Z. Phys. Chem.2l7 (2003) 161-t76by Oldenbourg Wissenschaftsverlag, Miinchen

Fine Theoretical Spectroscopy Using SAC-CIGeneral-R Method: Outer- and fnner-ValenceIonization Spectra of N20 and HN,

By Masahiro Ehara, Shinobu Yasuda and Hiroshi Nakatsuji*

Department of Synthetic chemistry and Biological chemistry, Graduate schoolof Engineering, Kyoto University, Kyoro 606-8501, Japan

Dedicated to Prof. Dr. sigrid Doris peyerimhoff on the occasionof her 65'h birthday

(Received September 5, 2002; accepted October 16, 2002)

sAC-u General-R / Ionization spectra / Inner-valence Ionization /Satellite Peaks / N2O / HN3

Fine theoretical spectroscopy for the outer- and inner-valence ionization spectra hasbeen presented by using the SAC-CI (symmetry adapted cluster-configuration interaction)general-R method applied to N2O and HN3. The SAC-CI general-R method accuratelysimulated the experimental spectra and the detailed assignments of the satellite peakswere proposed. The continuous peaks 1 - v of N2o observed by the dipole (e,2e)spectroscopy were finely reproduced. In particular, the low-lying satellites were calculatedin good agreement with the experiment; two 2II shake-up states at the foot of theC state, zE and 2I7 states for the peak I. For HN3, new interpretation was proposedfor the outer-valence region, namely, peaks 3 - 5 are composed of the mixture or tn.single-electron main peaks and the two-electron shake-up peaks. Inner-valence ionizationspectrum of HN3 was theoretically predicted for which no experimental spectrum hasbeen reported.

1. Introduction

Accurate descriptions of excited and ionized states of molecules have longbeen a challenging subject in quantum chemistry. Chemistry involving thesestates has shown a rich variety of phenomena that were quite appealing butcould not be fully understood without the knowledge of their electronic struc-ture. However, it was generally believed to be difficult in 1970s to describeaccurately the electronic structures of excited and ionized molecules because

x Coresponding author. E-mail: hiroshi@sbchem.kyoto-u.acjp

162 M.Eharaet al.

of their open-shell nature, high-energy nature, and the existence of manystates in narrow energy region. Among various efforts, Peyerimhoff has es-tablished with Buenker the multi-reference CI (MR-CI) approach [1-10] andreported a lot of very accurate and extensive theoretical works on molecu-lar spectroscopy involving electronic excitation spectrum [3], potential energysurfaces of the excited states [8], vibronic structure and the Renner-Teller ef-fect17,11l, spin-orbit effects including electron correlations [10], the lifetimeof the electronically excited states [9], and so on. These studies have beensummarized in more-than-four hundred research papers and she named it astheoretical spectroscopy tl11. These studies certainly constitute a milestone intheoretical spectroscopy and show an importance and utility of quantum chem-istry in the studies of excited and ionized states of molecules and molecularsystems.

A different approach for describing excited and ionized states wasdeveloped by the present author as SAC-CI (symmetry adapted cluster-configuration interaction) method 112-161. The basis is to calculate first theelectron correlation in the ground state accurately by the SAC method [17]and then describe the electron correlation in the excited state by modifying theground-state correlation. This method is easier than calculating electron cor-relations separately for different electronic states and furthermore, a balancedresult between the ground and excited (ionized) states is obtained. Further,by using SAC-CI general-R method [18-21], we can perform fine theoreticalspectroscopy. We would like to dedicate an example of fine theoretical spec-troscopy by calculating the ionization spectra of N2O and HN3 for celebratingthe achievement established by Professor Sigrid Peyerimhoff.

Many of the excited and ionized states are described as one-electron pro-cesses from the ground state. However, there exist a lot of excited and ionizedstates that are chatactertzed by two- or more-electron excitation processes.Satellite peaks that are observed in the valence-ionization spectrum are onesuch example and have attracted considerable interest since they contain the in-formation of the electron correlations of molecules. Recently, fine analyses ofthese peaks have become possible due to the cooperative interplays between thequalified theoretical and experimental works.

