A theoretical investigation of vibrational fine structure accompanying core ionization in hydrogen cyanide and acetylene

Journal of Eiectron Spectroscopy and Related Phenomena, 13 (1978) 3 17-326 @ Elsewer Saentlfic Pubhshmg Company, Amsterdam - Prmted m The Netherlands

A THEORETICAL ACCOMPANYING ACETYLENE

INVESTIGATION OF VIBRATIONAL FINE STRUCTURE CORE IONIZATION IN HYDROGEN CYANIDE AND

D T CLARK and L COLLING Department of Chemutry,

Unwerszty of Durham, South Road, Durham City (Gt Bntum)

(Received 11 October 1977)

ABSTRACT Non-emplncal calculations at the STO-4 31 G level are reported on the groundstate and core-lomzed states of HCN and H,C, An analysis of the changes m bond lengths and force constants for the normal modes mvolvmg stretching vlbratlons allows direct computation of the overall band profiles for the core-lomzed levels The dlstmct asymmetrles arlsmg from the vlbratlonal excrtatlons accompanying core lomzatlons suggest that the experimental mvestlgatlons of these systems would be eminently worthwhlle INTRODUCTION Although vibrational fine structure accompanymg valence photoromzatlon m UPS 1s well documented and comparatively well understood’, It 1s only with the recent advent of high-resolution FSCA mstrumentatlon mcorporatmg fine focus X-ray monochromatlzatlon that the presence of vlbratronal fine structure accompanymg core lomzatlon has been demonstrated Theoretlcal and experimental data however are still scarce and are restricted to a number of simple molecules’* 3 An extensive experimental and theoretical mvestlgatlon of the Cl, and N,, the spectra of CH4, CO and N, has been reported by Slegbahn and co-workers3, expenmental data bemg interpreted m terms of Franck-Condon factors derived from calculations on equivalent core species Recent theoretical work4, however, has m&cated a slgmficant difference m bond length and force constant between equlvalentcore and hole-state species, and this led to a further theoretlcal study of CO and N, using m which the experimental C Is, N,, and 0 Is spectra were well reproduced Franck-Condon factors derived from calculations at the triple zeta level’ An alterformalism, employing native approach has been developed5* 6 using a many-body Green’s functions to generate one-particle couplrng constants and hence vibrational envelopes In cases which have been studied by both methods the agreement IS good

318

5a2 The many-body formalism provrdes an elegant and powerful means of mvestlgatmg vlbratlonal excltatlons accompanying core lomzatlon, nonetheless such an approach has considerably less conceptual appeal than the strarghtforward ASCF approach which can provide conslderable chemical insight to the experlmentahst wlthm a one-electron framework For this reason and for the fact that such an approach can be made at modest computational expense, we report here computations of aspects of the potential energy surfaces for the ground and core-lomzed states of acetylene and hydrogen cyamde within the ASCF formalism The advent of a new generation of ESCA mstrumentatlon characterized by both high resolution and sensltlvlty will undoubtedly lead to detailed mvestlgatlons of vlbratlonal fine structure accompanying core lomzatlons m simple molecules and m antlclpatlon of thrs we report here a detailed theoretical analysis for the 1soeIectromc senes N,, HCN and H2C2, and for comparison purposes CO Even for such simple systems as these the number of computations required to provide a detailed analysis of the vlbratlonal fine structure IS not mconslderable and therefore a compromise must be made between computatlonal expense and quality of basis set This IS particularly the case If comparisons are to be drawn with larger systems for which computations are only available with basis sets of modest quahty In previous papers” 4* “9 lz It has been shown that optnmzatioe of exponents within the splnt of the equivalent-cores concept provides a means of accurately descrlbmg both absolute and relative bmdmg energes, and geometry and forceconstant changes accompanymg core lomzations, with basis sets at the STO-4 31G 1eveI In this work therefore we describe the results of ASCF computations at the STO-4 3 1G level for the Isoelectronic series of molecules which provide an mterestmg insight into the structural-dependence of changes m equlhbrmm geometry accompanymg core ionization COMPUTATIONAL

