, p o , d o . . . . and p~r, d ~ . . . . R y d b e r g virtual orbitals are expected to contribute to 1~ and 30 excitation series. In contrast to previously reported c o m p u t a tional studies of excited states in H F [31-34], the large basis set (table 1) employed in the present s t u d y can be expected to provide converged R y d berg orbitals for the first two or three members of each series. In addition, a c o m p a c t o* orbital, referred to as 4 0 or 2 p o in the sequel, will appear in single-channel excitation series, and should be well described and distinct from n p o (n >1 3) R y d berg orbitals in the present basis set.

4. Valence-shell dipole excitation spectrum in HF The experimental and theoretical dipole excitation spectra in H F obtained from the present studies a r e ' r e p o r t e d in figs. 1 - 3 and tables 3 - 5 . Fig. 1 shows low- and moderate-resolution ( = 0.9 a n d 0.5 eV fwhm) versions of the absorption cross section in the ~ 6 to 40 eV interval, fig. 2 shows the higher-resolution (---0.06 eV fwhm) valenceshell spectrum in the = 8 to 21 eV interval, and fig. 3 reports further detail in the ~- 12 to 17 eV interval. Since the procedures employed in cons ttTucting the a b s o l u t e cross sections o f f i g s . 1 - 3 from inelastic forward-scatterng electron intensities [10,11] have been described in section 2 above, further discussion o f this aspect of the s t u d y is unnecessary. Figs. 1 - 3 also include spectral assignm e n t s of prominent features, b a s e d on the theoret-

A.P. H!tchcock et al. / Spectrum and cross section o f H F

72

Table 3 S i n g l e - c h a n n e l I V O a n d c o u p l e d - c h a n n e l R P A E c a l c u l a t i o n s o f v e r t i c a l d i p o l e e x c i t a t i o n e n e r g i e s a n d f n u m b e r s i n H F a) C o u p l e d - c h a n n e l R P A E r e s u l t s ¢)

S t a t i c - e x c h a n g e r e s u l t s b) energy (eXO/f number

n

energy (eV)/f number

v e c t o r d)

v e c t o r d}

1,~ -* n p o 10.09/0.0499 13.89/0.0023 14.97/0.0008 ].~ --~/'/so I2.99/0.0387 14.73/0.0008 15.27/1.rr ---* n d o 14.65/0.0164 15,25/0.0066 15.52/0.0035 3 0 ~ np~r 16.25/0.0095 17.82/0.0065 18.35/0.0042 3 o --* nd~r 17.81/0.0659 18.35/0.0020 18.62/0.0011

l~-tno 1.00 1.00 1.00

3a-ln~r 0.00 0.00 0.00

1.00 1.00 1.00

0.00 0.00 0.00

1.00

1.00 1.00

0.00 0.130 0.00

0.05 0.00 0.00

0.95 1.00 1.00

0.20 0.00 0.00

0.80 1.00 1.00

1.'r -* n p ~ / 3 o --* n p o 13.21/0.0421 14.01/0.1241 14.85/0.0139 15.68/0.0150 l'rr ~ n d ~ 14.75/0.00339 15.29/0.00145 15.55/0.00077

lcr- tn~ 0.71 0.36 0.94 0.90

3o-lno 0.29 0.64 0.06 0.10

1.00 1.00 1.130

0.00 0.00 0.00

3 0 "-* n p o / l ~ --* n p ' ~ 14.01/0.1241 17.06/0.0584 18.03/0.0068 3 0 -'~ n s o / l ~ r --* n p r , 16.31/0.0132 17.75/0.00018 18.38/0.00201 3o'~ ndo 17.80/0.00405 18.36/0.00174 18.62/0.00092

lxr-ln~r 0.36 0.05 0.16

3o-lno 0.64 0.95 0.84

0.51 0.10 0.00

0.49 0.84 1.00

0.130 0.00 0,00

1.00 1.00 1,00

X t S * ..~ t i i s p e c t r u m 1.':r ~ n p o 10.15/0.0530 13.90/0.0025 14.98/0.0009 l'r:, -'-* n $ o 13.01/0.0357 14.73/0.000g 15.27/I.'.z --* n d o 14.66/0.0152 15.25/0.0066

n = 2 (o" ) n = 3 n = 4 n = 3 n = 4 n = 5

15.52/0.0035

n = 3 n = 4 n ~ 5

3 0 --* np~r 16.28/0.0118 17.83/0.0094 18.35/0.0042

n = 3 n = 4 n = 5

3o-'-*nd'~ 17.79/0.0045 18.35/0.0020 18.62/0.0011 X~

+ ~

1.':r -~ np.-z 13.45/0.00195 14.80/0.00157 15.70/0.0007I 1~ ~ n d r , 14.75/0.00325 15.29/0.00145 15.55/0.130077 3 0 --* n p o 14.15/0.1967 17.17/0.0559 18.15/0.0383 3 0 --* nso 16.50/0.00049 17.88/0.00016 18.38/0.00001 30 ~ ndo 17.81/0.00392 18.36/0.00174 18.69-/'0.00092

n = 3 n = 4 n = 5 spectrum n -----3 n : 4 n = 5 n = 3 n = 4 n = 5 n = 2 (o*) n = 3 n = 4 n = 3 n = 4 n = 5 n = 3 n = 4 n = 5

