Theor Chem Acc (1999) 102:161±164
DOI 10.1007/s00214980m103

Regular article
SAC-CI general-R study of the ionization spectrum of HCl*
M. Ehara1, P. Tomasello2, J. Hasegawa1, H. Nakatsuji1,3
1Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
Dipartmento di Fisica, Universita di Catania, I-95129 Catania, Italy
3
Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyou-ku, Kyoto 606-8103, Japan
2

Received: 26 June 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999

Abstract. The valence ionization spectrum of HCl isstudied by symmetry-adapted-cluster con®guration-interaction general-R and SD-R methods. The general-R
method describes well the peak positions and intensities
of seven satellite lines observed below the double
ionization threshold. The twinning shake-up states dueto the (4r))1 state and the Rydberg states of HCl+ arecorrectly reproduced.
Key words: Symmetry-adapted-cluster
con®guration-interaction ± HCl ± Ionization spectrum ±Electron correlation ± Shake-up state

1 Introduction
Many satellite peaks are found in the inner-valence
region of the ionization spectrum. These peaks are of
considerable interest since they re¯ect electron correlations in molecules. Recently, these peaks have been
intensively studied by high-resolution X-ray photoelectron spectroscopy (XPS), synchrotron radiation photoelectron spectroscopy (SRPS), and electron momentum
spectroscopy. The satellite lines of HCl [1±5] werestudied in detail by Adam [3, 4] and Svensson et al. [5]and the valence ionization spectrum was recorded up to52 eV using XPS and SRPS [5]. Eleven satellite lines
were observed and seven of them were found to lie below
the continuum of the doubly ionized state. Some of thepotential curves were also studied by the isotope eect
and the photon-energy dependence of the intensity.
The satellite peaks of HCl [6] have also been studied
theoretically by the Green function method, algebraic
diagrammatic construction (ADC) (3) and approximated ADC (4) [7±9]. Seven satellite lines were analyzed
with respect to vertical ionization [6]. Some of thepotential curves for HCl+ were studied by the multireference con®guration interaction method and ®ve lines*Contribution to the Kenichi Fukui Memorial Issue
Correspondence to: M. Ehara

were assigned by taking account of the Franck±Condon
factors from the neutral ground state [10]. However, it
still seems to be important to perform reliable calculations with extended basis sets including sucientamount of electron correlation, especially for the assignment of the high-lying shake-up states. In particular,
there are congested satellite peaks which are considered
to be due to the Rydberg states converging to the doublyionized states [5, 6, 10].
The symmetry-adapted-cluster con®guration-interaction (SAC-CI) method [11±16] has been successfully
applied to several molecular spectroscopic problems including ionization spectroscopy [17±24]. There are twostandard choices of the linked operators (R) in the SACCI methods, namely, single double (SD)-R and generalR methods [25±28]. Details of the general-R method canbe found in Ref. [25] The SAC-CI general-R method isdesigned to describe multiple-electron processes withhigh accuracy and has been shown to be useful forstudying many dierent kinds of states in ionization
spectra [25, 29]. In a recent series of applications [29±31],
we studied the details of the shake-up states using theSAC-CI general-R method.
In this paper, we study the ionization spectrum of
HCl up to the double ionization threshold by the SACCI general-R and SD-R methods.
2 Computational details
In the preceding study of HCl by ADC [6], several basis
sets were systematically examined and diuse functions
were found to be important, while the f functions on Cland the d functions on H did not have much eect on theresults. Therefore, we chose ``basis set I'' in Ref. [6] forour basis set; (12s9p)/[8s6p] GTOs of McLean andChandler [32] augmented with two diuse s and pfunctions of fs  0.06, 0.015 and fp  0.04, 0.01, plus fourd functions of fd  0.7, 0.25, 0.08, and 0.02 for the Clatom, and (5s)/[3s] GTOs [33] plus two p functionsof fp  1.0 and 0.3 for the H atom. The resultant basis
set is (14s11p4d/5s2p)/[10s8p4d/3s2p]. The internucleardistance is 1.2746 AÊ of the experimental ground state[34] and vertical ionizations are studied.