DETAILS

Calculations were cmed out within the ASCF Hartree-Fock formalism smce there IS evidence to suggest that the predlctlon of changes m bond lengths, force constants and absolute core bmdmg energies for first row elements are msensltlve to &fTerences m relatlvlstlc and correlation energes ’ The calculations were performed using the ATMOL system of programs* implemented on an IBM 370/195 The basis sets used were at the STO-4 31G level and for the core-lomzed species exponents appropriate to the equivalent core species9 (“optlmlsed STO-4 31G”) were employed The computations m all cases correspond to the localized hole states The vlbratlonal envelopes for core lomzatlons m HCN, H2C2, N2 and CO were generated using the theoretically calculated energy separattons of the mdlvldual component peaks, and the Franck-Condon factors which were computed from the calculated bond length changes and force constants for the ground- and hole-state species using the recurrence relations denved by Ansbacher” The vibrational

319 analysis presented here IS wlthm the harmonic approxlmatlon, the changes m vlbratlonal separations which arlse from anharmomclty having been shown to be neghgable’ The full width at half maximum (FWHM) of the component peaks was taken to be 0 32 eV, a value believed to be consistent with the llmlt of resolution with the most recent mstrumentatlon techmques2 RESULTS

AND

DISCUSSION

Bmdmg

and relaxation energres We have previously noted’> 4 that bmdmg energes for core lomzatlon can be calculated at the STOlC 31G level with an accuracy comparable with that obtained when employmg a triple zeta basis set, provided that the effective change m potential experienced by the vaIence electrons on core lomzatlon 1s accounted for by usmg valence exponents appropriate to the equivalent core species m the calculations on the core-Ionized species The calculated absolute and relative bmdmg and relaxation energies are dlsplayed m Table 1, and for comparison purposes, m the particular cases of nitrogen and carbon monoxide, data for mole extended basis set computations are included Also included are the results of prewously reported computations at the ST04 3 1G level with Identical exponents used for both the neutral and corelomzed species It IS clear from these data that the use of the optlmlzed exponents within the ASCF formalism provides an excellent description of both the absolute and relative bmdmg energies for the Cls, N1, and O,, core levels For the C,, levels the relaxation energy mcreases m the order CO < H-CN < H2C2, which 1squahtatlvely reasonable on the basis of the contrlbutlons ansmg from contractlon of the local electron density about carbon and the migration from the attached atoms Slmllarly the relaxation energy for N1, core lomzatlon IS larger for HCN than for N2 Bond lengths and force constants for neutral molecules As a prelrmmary to the study of the core-romzed species, force constants and bond lengths were first calculated for the senes of neutral molecules The procedure was to use, as a startmg geometry, the bond lengths optlmlzed by Pople and coworkersI with a 4 31G basis set, and to compute the parabohc varlatlon of energy as a function of the length of the relevant bond or bonds A process of successive energy mmlmlsatlon was used, the geometries correspondmg to the mlmma bemg taken as startmg geometries until the final smallest extension and compression of the reIevant bond length was 0 01 a u Havmg defined the parabola, force constants were then calculated from the shape of the potential energy curve m the vlcmlty of its mmlmum For HCN and H2C2, only stretching modes were considered smce prehrmnary calculations mdlcated mmlmal change m the force constants for the relevant bendmg

4117

2951

ii

H-C= C-H 6

5420

298 1

4108

2911

4070

2935

5419c

296gc

4102c

2913

4061

2933

5423

2962

4099

Thiswork ExpertSTO-431G mentalb “opt”

5419

2978

4108

Ref 13 Triplezeta

Adrubatrc

2909

4069

2933

5418C

296 6O

410 1c

Thuswork ST&4 3lG “Opt ”

110

137

100

151

a3

123

20 8

119

164

151

185

139

22 7

124

172

Thiswork Ref 13 ST0-4 SIG Triplezeta ST@4 31G “opt”

Relaxatranenergy

&Verticalbmdmgenergesare calculatedat the theoreticallyoptlmlzedeqmhbrmmgeometryof the groundstate Adiabaticbmdmgenergiesare calculatedas energydifferences for the theoreticallyoptlmlzedgroundand hole-stategeometries b Refs 14-16 C Ref 2

2974

i:

5484

ci

HC=N

3009

i?