") V a l u e s as i n d i c a t e d o b t a i n e d f r o m I V O a n d R P A E c a l c u l a t i o n s a t R e = 1.733 a o e m p l o y i n g t h e b a s i s s e t o f t a b l e 1. b) T h e c a l c u l a t e d t e r m v a l u e s a r c r e f e r e n c e d to e x p e r i m e n t a l i o n i T a t i o n p o t e n t i a l s o f 16.039 (l"rr - 1 ) a n d 19.118 e V ( 3 a - 1 ) [17,18] i n c o n s t r u c t i n g t h e i n d i c a t e d v e r t i c a l e x c i t a t i o n e n e r g i e s . T h e 1 ~ ~ n p o a n d 3 0 --~ n p o s e r i e s i n c l u d e n = 2 m e m b e r s c o r r e s p o n d i n g t o e x c i t a t i o n s i n t o t h e 4 0 ( 0 * ) o r b i t a l , w h e r e a s t h e o t h e r s e r i e s i n c l u d e n = 3, 4, 5 R y d b e r g m e m b e r s o n l y . T h e b a s i s s e t o f t a b l e 1 is s u f f i c i e n t t o p r o v i d e a c c u r a t e e n e r g i e s a n d f n u m b e r s f o r n s a n d n p s e r i e s u p t o n ----5, w h e r e a s f o r d s e r i e s o n l y t h e f i r s t t w o ( n = 3 a n d 4) s t a t e s w e r e j u d g e d a d e q u a t e , t h e h i g h e r m e m b e r e s t i m a t e d o n b a s i s o f t h e c a l c u l a t e d q u a n t u m d e f e c t . A s i n p r e v i o u s s t u d i e s [35], t h e i n d i c a t e d s, p, a n d d s e r i e s a r e i d e n t i f i e d i n t h e c a l c u l a t i o n s o n b a s i s o f q u a n t u m d e f e c t v a l u e s a n d t h e s p a t i a l characteristics of the associated orbitals. ( F o o t n o t e s c o n t i n u e d o n n e x t page.)

::.

_ A.P. Hitcheock e! aL / Sl~O.etno~ and cross seit~n o f ~/F:- Table 4 -: -" Comparisons ot:-experlmental and theoretical exciLation energies and oscillator st rengtl~ in SLate designa"tion and character a)

Present results experiment b)

(1~)- 14o)At H, continuum 10.35/0.098 ( l ~ - 1 3 p ~ r / 3 o - 1 4 o ) B l ~ , diffuse - 13.2.0/0.025 (l"rr- 13so)C lI-l, sharp 13.03/0.056 (3o-14o/l~r-13p,#)D l ~ + sharp 13.91/0.12-0.24

HF"

Previous calculations d)

_

73

:

theory o-

"ref, [31] ~)

ref. [32] ~

reL [33] 9

ief. [34] s)

10.09/0.050 . 13-21/0.04212.99/0.039. 14.01/0.124 :

10.98/0.03 13.99/0.01 17.40/0.02 16.62/0.39

10.70/13.7/-

10.80/13.g4/13.52/0.014 14.57/0.28

10.42/0.07 13.40/0.16 13.07/14.46/0.0023

a) Principal configurational assignments and state designations at Rc based on the IVO and RPAE calculations of table 3. Note that the B and D states are mixed Rydberg-valence conjugates and interchange character at larger R, as indicated in fig. 4. b) Vertical excitation energies of figs. 2 and 3; the correspondingf numbers are obtained from a calibrated cut-and-weigh integration procedure over the appropriate bands, with uncertainties of = -)-20~g suggested. Note that the adiabatic onsets of the X --) A and B bands, are estimated to be ---9.0 and 12.7 eV. respectively, from figs. 2 and 3. The X - - B and C state f numbers have been esthnated from the combined measured value of 0.081 in an appropriate manner, as is discussed further ~n the text. Because of extensive vibrational excitation in the X --- D transition (see figs. 2-4) the integrated f number is difficult to extract from the measured cross section, the indicated values providing approximate lower and upper limits in this case. c) RPAE excitation energies and f numbers of table 2. Recall the calculated term values are referenced to the experiment ionization potential of 16.039 eV [17,18]. d) Vertical excitation energies and f numbers at R= taken from indicated citations. o The calculations of Bender and Davidson [31] and Dunning [32] do not include diffuse basis functions and, consequently, cannot provide adequate representations of the B, C, and D states, which include contributions from Rydberg configurations (table 3). o 8egal and Wolf [33] assert their calculated X --~ A transition is in accord with a dissociation continuum having an onset at = 8.9 eV reported in optical studies [5,6]; the assertion is fallacious, since the optical studies referenced refer to the X--~ B IZ+ transition [5,6]. The basis set of Segal and Wolf [33], although including both diffuse and compact functions, is apparently unable to describe Rydberg-valenee mixing in the ly.+ spectrum; these authors apparently assign the B state as (30-13so)lY-~ at small R, and obtain an overestimate of the X -=) D ~Y-+ f number at the equilibrium internuclear separation. s) Bettendorf et at. [34] assert their calculated X ~ A transition and related triplet excitations are in accord with an absorption continuum having an onset at = 7.5 eV and a maximum at -- 7.7 eV [1-3]; this assertion is dearly incorrect, their X - ) A excitation energy and f number evidently being in good accord with the present results. Note that different basis sets are employed in the energy and f number calculations of Bettendorf et al. [23]. Although their calculated energies for the B, C, and D states are satisfactory, the reported f numbers for the X --) B and D transitions are clearly at variance with the prese.nt results.