Among the extensive works on the valence-ionization spectra of molecules,the inner-valence region of N2O has been intensively studied by various spec-troscopies, since there are many satellite peaks starting from relatively lowenergy region. For examples, the photoelectron spectroscopy (PES) usingHeIl l22l and Al K" [23] radiations, and dipole (e,Ze) spectroscopy 2a-261have been reported. X-ray PES [27] was also reported with photon energies upto I20 eV and the assignments of the satellite peaks were discussed in com-parison with other experimental and theoretical works. However, theoretical

studies on the detailed analysis of the satellites have been very limited; onlySAC-CI method [28] and 2ph-TDA (two-particle-hole Tamm-Dancoff approx-imation) method [25] were applied to the inner-valence region. It seems that

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . 163

both of these calculations are now insufficient in the present level of computa-tional technology.

on the other hand, the valence-ionized states of HN: have been much lessinvestigated, though it is iso-electronic with Nro. He r 129,301 and He IIPES [31] were applied to the gaseous HN3, however, inner-valence region wasnot examined except for the solid HN. [31]. Recently, detailed analysis wasperformed with the Penning ionization electronic spectroscopy (PIES) and He IUPS with the help of outer-valence Green's function (OVGF) calculations [32].Theoretical study was limited only for the main peaks with perturbation the-ory [33]. Thus, it is worth presenting an accurate theoretical spectrum of thismolecule and giving detailed assignments of the main and satellite peaks.

The SAC/SAC-O method has now been well established as a use-ful quantum-chemical method for studying molecular ground, excited, ion-ized and electron attached states of molecules in singlet to septet spin-multiplicities 112-16,341. We can also calculate the energy gradient associatedto these various electronic states [34-33]. For ordinary single electron exci-tation and ionization processes, we use SAC-CI SD(singles and doubles)-Rmethod, but for multiple-electron processes like those involved in shake-upsatellite peaks, the sD-R method is insufficient and the SAC-GI general-Rmethod [18-21] has been shown to be a powerful tool. By the general-Rmethod, we can not only describe accurately the multiple electron processes,but also calculate a large number of states appearing in the ionization spec-tral39,40l. Recently, we have applied systematically the general-R method tothe outer- and inner-valence ionization spectra of several molecules t4I-461and gave detailed charactertzations of the main and satellite peaks. In particu-lar, we have given fine theoretical spectra of co2 [43], cs2 and ocs [46]that are iso-electronic with N2O and HN3 studied in this paper. The moleculesCO2, CS2 and OCS have shown to have strong electron correlations and con-sequently to exhibit many shake-up states even from the outer-valence region.Thus, in this work, we investigate the ionization spectra of N2o and HN3by the sAC-o general-R method, aiming ar the detailed and quantitariveassignments of the satellite peaks appearing in the outer- and inner-valenceregions.

2. Computational details

Vertical ionization spectra of NzO and HNr were studied and the ground-state experimental geometries were used for the calculations; namely,RNN:-T.I282A and RNo: l . lg4zl t+l l for N2O in C-, and Rn*,,, -1 .015 A, R*( , ) * ( r ) : I .243 A ' , R*( r ) ,u( : , : 1 .134 i t , zHN(1)N(2) :1108.8 ' ,IN(1)N(2)N(3):Ll l ' I .3' [48] for HN3 in Cs. The basis set was selected asflexible to describe the electron correlations of the shake-up states, namelyvalence tiple zeta (VTZ) of Ahlrichs [49]; (10s6 p)/l6s3pl GTOs for N and

r64 M.Eharaet al.

O and (5s)/[3s] for H augmented with two d-type polarization functions of(a : I.654, 0.469 for N and la

-- 2.314, 0.645 for O, one p-type polarizationfunction of 1o:0.8 for H t501. The resultant scF dimensions were 8l and 87for N2O and HN3, respectively.

The ionization spectra of N2O and HN3 were calculated by the SAC-CIgeneral-R method in both outer- and inner-valence regions. From the prelim-inary calculations, most of the shake-up states were shown to be dominantlydescribed by two-electron processes, and therefore the R-operators were in-cluded up to triples. The ls orbitals of N and O were kept as frozen core andall the other MOs were included in the active space; the SAC-CI active spaceconsists of 8 occupied and 70 unoccupied MOs for N2O, 8 occupied and 76 un-occupied MOs for HN3.