CO

415 1

I4

Ref 13 ST0-4 3ZG Triplezeta

Vertical

Bindingenergy

NZ

Species

BINDINGENERGIESANDRELAXATION ENERGIES(eV)FOR CO,Nz,HCNANDH&Z&

TABLE1

2015

HC&

HCrN

2 303

H-C!=C-H

* b r d e

CH

0 021 0061

1993

1953

2 075

6-H

C-H

0104 1 98@

2 249l

1 986l

2 1541

b

2005

2 277

2009

2 183

2 132

2 074

Expt c

6 93 7 01 6 93 6 70

VsymC-H YSYmC-H ySntisymc_H

24 44

19 15

7 01

7 01

26 15

28 02

22 57

15 OY

30 70e

22 10e

30 70e

28 10

&

Calculared

4 49

00

-27 64

00

-15 86

-24 14

31 90

-38 91

-925

A%

Force constant

y&ntisymC_H

UC-C

‘W-H

UC-N

W-O

W-N

Mode

This work 1 Pople and co-workers17,2 Blom et al 20,3 Bagus et al ‘21,4Pulay and Meyer22 Sutton23 Herzberg= Clark and Muller2

H&

2 014

H-C= C-H

C-H

2 199

H-i% C-H

C-C

1965

H&N

0 05

0 088

2 124

H&N

C-H

0 080

2 212

-0 070

0 108

0064

2 132

C-N

2 237e

CE6

HC=N

2 059e

2 167e

206Oe

2 124e

Calculated & a

Bond length

ES.0

CEO

c-o

N-N

N=N

N&i

Bond

Specres

6 633, 6 98*

20 42, 16 63,18 04

b

5 92

15 80

5 85

1790

1900

22 96

Expt d

CALCULATED AND EXPERIMENTAL EQUILIBRIUM BOND LENGTHS (ATOMIC UNITS) AND STRETCHING FORCE CONSTANTS (MDYN 8-X) FOR Nz, CO, HCN, AND C2H2, AND THEIR RESPECTIVE CHANGES ON CORE IONIZATION

TABLE 2

322 modes* Since the mteractlon constants are small1g9 lg, and m any case the observation of vlbratlonal fine structure accompanying core ionization lmphes rather gross changes m potential energy surfaces on going from the ground state to the core-hole state, the vlbratlonal analysis has been m terms of the stretching modes for the C-H (vJ) and C-N (vl) bonds for HCN Also, since the creation of a C,, hole m the case of acetylene lowers the symmetry from Da,, to C,,, It IS possible to couple to both symmetnc and antlsymmetrlc modes, and the analysis has therefore been made rn terms of the three normal modes m acetylene, the symmetric C-H stretch (vl), the C-C stretch (vZ) and the antlsymmetrlc C-H stretch (v3) The results of these calculations for the neutral species are &splayed m Table 2 along with the relevant experimental and previously calculated data Agreement with expenment IS good for the bond lengths (l-3%), although the force constants are consistently overestlmated, as might have been antlclpated for the modest basis sets employed In consldenng vlbratlonal fine structure accompanymg core lomzatlon the important factors are changes rn equlhbrmm bond lengths and ratios of force constants for ground and core-lomzed species The basis sets employed m this work have previously been shown to provide an excellent descnptlon of such vlbratlonal fine structure and this IS readlIy understandable since the descrlptlon of changes m bond lengths and mdeed absolute values are well described as are the ratios (as opposed to absolute magmtudes) of the force constants In addxtlon, smce the energy separation between components (1 e vlbratlonal frequency) mvolves the square root of the relevant force constants, the overestlmatlon m absolute terms of the latter becomes somewhat attenuated when computations of vrbratlonal fine structure are involved VlbratlonaEfine structure accompanymg core lomzatlon The correspondmg data for the core-ionized species are also displayed m Table 2 and form an mterestmg comparison for these trlply bonded systems C,, core lomzatlon m all cases leads to a decrease m equlllbrlum bond length of ca 0 1 a u In the cases of hydrogen cyanide and acetylene the CH bond lengths are also computed to decrease, however the shortemng 1s somewhat smaller than for the C-X bond For core lomzatton of the N,, levels m mtrogen and hydrogen cyanide the calculations again predict a decrease m bond length, that for HCN bemg slgmficantly the larger Indeed the computed change m bond length for the CN bond 1s slightly larger for core lomzatlon of the N,, as opposed to the C,, levels This can partially be attributed to the mltlgatmg effect of electronic reorganization m the CH bond accompanymg C 1s core lomzation since previous work suggests and experiment confirms that, for carbon monoxide and nitrogen, whrlst C Is and N,, core lomzatlons