ical calculations described in section 3 and discussed further below. The indicated ionization potentials refer to adiabatic values taken from previously reported photoelectron spectra [11-18]. In table 3 are shown the calculated electronic e x c i t a t i o n e n e r g i e s a n d o s c i l l a t o r s t r e n g t .hs i n b o t h single-channel static-exchange and rand0m-phase approximations, table 4 reports intercomparisons between experimental and theoretical positions and intensifies for selected transitions, and table 5

presents a deailed tabulation and assignment of the m e a s u r e d s p e c t r a l features, as well as p o s i t i o n s and assignments taken from high-resolution VUV studies [5-7]. The results reported in these figures and tables are discussed in further detail immediately below. Referring first to the overview of the spectrum provided by the low- and moderate-resolution cross s e c t i o n s o f fig. 1, t w o p r o m i n e n t f e a t u r e s a r e e v i dent in t h e s e b e l o w the (1-#-I)X2yf HF +

c) The calculated RPAE excitation energies, constructed employing a H hole-particle and particle-hole excitations (248 in each symmetry) from 20, 30, and f-a orbitals, are referred to experimental rather than Hartree-Fock (Koopmans) ionizatitn potentials [43]: Note that the 30 ~ 4 o / I ~ -+ 3p~ excitation has been entered twice in the table to emphasize its role as an intravalence interloper in the 1-rr-~ np-~ Rydberg series. "-" d) Values cited refei to the sum of sciuares of appropriate hole-particle vector coefficients. As in previously reported studies in F2 [35], the calculated particle-hole vectors in H F were found to be entirely negligible. The present RPAE results~ consequently, correspond to coupled-channel static-exchange or Tamm-Dancoff calculations [43]._

74

A.P. Hitchcock et a L /

Spectrum and cross section o f H F

Table 5 Valence-shell dipole excitation s p e c t r u m o f H F =) Electron i m p a c t m e a s u r e m e n t s b)

Optical VUV measurements o

e n e r g ) (eV)

assignment

e n e r g y (eV)

assignment

9.0-12-5 12.7-13.5

( I ' r - 14o) ( l - r - t3p-r)

A ! I-[ B IX +

(1-r-t4o)

13.03 13.26 13.35 13.66

( l - r - 13so)

C 3H ( v = 0)

= 11.0 ¢) 11.940-14.672 12.939 13.029

13.91

14.27 14.49 14.57 I4.69

(1~-

t3po)

(3o-14o)

(l .'::- t 3 d o )

14.88 15.21

(1 .,:r- 14po) (I .-.- t 4 d o )

-

15.35 15.52 -

15.58 15.67

13.911 13.968

D I Z ÷ ( t , = 0) C t H ( t ' = 3)

(l~-t3po) (1~-13po)

13.271

C ll-I(u = 1 ) C t H ( u = 2)

( l - r - 1 3 d .':,) (1-r-14so) ( l - r - t4p-r)

-

13.356 13.669

A l ['I ¢) B~,y+ b 3 I ' I ( u = O) C a H ( v = O) b3H(t , =1) CtlI(u=l) C I H ( o = 2)

(l-r- t5so) ( I.-. - 14d-r ) ( 1 ~ - 15p~) (lr,-'Spo)

( l - r - 15do ) ( l - r - t5d ,--:) n ----6 - 7

15.74

n = 7-8

15.87

n = 8-9,

16.03 16.039 16.20 16.47 17.6-18.5

n = 9-10 ( l - r - x) 4 3 o - 13p-r) (30- t3so) (mixed) d)

19.118

0 0 -1 )

li- I DI.~+

(v

= 0)

DlX+(v =1) tYI(v = 0) DRY-+ ( v = 2) lX+(v=0) tH rE+ (v = 0). DtX÷(v=3) tFI ii1. DtX*(v=4) tlI XFl ix,* DtX+(v=5) ill tH

D'E*

(t, = 6)

X 2l'I(u = O) tH IT+

17.562-18.026 18.248-18.642

(3o- t3d-r) ( 3 o - 1 4 d ,~)

Y IYI(v = 0 to 4) Z 1FI(e = 0 to 3)

A - ' E - ( v = O)