162

Both SAC-CI general-R and SD-R calculations areperformed. Since most of the shake-up states of HCl aredescribed by two-electron processes, higher excitation
operators in the general-R method were limited up totriples. In the SD-R method, unlinked terms written as
abbcand Raij Skl, were included; namely the ``3,4-excited''
Ri Sjkcalculation [18] is performed. In the SAC-CI calculation,1s, 2s, and 2p orbitals of Cl were frozen as cores andthen the active space consists of 4 occupied MOs and 58
unoccupied MOs. Perturbation selection was performed
for the linked operators higher than doubles to reducethe computational eort. For the ground state, thethreshold for the linked doubles is kg  1 ´ 10)5 a.u. andthe unlinked terms are written as the products of theimportant linked terms whose SDCI coecients arelarger than 0.005. For the ionized states, the thresholdfor the linked operators is ke  1 ´ 10)5 a.u. The
thresholds of the CI coecients for calculating theunlinked operators are 0.1 and 0.001 for the R and S
operators which are the SAC and SAC-CI operators,respectively.
The HONDO8 program [35] is used for the HF SCF
calculations and the SAC-CI96 program [36] is used for
the SAC-CI calculations.

10±40 eV in Fig. 1. The spectrum includes (2p))1 and(5r))1 states and the seven higher bands which are due tothe shake-up states borrowing their intesities mainly
from the (4r))1 single-hole state. The intensity of thepeak is calculated by the monopole approximation including initial- and ®nal-state correlation eects [37],though the monopole intensity does not necessarily givethe quantitative cross-section of the photoelectron
spectroscopy. Each peak in the theoretical spectrum is
convoluted with the dierent line width as obtained fromexperiment [5]. The present convolution is symmetricin higher- and lower-energy directions, though the line
shape should be asymmetric when the Franck±Condon
factor is taken into account [10]. The main con®gurations of each peak, together with the peak position andintensity are shown in Table 2. They are shown for thestates up to 35 eV and 38 eV for general-R and SD-R,
respectively, with calculated intensities greater than
0.005 except for some low-lying 2P states. The experimental ionization potentials (IPs) and intensities are

3 Results and discussion
The ionization spectrum up to the double ionizationthreshold, i.e. about 35 eV, was studied by the SAC-CI
general-R and SD-R methods. The satellite states belong
mainly to 2S, so that 40 and 15 ionized states werecalculated for 2S and 2P symmetries, respectively. The
number of reference con®gurations used for the perturbation selection, and the dimensions of the linked
operators in the general-R calculations together withthose before perturbation selection are summarized inTable 1. Since most of the shake-up states are described
predominantly by two-electron processes, the referencecon®gurations are 73 and 56 singles and doubles
con®gurations selected for the 2S and 2P states, respectively. The dimensions of the SAC-CI general-R calculations are about 7,600 and 5,800 for the 2S and 2Pstates, respectively.
The ionization spectra of HCl calculated by the SACCI general-R and SD-R methods are compared with theX-ray photoelectron spectrum [5] in the energy region
Table 1. Numbers of the reference con®gurations and the dimensions of the linked operators in the symmetry-adapted-cluster
con®guration-interaction (SAC-CI) general-R calculations for theionized states of HCl
State

Singles

Doubles

Triples

Total

Numbers of reference con®gurations
2S
2
71±2
P
155±7356

Dimensions of SAC-CI general-R calculationsa
2S
2/2
237/272
7,360/17,5362P
1/1
185/224
5,682/17,220

7,599/17,810
5,868/17,445

aDimensions after perturbation selection/before perturbation selection

Fig. 1. Ionization spectra of HCl by a X-ray photoelectron
spectroscopy, b the symmetry-adapted-cluster con®guration-interaction (SAC-CI) general-R method, and c the SAC-CI single
double (SD)-R method. Each peak in the theoretical spectra isconvoluted with the dierent line widths as obtained fromexperiment [5]. Intensity of (2p)1) is normalized to 2