* Smce the wbratlonal spacmgs are so close for the bending modes, and smce the nature of the expenmental and theoretwal lrrmts of resolution are relatively large, It seems unhkeiy that the excltatlon of bendmg modes ~111 be demonstrated for core-lomzed systems

323 lead to a decrease m bond length (that for the C,, levels bemg substantially the larger), 0 Is core lomzatlon actually leads to an Increase m bond length Since the CH bond length m hydrogen cyamde IS Identical to that m acetylene no change m bond length of the CH bond IS to be antlclpated for photolomzatlon of the N1, level m hydrogen cyanide The changes m force constants follow the order that might have been antlclpated

FWHM 038ev

:-

-----Li 1’ ,’ I\

t,

’

I I

’

f

/j

I

:

/,-& ,--:_-

.I

_

-.$.

I

: ,1 \ , \ \

’

L

\\

),

,

I

:

I

,r.

I I

:

\I ‘8

/\\

‘\

.

‘\\ \\

HC.:H I

FWHM

0390~

--I

I :1 \ 1 I

:

I I I

I

29L

293

292

291

P”

Figure 1 The Cl8 spectra for HCN and HzC2 showmg the relative contnbutlons modes and then vlbratlonal components

of the stretchmg

324

FWHM

Lll

LlO

Figure 2 The Nls spectra N-X stretchmg vlbratlon

LO9

for Nz and HCN

LO8

showmg

LO7

the vlbratlonal

components

resulting

from the

m the light of the mformatlon on the computed changes m bond lengths Thus m the series CO, HCN, H,C,, C,, core lomzatlon 1saccompamed m all cases by substanttal increases m the force constant correspondmg to the CX stretchmg mode By contrast the modes mvolvmg CH stretchmg frequencies remam essentially the same, and as a result the Franck-Condon factors for excrtatlons of these modes pertam essentially to the O-O transltlons We have previously described m some detail the vlbratlonal profiles for the dgrect photolomzatlon peaks correspondmg to the core Ievels of CO and NZ and we confine the remamder of the dlscusslon therefore to the data pertaining to HCN and CZH, for which high-resolution data are as yet not avadable The computed FranckCondon factors therefore form the basis for the predIctIon of the overall band profiles for core lomzatlon m these systems The components and computed overall band profiles for core lomzatlon of the