=) Spectral positions a n d a s s i g n m e n t s o b t a i n e d f r o m 2.5 keV i n c i d e n t e l e c t r o n energy-loss m e a s u r e m e n t s , s t a t i c - e x c h a n g e a n d R P A E calculations, a n d previously r e p o r t e d optical V U V studies [5-7], as indicated. C o m p a r i s o n s b e t w e e n t h e p r e s e n t results a n d previous theoretical studies o f X --* A, B, C, a n d D excitations are r e p o r t e d in t a b l e 4. b) Spectral positions r e p o r t e d c o r r e s p o n d to t h e p r o m i n e n t features o f t h e 2.5 keV c r o s s sections o f figs. 2 a n d 3, i n d i c a t e d in the latter by vertical tic m a r k s b e l o w the m e a s u r e d profile. A s s i g n m e n t s a r e b a s e d o n the s t a t i c - e x c h a n g e a n d R P A E calculations o f t a b l e 3. T h e indicated ionization potentials a r e taken f r o m m e a s u r e d p h o t o e l e c t r o n s p e c t r a [ I 2 - 1 8 ] . ¢) Positions a n d a s s i g n m e n t s taken f r o m high-resolution optical V U V studies [5-7], with t h e e x c e p t i o n o f values for t h e X --) A transition, w h i c h are taken f r o m previously r e p o r t e d electron energy-loss m e a s u r e m e n t s [8]. T h e B-state p r o g r e s s i o n r e p o r t e d in the optical V U V s t u d y gives a n e x t r a p o l a t e d To value o f 10.51 eV, in g o o d a c c o r d with calculated values [31-34], as i n d i c a t e d in fig. 4. d~ Possible a s s i g n m e n t s for t h e weak features a p p e a r i n g in this e n e r g y region in the c r o s s s e c t i o n o f fig. 2 are s e e n f r o m t a b l e 3 to include 30 excitation into n p - r , n d - r , n p o , n s o , a n d n d o R y d b e r g series. O n basis o f calculated strengths, 30 --* n p o e x c i t a t i o n s are seen to c o n t r i b u t e m o s t significantly, as is d i s c u s s e d f u r t h e r in t h e text.

-

~ A . P . - H i t c h c o c k et a L _ / : S p e c t r u m a n d cross section o f H F -

threshold, and a broad, and strong-- f e a t u r e is apparent --i n b o t h .cross~ sections: a b o v e - the (3o-1)A25~ -+- threshold; ARh0ugh - the lbw-- a n d moderate:resolution cross:secfi0ns of fig_ 1 are not suitable for detailed s p e c t r ~ assignments, it is satisfying that sensibl e designations on a molecular:orbital :level o f a p p r o x i m a t i o n . =. which are b a s e d u p o n c a l c u l a t i o n s a n d the higlier-resolution spectra discussed b e l o w - - can b e .made o f the prominent features observed in the lower resolution spectra. Specifically, in accordance with discussion given further below,, the strong feature at = 1 0 eV is identified as 1,rr -~ 4 o ( o * ) , and that at --- 15 eV is largely 3o -~ 4 o ( o * ) , whereas the b r o a d m a x i m u m above threshold at = 20 eV in fig. I is attributed largely to 1~--g k d 8 continuum excitation on basis of closely related photoionization studies [47,48]. The measured a n d calculated cross sections of the present study do not include strong absorption features below the = 9 eV onset of the 1 ~ - - * 4 o ( o * ) band shown in fig. 1. By contrast, previous optical studies report lower-lying excitations [1-3], which can possibly be attributed t o impurity contamination or other experimental considerations [9]. Referring to the higher-resolution cross section of fig. 2, it is seen that the = 15 eV 3 o - * 4 o ( o * ) feature of fig. I has been resolved into a n u m b e r o f distinct bands, whereas the ----10 eV 1~-~ 4 o ( o * ) feature remains b r o a d and unstructured. The assignments shown in the figure are based largely on the single- and coupled-channel calculations reported in table 3, to which attention is now directed. It is seen that the lowest excitation in the calculated spectrum of table 3 corresponds to the first m e m b e r of the l~r ~ n p o series at 10.09 eV, which is the 1 ~ - , 4 o ( o * ) intravalence transition of fig. 1. Moreover, configuration mixing evidently introduces relatively small shifts in excitation energy and f n u m b e r in this case, since the static-exchange and R P A E results are in good agreement. " Additional support fo r assignment of the broad b a n d centered at 10.35 eV in fig. 2 as X--* (1~-14o)Atl-I is provided by the quantitative comparison between theory and experiment shown in table 4. T h e m e a s u r e d position and f n u m b e r of this b a n d are seen to b e i n g o o d a c c o r d with the present calculations, as w e l l as with previously

_-

75

-_ 5:"

•

> 10

_

--_-

B

t~.

-

_,,, 2 A~'Ff 0

0

I 2

[ ! I 3 4 5 I n t e r n u c l e a r Distance R (a o)

6

Fig. 4. Potential energy curves for selected states in H F adopted from previously reported theoretical studies [31-34]. The dashed curve provides an approximation to the (3o-14o)Vo configurational state energy, adopted from previously reported valencebasis calculations [31].

reported theoretical studies also shown in the table [31-34]. Moreover, calculated potential-energy curves confirm the dissociative nature of this state [31-34], clarifying the width of the absorption b a n d and the absence of resolved vibrational structure in the measured cross section. In fig. 4 are shown potential energy curves for the lowest few dipole excited states in H F , as well as the H F + ground-state curve, a d o p t e d from previous calculations [31-34], as i n d i c a t e d in the figure caption. The dissociative nature of the A I I I state is evident from the figure. Finally, the most recent and elaborate configuration-mixing calculations Of the X---* AII'[ transition in H F [33,34] are seen from table 4 to b e in excellent a g r e e m e n t with the present experimental and theoretical results. I t i s surprising, therefore, that one o f ~ e s 6 studies [_',4] purports to. b e in accord with e a r l i e r o p d c a i measurements reporting a band onset at 7.51 eV and a m a x i m u m at --7.7 e v [1-3], whereas the Other [33] purports to b e in a c c o r d with optical V U V