163

from XPS and SRPS [5]: the intensities are shown relative to that of line 2.
The two main peaks at 12.8 and 16.6 eV in the experimental spectrum [5] are reproduced well by both theSAC-CI general-R and SD-R methods. The general-R
method calculates the (2p))1 and (5r))1 states to be at
12.41 and 16.46 eV, while they are calculated to be at
12.50 and 16.56 eV by the SD-R method. Inclusion ofhigher excitations in the SAC-CI operators R does notaect much the main-peak positions and their intensities;
this has also been shown by other examples [25, 29±31].
For the seven bands above 20 eV, remarkable differences are seen between the general-R and SD-Rresults. The general-R method nicely reproduces thepositions and the intensities of the shake-up states. It is
important to include higher-than-doubles excitation
operators in the linked operators to describe well theshake-up states, which are essentially the two-electronprocesses relative to the ground state. This was also
found in a series of recent applications [29±31]. Amongthe seven bands observed in the energy region 22±36 eV,the ®rst twinning peaks centered at about 25 eV originate from the (4r))1 state [5, 6, 10]. They are calculated
to be at 23.96 and 26.38 eV in comparison with the experimental IPs of 23.5 and 25.8 eV. These states have thecharacter of (2p)2nr) as shown in Table 2. The relative
intensity of line 1 to line 2 is evaluated as 0.58 by thegeneral-R method; this is slightly larger than the experimental value of 0.417. By the SD-R method, the twinning states are calculated to be at 25.51 and 28.39 eV
and their relative intensities are reversed. The dierence
between the general-R and SD-R methods for describing
these states is shown in Table 3. In the general-R
method, the weight of the con®guration (2p)2nr) islarger in the 22S state than in the 32S state, while the SDR method gives the opposite picture; therefore, the relative intensity of these peaks is calculated dierently by
the two methods. The weight of triples is not so large forthese states. Small asymmetry of the peak was observed
for band 2 and this was attributed to the 32P state [10].
This 2P state is calculated by the present general-Rmethod to be at 27.88 eV with a small monopole
intensity of 0.001 as shown in Table 2.
Table 3. Main con®gurations (C>0.2) of the 22S and 32S states
calculated by the SAC-CI general-R and SD-R methods
State SAC-CI general-R

SAC-CI SD-R

22S

0.46(4r)1)+0.42(2p)211r) 0.76(4r)1)+0.26(2p)211r)+0.42(2p)211r)+0.26(2p)211r)

32S

0.60(4r)1))0.24(2p)211r))0.24(2p)211r)

0.39(4r)1))0.45(2p)211r))0.45(2p)211r)+0.24(2p)29r)+0.24(2p)29r)

Table 2. Excitation level, ionization potential (IP) (in eV), monopole intensity, and main con®gurations of the ionized states of HCl
calculated by the SAC-CI general-R and single double (SD)-R methods
StateExptl.aIP

Intensityb

1

16.6
23.65

2
3

Line
No.

IP

Intensity

Main con®gurations (C>0.3)

IP

Intensity

0.417

12

16.46
23.96

0.899
0.211

16.56
25.51

0.947
0.578

25.85
28.5

1.0
0.043

22

26.38
28.78

0.365
0.028

28.39
32.01

0.153
0.006

429.8

0.164

230.04

0.006

34.41

0.027

532

0.194

22

31.27
32.43
32.71

0.039
0.009
0.012

36.26
36.52
37.74

0.009
0.030
0.013

6

33.2

0.164

233.92

0.016

37.88

0.018

2234.01
34.14

0.021
0.069

234.650.007

0.94(5r)1)
0.46(4r)1)+0.42(2p)211r)+0.42(2p)211r)
0.60(4r)1)
0.33(2p)29r)+0.33(2p)29r)+0.32(2p)212r)+0.32(2p)212r)
0.43(5r)211r))0.36(2p)22d))0.36(2p)22d)0.43(5r)211r)
0.46(5r)12p)15p)
0.41(5r)12p)16p)+0.41(5r)12p)16p))0.30(2p)21d)0.58(2p)15r)15p))0.58(2p)15r)15p)+0.36(2p)15r)13p)-0.36(2p)15r)13p)+0.33(5r)12p)15p)-0.36(5r)12p)15p)
0.42(2p)28r)+0.42(2p)28r)
0.34(2p)28r)+0.34(2p)28r)+0.32(2p)15r)16p)+0.32(2p)15r)16p)
0.53(2p)27r)+0.53(2p)27r)