325 C,, levels of HCN and H,C2 are shown m Fig 1 The most strongly excited vibration corresponds to the stretchmg mode for the CN and CC bonds, respectively The vlbratlonal excltatlon of the CH stretching modes m acetylene accompanying core lomzatlon IS largely confined to the antlsymmetrlc vibration The FWHM for the overal line-shapes of 0 38 eV and 0 39 eV are slgmficantly larger than for that dppropnate to a smgIe component (0 32 eV), however the mam mamfestatlon of vlbratlonal excltatlon 1s the considerable asymmetry of the overall profiles With state of the art mstrumentatlon both this and the increase In hne-width shouId be readily detectable For comparison purposes the data for the N,, levels of HCN dIsplayed m Fig 2 are accompamed by the correspondmg data for N,, the FWHM being taken as 0 32 eV for the mdlvldual components The strong excltatlon of the stretching mode m each case IS mamfest m the case of HCN by a large increase m FWHM for the overall band profile which should readily be detected with current mstrumentatlon For comparison purposes It may be noted that the ab mltlo computed Franck-Condon factors for N, using triple zeta Slater basis sets suggest that the extent of vibrational excltatlon will onIy be shghtly overestimated with the data taken from the optlmlzed ST04 3 1G basis set computatrons Comparison of the overall line-shapes at appropriate resolution computed from the two basis sets and the experImental data provides strong evidence that the data dlsplayed m Figs 1 and 2 will form a sound basis for the mterpretatlon of the experimental data when these become available ACKNOWLEDGEMENTS

Thanks are due to S R C for provlslon and for computmg faclhtles (IBM 370/195)

of a fellowship

to one of us (L C )

REFERENCES 1

2 3 4 5 6 7 8 9 10 11 12 13

D W Turner, C Baker, A D Baker and C R Brundle, Molecdar Photoelectron Spectroscopy, Wiley, New York, 1970, J W Rabalals, Prznczples of Ultvavtolet Photoelectron Spectroscopy, Wiley, New York, 1977 D T Clark and J Muller, Theor Chrm A&a, 41 (1976) 193 U Gehus, S Svensson, H Slegbahn, E Baslher, A Faxalv and K Slegbahn, Chem Phys Lett , 28 (1974) 1 D T Clark, 1 W Scanlan and J MulIer, Theor Chzm Acta, 35 (1974) 341 W Domcke and L S Cederbaum, Chem Phys Lett , 31 (1975) 582 L S Cederbaum and W Dotncke, J Chem Phys , 60 (1974) 2878 E Clement1 and H Popkle, J Am Chem Sot , 94 (1972) 4057 V R Saunders, I H Hllher, M F Chm and M F Guest, Atlas Computmg Laboratory E CIementl and D L Ralmondl, J Chem Phys , 38 (1963) 2686 F Ansbacher, 2 Naturfirsch A, 14 (1959) 889 R McWeeny and A A Velemk, Moi Phys , 24 (1972) 1421 A D Buckmgham, N C Handy and R J Whltehead, J Chem Sac Faraday Trans 2,l (1975) 95 J Muller, TheoretIcal Aspects of Relaxation Phenomena Accompanymg Photoiomzatlon of Core and Valence Electrons, Ph D Thesis, Uxnverslty of Durham, Durham, 1976

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15 16 17 18 19 20 21 22 23 24

K Slegbahn, C Nordhng, G Johansson, J Hedman, P F Heden, K Hamrm, U Gelms, T Bergmark, L 0 Werme, R Manne and Y Baer, ESCA Applied to Free Molecules, NorthHolland, Amsterdam, 1969 T D Thomas, J Chem Phys , 52 (1970) 1373 D W Davis, J M Hollander, D A Shirley and T D Thomas, J Chem Phys , 52 (1970) 3295 R Ditchfield, J Del Bene and J A Pople, J Am Chem Sot ,94 (1972) 4806 E B Wilson, J C Deems and P C Cross, Molecular Vzbratzons The Theory of Infra-red and Raman Vzbratzonal Spectra, McGraw-HIl, New York, 1955 J C D Brand and J C Speakman, Molecular Structure, The Physzcal Approach, Edward Arnold, London, 1960 C E Blom, P J Slmgerland and C Altona, MoZ Phys , 31 (1976) 1359 P S Bagus, J Pacansky and U Wahlgren, J Chem Phys , 67 (1977) 618 P Pulay and W Meyer, MoI Phys , 27 (1974) 473 L E Sutton, Tables of Interatomzc Bzstunces Supplement, Special Pubhcatlons No 18, London Chemical Society, Burlmgton House, 1965 G Herzberg, Molecular Spectra and Molecular Structure If Infra-red and Raman Spectra of Polyatomzc Molecules, D van Nostrand, New York, 1945