76

A.P. Hitchcock et a L /

Spectrum a n d cross section o f H F

d a t a p e r t a i n i n g to the B IE ~- state [5-7]. T h e s e assertions o f a g r e e m e n t b e t w e e n r e c e n t calculations [33,34] a n d the earlier d a t a [ 1 - 3 , 5 - 7 ] c a n p e r h a p s b e a t t r i b u t e d in p a r t to ambiguities that arise in precise identification o f the d e t e c t a b l e o n s e t o f dissociative c o n t i n u a . T h e hioJaer-lying m e m b e r s o f the l ~ r ~ n p o series o f table 3 are R y d b e r g in nature, with a d e f e c t ( 8 - 0.48) s o m e w h a t smaller t h a n a c c e p t e d values for p series [49]. By c o m p a r i s o n , p - s t a t e defects in a t o m i c f l u o r i n e r a n g e f r o m ~ 0.74 to 0_89 [50]. T h e s t a t i c - e x c h a n g e a n d R P A E results are seen to b e in essential a g r e e m e n t for this series, f u r t h e r c o n f i r m i n g its R y d b e r g nature. Since these transitions are q u i t e weak. discussion o f their prese n c e in the m e a s u r e d s p e c t r u m is given f u r t h e r below. In c o n t r a s t to these transitions, the calculated 1,-r ~ n s o a n d n d o R y d b e r g series o f table 3 are seen to include relatively s t r o n g r e s o n a n c e ( n = 3) m e m b e r s . T h e c a l c u l a t e d d e f e c t s in these cases o f 8-----0.78 a n d --0.15, respectively, are generally a p p r o p r i a t e for s a n d d series [49], with c o r r e s p o n d i n g s a n d d series a t o m i c f l u o r i n e values ranging f r o m = 1.13 to 1.30 a n d - 0 . 1 2 to 0.04 [50], respectively. T h e c a l c u l a t e d series are evid e n t l y little a f f e c t e d b y c o n f i g u r a t i o n mixing, furt h e r c o n f i r m i n g their R y d b e r g natures. T h e c o m p u t e d e x c i t a t i o n e n e r g y a n d f n u m b e r f o r the strong X~(lv-~3so)C"H t r a n s i t i o n are seen f r o m table 4 to b e in g o o d a g r e e m e n t with the m e a s u r e d intensities in the = 12.5 to 13.5 eV interval, o n which basis the spectral a s s i g n m e n t s are m a d e . M o r e o v e r , the v i b r a t i o n a l spacings bet w e e n these three assigned b a n d s in the X --, C ~I I e x c i t a t i o n c o r r e s p o n d closely to those o b s e r v e d in the (1.-.-~)X 2II H F -~ ionic state [17,18], as indic a t e d in fig. 2. It s h o u l d b e n o t e d in this c o n n e c t i o n that a s m o o t h u n d e r l y i n g dissociative c o n t r i b u t i o n has been s u b t r a c t e d f r o m the i n t e g r a t e d f n u m b e r f o r the X --, C b a n d s a n d a t t r i b u t e d to the X --~ B transition, as discussed f u r t h e r below. T h e higher-lying m e m b e r s o f the 1~--, n s o series, as well as the 1~ -* n d o . 30 ---, np-rr, a n d 3o --~ nd~r series o f X --, ~II s y m m e t r y , w h i c h are seen f r o m t a b l e 3 to b e R y d b e r g in nature, are also discussed f u r t h e r below. R e f e r r i n g n o w to the X - - , l ~ + excitations o f table 3, the c a l c u l a t e d vectors indicate s t r o n g R.yd-