12

12.41
27.88

0.907
0.001

12.50
34.34

0.950
0.007

22
2

28.58
29.55
29.98

0.001
0.001
0.006

230.24

0.002

72P

ab

SAC-CI SD-R

Excitation
level

2S

SAC-CI general-R

34.65

0.143

12.8

Ref. [5]Intensity relative to the second line

0.95(2p)1)
0.50(2p)26p))0.47(5r)12p)111r)+0.38(2p)26p)+0.30(5r)12p)19r)
0.56(2p)25p)
0.48(2p)26p))0.34(5r)12p)19r)
0.56(2p)25p)+0.35(2p)25p)+0.34(2p)23p))0.34(2p)25p)+0.33(2p)25p)
0.58(2p)26p))0.30(2p)25p)

164

The next ®ve bands with smaller intensities were observed above the twinning peaks and were considered tobe due to the Rydberg states converging to the doubly
ionized state [5, 6, 10]. For these peaks, many shake-up
states are calculated both by the general-R and SD-R
methods with relatively small intensities as in the experimental spectrum. Their intensities are due to 2Sstates, mostly from (4r))1 and (5r))1 states, through ®nal-state correlations: main con®gurations have the nature of 2h1p. Band 3, observed at 28.5 eV, is clearly
assigned to the 2S state calculated to be at 28.78 eV, andis characterized as a (2p)2nr) state, though the assignment of this state is the subject of controversy [5, 6]. The2P state is also calculated to be at 28.55 eV.
For the other peaks, our assignments are given in thegeneral-R spectrum shown in Fig. 1. Two or three
shake-up states are assigned to each band. Here, ourassignment is based on the calculated IPs, since
the intensity is a rather delicate quantity. We calculate
two 2S shake-up states, both (5r)2nr), at 30.04 and31.27 eV and they are the candidates for line 4 observed
at 29.8 eV. The convolution of these states gives twobands, however. In this region, 2P states with small
intensities are also calculated to be at 29.98 and30.24 eV as seen from Table 2. For line 5, foundat 32 eV, we assign two 2S states calculated to be at
32.43 and 32.71 eV, both of which are characterized as(5r)12p)1np). Three shake-up states calculated to be at
33.92, 34.01, and 34.14 eV are attributed to line 6
measured at 33.2 eV. These states are described by alinear combination of (5r)12p)1np) and (2p)2nr). Finally, the 2S shake-up state calculated to be at 34.65 eV
whose dominant con®guration is (2p)2nr) is assigned toline 7 observed at 34.65 eV. Considerable mixing of dorbitals is found for these shake-up states, indicating
the importance of the d-type Rydberg functions as
pointed out in Ref. [6]. The SD-R method also gives
these shake-up states, however, their IPs are evaluatedto be 2±3 eV higher than the general-R method asshown in Table 2.
4 Conclusion
The valence ionization spectrum of HCl is studied by theSAC-CI general-R and SD-R methods. The main peaks,(1p))1 and (5r))1 states, are described well by both thegeneral-R and SD-R methods, but the general-R method
is necessary for describing the shake-up states in ahigher-energy region. In particular, seven satellite peaksin the range 20±35 eV are well-reproduced by thegeneral-R method. The twinning peaks centered at25 eV are very nicely reproduced and are due to (4r))1
interacting with (2p)2nr). The next ®ve bands with small
intensities are attributed to the Rydberg states of HCl+converging to the doubly ionized state. These states aredescribed by linear combinations of the con®gurations(5r)2nr), (5r)12p)1np), (2p)2nr), and (2p)2nd).

Acknowledgements. This study was supported by a Grant-inAid for Scienti®c Research from the Ministry of Education,
Science, and Culture of Japan, and by a grant from the Kyoto
University VBL Project. One of the authors (P.T.) thanks JSPS forgranting him a fund to do collaborative research at Kyoto
University.

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