To reduce the computational effort, perturbation selection [28] was per-formed in the state-selection scheme. The threshold of the linked terms forthe ground state was set to ).r: I x l0 7 for N2O and le: I x 10-6 for HN.r.The unlinked terms were described as the products of the important linkedterms whose SDCI coefficients were larger than 0.005. For ionized state, thethresholds of the linked doubles and triples were set to ,1.. : 1 x 10-7 andl" : 1 x 10-6, respectively. The thresholds of the CI coefficients for calculat-ing the unlinked operators in the SAC-CI method were 0.01 and 1 x l0-8 forthe R and S operators, respectively.

The ionization cross-sections were calculated using the monopole approx-imation l5l,52l to estimate the relative intensities of the peaks. The degener-acy of the states involved is reflected in the intensity. For the calculations ofmonopole intensities, the correlated SAC/SAC-U wave functions were usedfor the ground and ionized states to include both initial- and final-state correla-tion effects. Theoretical peaks were convoluted with the Gaussian envelopes tosimulate the experimental spectrum. The envelopes are described by the Frank-Condon width and the resolution of the spectrometer. In the present calculation,the FWHM (Full Width at Half Maximum) of the Gaussian was determined soas to reproduce the line width of the main peak and used for all the calculatedpeaks. In the present calculation, the widths of 0.1 x A,E and 0.05 x LE (in eV)were used for NrO and HN3, respectively.

The SAC/SAC-0 calculations were executed using the SAC96 programsystem [53], which has been incorporated into the development version of theGaussian suite of programs [34].

3. Results and discussions

3.1 N2O

The ground state electronic structure of N2O is described by (core)6(4o)7(5o)2(6o)2 (Ir)a(7o)2(2n)0. The outer- and inner-valence regions of the ioniza-tion spectrum of N2O up to c.a. 43 eY were studied by the SAC-CI general-R

Fine Theoretical Specrroscopy Using SAC-CI General-R Method . . . 165

method. For calculating the spectrum in this region, 80 and 60 solutionswere obtained for 2E and 2rr symmetry, respectively. The perturbation se-lection was performed with the SDCI reference states and the resultant SAC-cI general-R dimensions were summarized in Table 1. In Fig. l, the sAC-cI general-R spectrum was compared with the dipole (e,2e) spectrum [24].Table 2 summarizes the IPs, monopole intensities, and main configurations ofthe outer- and inner-valence peaks, whose intensities are greater than 0.01 withseveral experimental IPs 122, 24, 25, 2ll.

Four main peaks were dominantly described by one-electron process;namely, (2t)-', (7o)*', (ln)*t, and (6o)-r, and they were observed at 12.89,16.38, 18.24,and2o.1lev, respectively, by rhe He II pES t221. These stateswere accurately estimated by the previous SD-R calculation t281. In the presentwork, their IPs were calculated as 12.64, 16.27, IB.Z5, and 20.05 eV for Xrn,A", Bzn, and c 2) states, respectively, in agreement with the experimentalIPs. The intensity of the BzlT state was considerably distributed to the shake-up state through the interaction with (2r-23r) as seen from the monopoleintensity of 0.63, which was also obtained in rhe sAC-cI sD-R [2g] and2ph-TDA [25] works.

First shake-up state was calculated at 19.95 ev below the peak C andwas characteized as (2tr-23r). This state was not identified by the dipole(e,2e) 124-261, but was detected with the He II PES lz2lby Pofts and williamsat 19.5 eV. The relative intensity of this satellite to B2n sate was calculated tobe0.147, which is compared with rhe experimental ratio of 0.125 [22]. Another2lT state of the same ionization character was obtained at 2l .57 ey .