b e r g - v a l e n c e m i x i n g b e t w e e n the 1 ~ - - - n p , r r series a n d the 3 0 ---, 4 0 ( 0 * ) excitation, the l a t t e r a p p e a r ing as a n i n t r a v a l e n c e i n t e r l o p e r in the f o r m e r series. As a c o n s e q u e n c e , the t w o c a l c u l a t e d lowest-1)dng X _._~l~.+ e x c i t a t i o n s o f t a b l e 3 are a c o n j u g a t e m i x e d R y d b e r g - v a l e n c e pair, receiving t h e des~ign~itions ( l ~ r - 1 3 p ' r r / 3 o - ~ 4 o ) B ~ ; ÷ a n d ( 3 o - ~ 4 o / l ~ - 1 3 p ~ r ) D l ~ + at the g r o u n d - s t a t e e q u i l i b r i u m i n t e r n u c l e a r s e p a r a t i o n . T h e calculated R P A E vertical e x c i t a t i o n energies a n d f n u m bers o f table 4 for these transitions are e v i d e n t l y in s a t i s f a c t o r y a c c o r d with the p r e s e n t e l e c t r o n energy-loss m e a s u r e m e n t s . P o t e n t i a l e n e r g y curves f o r the B a n d D 1E+ states, a d o p t e d f r o m p r e v i o u s c a l c u l a t i o n s [31-34], are d e p i c t e d in fig. 4, f u r t h e r classifying their n a t u r e s . It is seen f r o m this figure t h a t the B state, which is largely i n t r a v a l e n t at larger R. u n d e r g o e s a n a v o i d e d crossing in the F r a n c k - C o n d o n z o n e o f the g r o u n d state with the D state, w h i c h is largely 3p'rr R y d b e r g at larger R. A t R c the two states h a v e i n t e r c h a n g e d their R y d b e r g - v a l e n c e nature, however, w i t h the higher-lying D state c a r r y i n g the larger oscillator s t r e n g t h d u e to its larger 3 o - 1 4 o ( o *) c o m p o s i t i o n (table 3). T h e lower-lying B state is seen to b e repulsive in n a t u r e at Re, giving rise to a b r o a d a b s o r p t i o n b a n d that c o i n c i d e n t l y underlies the s t r o n g X - - , C tYI transition. T h e v i b r a t i o n a l spacings o f the s t r o n g X --* D p r o g r e s s i o n in fig. 2 are in general a c c o r d with that in the ( I ~ r - I ) X 2 F I H F + ionic state [17,18]. I n s p e c t i o n o f the D - s t a t e p o t e n t i a l c u r v e clarifies this c i r c u m s t a n c e , a n d also a c c o u n t s for the significant d e g r e e o f v i b r a t i o n a l e x c i t a t i o n in the X ~ D ~ . + transition. A l s o s h o w n in fig. 4 as a d a s h e d c u r v e is a n e s t i m a t e o f the u n p e r t u r b e d ( 3 o - ~ 4 o ) B ~E+ p o t e n t i a l e n e r g y c u r v e as it w o u l d a p p e a r in the a b s e n c e o f R y d b e r g - v a l e n c e m i x i n g [31]. Finally, in c o n n e c t i o n w i t h the X ---, B a n d D i E + e x c i t a t i o n s o f tables 3 a n d 4, it is seen t h a t r e c e n t e l a b o r a t e c o n f i g u r a t i o n - m i x i n g calculations o f these transitions a t t r i b u t e a larger f n u m b e r to the lower-lying B s t a t e t h a n to the D s t a t e [34]. Since the f n u m b e r s h a v e a p p a r e n t l y b e e n c a l c u l a t e d with a smaller a n d u n s p e c i f i e d basis set t h a n e m p l o y e d in c o n s t r u c t i n g p o t e n t i a l e n e r g y c u r v e s in these studies [34], it is n o t possible to c o m m e n t f u r t h e r o n the d i s c r e p a n c y . It s h o u l d b e n o t e d , h o w e v e r , that these r e c e n t corn-

A.P. Hitchcock et aL / Spectruin -and cross section o f H F

putational studies report strong mixing between 1¢r-t3d,tr a n d 3 0 - t 4 o configurations, whereas the present R P A E studies indicate no such mixing (table 3). Use of a very small Rydberg basis in the configuration-mixing calculations [34] m a y prevent proper separation o f 3p~r and 3d~r terms, giving rise to spurious l ~ r - t 3 d ~ - 3 o - t 4 o mixing, accounting for an X - ~ D 1~+ f n u m b e r (0.0023, table 4) f r o m these studies that is more in accord with the present 11r --* 3dxr value (0.0034, table 3) than with the stronger X --~ D t y + result (0.124, table 4) *. Although the earlier calculations [31-33] reported in table 4 give X ~ D ~?g+ transition energies that are somewhat larger than the present values, the associated oscillator strengths are seen to be in general accord with the R P A E calculations. Fig. 3 and table 5 provide detailed positions a n d assignments of the dipole spectrum in HF. Also shown in table 5 are positions and assignments taken from previous optical VUV studies [5-7]. The calculated excitation energies of table 3 are, o f course, not in precise agreement with the measured values of table 5; nevertheless the calculations are of sufficient accuracy to provide reliable assignments, a n d they furthermore furnish a basis for construction of individual b a n d oscillator strengths when combined with appropriate vibrational wavefunctions. The X---~(l~r-14o)AIY[ (10.35 eV, fig. 2) and ( l x r - Z 3 s o ) C l I I transitions have been described above in connection with table 4, and require little further discussion. It should be noted, however, that optical VUV studies [5-7] do not report a feature corresponding to the dissociative X--~ A (10.35 eV) b a n d o f the present study. As indicated in a previous publication [10], such a broad unstructured feature, resulting in a very gradual change with wavelength of plate darkening, could go completely unnoticed on the plates of a high-resolution optical study. The present measurements of the X--~ A~H transition are in good accord, however, with values obtained from previously reported electron energy-loss stud-

-~ In private correspondence, S.D. Peyerimhoff has suggested that the discrepancy between the m e a s u r e d f n u m b e r and the calculations o f ref. [341 for the X --* B transition (table 4) can possibly be attributed to vibrational averaging o f the electronic transition m o m e n t not included in the calculations.

77

ies [8], the results of which are giyen in table 5. T h e X--¥BIF. + a n d D I Z + transitions have also been discussed above in connection with table 4. As indicated in table 5, optical studies report [5-7] a long series of bands which extend from 11.940 to 14.672 eV (R branches) [6] and which can be attributed to X--~ B ly.+ excitation. The extrapolated value o f To = 10.51 eV is in excellent accord with the calculated B1Y + potential curve [31-34] shown in fig. 4. This extended part of the X---* B ~Y.+ b a n d system is presumably not detected in the present electron energy-loss study due to the low intensity of the band heads, a consequence of the large rotational spacings in the B t ~ + state [10], and also o f the presence of overlapping stronger Rydberg transitions. Consequently, the X ~ B ~Y-+ bands appear in the present study as a broad unresolved structure largely underlying the sharper features of the X --~ C ~1-I transitions in the = 13 to 13.7 eV interval, as indicated in table 5 a n d fig. 3. Construction of a detailed synthetic spectrum of X --->B v i b r a t i o n - r o t a t i o n transitions would be required to confirm these assertions, although the general shapes of the X- and B-state potential curves of fig. 4 would seem to provide sufficient evidence for present purposes. The very long and strong vibrational progression associated with the X--> D ~ + transition can be attributed to the d o m i n a n t 3 o - 14a configuration in the D l y~+ state, and to the position of the associated potential energy curve relative to the X l y + curve (fig. 4), resulting in a m a x i m u m F r a n c k - C o n d o n overlap for the 0 --~ 2 excitation. Referring now to the additional X ---, t l I transitions of table 5 and fig. 3, it is seen that higher-lying (n = 4, 5) members of the 1"~--~ nso series are too weak (table 3) to be observed. Similarly, the weak lxr---, 3po excitation underlies the very much stronger X --, D l y + (v = 0) band, and the l~r --* 4po excitation is also too weak (table 3) to be detected in the energy-loss spectrum. These series members are all listed in table 5 at the appropriate energies in order to clarify their positions in the spectrum. The first three (n = 3, 4, and 5) members of the stronger lxr--*ndcr series, however, appear clearly in the measured cross section. Specifically, the l~r -~ 3do excitation appears as an interloper in the generally regular X - o D 1 Z +

78

A . P . Hitchcock et aL / Spectrum a n d cross section o f H F

vibrational progression, and the l~r ~ 4 d o excitation is approximately degenerate with the 0---, 4 transition o f the X ---, D IX* manifold, whereas the l~r---~5do excitation appears as a discernible shoulder in the measured spectrum. Certain o f the higher-lying features in the = 15.6 to 16.0 eV interval o f fig. 3 presumably also c o r r e s p o n d to n = 6 and higher states o f ~II symmetry, although detailed assignments on basis o f the present studies are not warranted in these cases. O f the additional X ~ l X - transitions of tables 3 a nd 5 and fig. 3. it is seen that the 0--~0 transitions o f the higher-lying m e m b e r s (n = 4,5) o f the 3 0 - 1 4 o / 1 ~ - lnp'rr mixed Rydberg-valence series are a p p r o x imately degenerate with the 0 -* 3 and 5 members o f the X --, D 122+ manifold, respectively. rendering a separation o f these transitions impossible at the present resolution ( = 0.06 eV fwhm). T h e n = 3, 4. and 5 members o f the weaker 1-rr--* nd,'rr R y d b er g series are clearly discernible as shoulders an d peaks in the measured spectrum. Finally. tentative assignments are provided in table 5 o f weak features observed above the ( l ~ r - l ) X ' - I I ionization limit in the present study (fig. 2) as well as in optical V U V measurements [7]. These 3o excitation assignments are m a d e entirely on basis o f the calculated IVO positions and f numbers o f table 3, the R P A E results in these cases providing possibly spurious values due to configuration mixing that arises f r om autoionization into underlying l~r -~ ionization continua. Specifically. the calculated positions and f numbers o f the 30---, 3p'rr and ---, 3so excitations o f table 3 are seen to be in good accord with features in the measured spectrum at 16.20 and 16.47 eV. respectively. Although the calculated 30 ~ 3d~r and 4 d ~ excitation energies are in general accord with previously assigned (30-13d~)Y lII and ( 3 0 - t 4 d ~ ) Z III bands [7]. ot her transitions having greater (30 ---, 4p~r. 5pxr) and weaker (30 ---, 4scr, 5so. 4 do . 5 d o ) intensities are also predicted to a p p e a r in these spectral intervals. Moreover. the relatively strong 30 ---, 3po and 4 p o excitations can be expected to co n tr i but e to high-resolution V U V studies, although such features have appar e n t l y not yet been observed.

5. Concluding remarks Joi nt experimental and theoretical studies are report ed o f the valence-shell dipole absorp tio n cross section o f h y d r o g e n fluoride, a c o m p o u n d t hat has proved difficult to deal with in previous experimental studies, and has lead to discrepancies and controversy in the published literature. T h e experimental cross section obt ai ned in the present work from suitably normalized fo~vard-scattering (small-moment-transfer) 2.5 keV electron energyloss measurements is seen to include a broad dissociative feature centered at 10.35 eV, as well as a n u m b e r of strong, sharp, regularly spaced bands in the = 13 to 16 eV interval. Assignments are provided o f all p r o m i n e n t features observed on basis o f single-channel static-exchange and coupledchannel R P A E calculations employing very large basis sets. T he dissociative band at 10.35 eV is given the assignment X l ~+ ~ (1,rr-14o)AIII, and is seen to be the lowest-lying dipole-allowed excitation in the spectrum, in contrast to previous experimental studies reporting lower-lying excitations, and theoretical studies purport i ng to be in accord with these earlier measurements. O f particular interest in the = 13 to 16 eV excitation energy interval is the presence of a 30 ~ 4 0 ( 0 * ) intravalence interloper in the 1-rr--->npxr R y d b e r g series, giving rise to a pair of conjugate mixed Rydb e rg valence states designated as ( l x r - 1 3 p ~ r / 3 0 - 1 4 o ) B ~X + and ( 3 0 - t4o/1-rr- 13p-rr)D t X +, respectively, at the ground-state equilibrium internuclear separation R~. C o r r e s p o n d i n g potential energy curves, a d o p t e d from previously reported c o m p u t a t i o n a l studies, indicate an avoided crossing occurs between the ( 3 o - 1 4 o ) valence and (lrr-13p*r) R y d berg configurational states, clarifying the nat u re o f the R y d b e r g B state at ---13.2 eV and a strong v i b r a t i o n a l p r o g r e s s i o n associ at ed with the higher-lying valence D state. T h e shape o f the B ~X + state potential curve at larger R f u r t h e r m o r e clarifies the origins of a long progression of weak b a n d s observed in optical V U V studies, which are apparent l y below the detection sensitivity o f the present experimentfil study or are obscured b y stronger overlapping R y d b e r g transitions. In addition to the X --, A transition and mixed Rydberg-valence l * r - t 3 p * r / 3 o - ~ 4 o series, l'rr --,

_

L

.~

.

.4.P_ Hitchcodc et al. / Spectrum and cross section o f H F

n s o , ndo, nd~r, and n p o Rydberg Series also contribute to the cross section-in t h e - - - 13 to 16 eV interval. O f t h e s e t r a n s i t i o n s , the X --~ ( l x r - 1 3 s o ) C t y I r e s o n a n c e e x c i t a t i o n is f o u n d to c a r r y t h e l a r g e s t f n u m b e r , t h e 1Ir--* n d o s e r i e s is f o u n d t o b e m o d e r a t e l y s t r o n g , a n d t h e l"rr --+ n d ~ r a n d n p o series are seen to be quite weak. T h e calculated and measured excitation energies a n d f n u m b e r s o f t h e l o w e s t l y i n g X1~- +--+ ( 1 , r r - 1 4 o ) A t y I , (1-rr-t3p,rr)BtY. + , ( 1 , r r - 1 3 s o ) C l I I , a n d ( 3 o - ~ 4 o ) D ~Y.+ t r a n s i t i o n s a r e i n s a t i s f a c t o r y quantitative agreement, whereas those for the h i g h e r - l y i n g ( n = 3, 4, 5) R y d b e r g e x c i t a t i o n s a r e in generally satisfactory qualitative accord. Finally, plausible assignments are provided of weak features observed above the (l"rr-t)X2yI ionizat i o n limit, in general accord with earlier V U V optical studies.

Acknowledgement A c k n o w l e d g e m e n t is m a d e t o t h e d o n o r s o f t h e Petroleum Research Fund, administered by the American Chemical Society, to the U.S. National S c i e n c e F o u n d a t i o n a n d to t h e N a t u r a l S c i e n c e s and Engineering Research Council of Canada for f i n a n c i a l s u p p o r t o f t h i s w o r k . I t is a p l e a s u r e t o t h a n k M. I n o k u t i , S.D. Peyerimhoff, a n d K. W o l f for their helpful comments and correspondence.

References [l] K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomie molecules (Van Nostrand, Princeton, 1979) p. 304. [2] E. Salary, J. Romand and B. Vodar, J. Chem. Plays. 19 (1951) 379. [3] E. Safary, Ann. Phys. (Paris) 9 (1954) 203. [4] J.W.C. Johns and R.F. Barrow, Proe. Roy. Soc. A251 (1959) 504. [5] G. DiLonardo and A.E. Douglas, J. Chem. Phys. 56 (1972) 5185. [6] G. DiLonardo and A.E. Douglas, Can. J. Phys. 51 (1973) 434. [7] A.E. Douglas and F.R. Greening, Can. J. Phys. 57 (1979) 1650. [8] ILW. Shaw and T.D. Thomas, Phys. Rev. A l l (1975) 1491.

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A . P . H i t c h c o c k et a t / S p e c t r u m a n d cross section o f H F

[43] G.R.J. Williams and P.W. Langhoff, Chem. Phys. Letters 78 (1981) 21. [44] T.H. Dunning and J.P. Hay, in: Modern theoretical chemistry. Vol. 3, ed. H.F. Schaefer III (Plenum Press, New York, 1976) ch. 1. [45] P.W. Langhoff, R.P. Hurst and M. Karplus, J. Chem. Phys. 44 (1966) 505. [46] P.W. Langhoff, S.T. Epstein and 1V[. Karplus, Re~: Mod. Phys. 44 (1972) 602.

[47] IC F~gri Jr. and H.P. Kelly, Phys. Rev. A23 (1981) 52. [48] M.R. Herm~nn S.R. Langhoff, G.R.J. Willi~m~ and P.W. I~nghoff. to be published. [49] M.B. Robin,-Higher excited states of polyatomic molecules, Vols. 1, 2 (Academic Press, New York, 1974). [50] C.E. Moore. Atomic energy levels, Vol. 1, USDC, NBS, Circular 467 (1949).