Peak I was observed at 24.0 eY l24l by the dipole (e,2e) spectroscopy, andlater this peak was reported to be composed of the two component s at 23.7 and,24.5 eY [25]. These peaks were attributed to the 2E and 2II states calculatedat23.95 and25.49 ev, respectively, whose assignments were the same as thedipole (e,2e) work [25] with the help of the 2ph-TDA calcularion. These statesare characterized as (7o-t3r2tr-') and (2tr-232). The intensity of the 2[r stateis calculated to be larger than that of 2E state by three times, which agrees with

Thble 1. SAC-CI general-R dimensions for rhe ionized states of N2O and HN3.

singles doubles triples total

NrO2E

2n4

2

1239

r034

24152000

120861 l22rr0t02847 103883

100273 10275475939 17941

HNr2A" 6/4', 2

r66 M.Eharaet al.

r

zl

&tt-m

x (a) dipole (e,2e) spectrum

NzOB

xB

(b) SAC'CI general'R

10 15 20 ,,*il*" ,*lo*o","u',u

40 45

Fig.1. Valence ionization spectra of N2O by (a) dipole (e,Ze) [24] and (b) the SAC-CIgeneral-R method.

the experimental ratio; the relative intensities of 0.02 and 0.06 were reportedfor the peaks at 22.6 and 24.1 eV by the He II PES 1221, though the intensityof He II PES does not directly reflect the pole strength. Peak II was observedat 28.5 eV by dipole (e,Ze) l24l and 28.7 eY by He II PES 1221. For this band,three 2E states and one zlf state was calculated at 28.34,28.93,29-69, and29.85 eV with the total pole strength of 0.15. Unfortunately, the relative inten-sity was not reported for this band by the dipole (e,Ze), whose cross sectionscan be compared with the pole strength.

Peak III observed at 33.0 and 33.1eV by the dipole (e,Ze) [24] and HeII PES 1221, respectively, were dominantly assigned to the 2.D states. Six 2)

states and one 2[I state with the considerable intensity were obtained in this

enelgy region with the total intensity of 0.43. Fantoni et al. [26] identified

the 11 structirre fdrthe peaks at26.0 and 33.0eV with the dipole (e,2e) spec-

troscopy. Accordingly, two 2I7 states were calculated at 25.49 and 31.90eV,

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . 167

-R

ilH ^ l ^ l ^ - i ^ ^

e ) T - b I H i H T 1c ' . ' , r , t l - h J r . C . l r - Fc o & B r : o r Y x j jo R l l

' o 9 9 - H i ! H b

+ c O 0 O r . a . q O O

€ € ! 5 . i 8 . i g t i^ c - , c . , t - - ^ l N 6 l N + t - = C - l

S : ' ' : X . o i i ' : c . ; ; i ; , X

n t s F 6 i . f i i . . , o . q c - )' * S d i + S o + o l i o. \ c r @ + j - x * ^ : - l - : * *\ - > - , c . : I 6 : l= o o r a A , R t s l k - 1i t 1 . \ i * e s t t s t s s+ F € ' i c o ̂ c . i ' ^ ' f r i ' i $ I Ea c Q a c Q . B l I i # ; r c a I c " . ) o o

: N i d| | r | | | T H R H T O O - i b T i\ b H F b H h c ' r * N * r D e 9 o x( \ F - - c ! \ o N r : X : ; N Y ^ c - l s F r - - 6 1v v v v v v v a a * * v ; ; - : i _ r - : v i _ )

5 S F F g F S . ; o o € ; d ? ; 8 Si o o i i i i + l + i I i i l i o

t r t t t r tr L.t tr r , .rd d d N

F{ nl

.1- S

O O

O\ tn9 0 cN c.l

X

though the intensity of the latter state was small. Peaks IV and V were at-tributed to the (5o)-t and (4o-t) states, respectively, which strongly interactwith the shake-up states. These peaks were observed at 35.5 and 38.0 eV bythe dipole (e,Ze) [24] and 35.5 and 38.5 eV by the X-ray PES [27]. For the

c l s o \ c o o o c a c o * l r ) | r )\ O O \ c { q \ o o * \ I . * * $o o F - \ o o F _ o o * O 6-i A -i -i -i -i -: -l --:v v v v e O

F{Fl--

\T l.t Ia) !a) !Q tt- t/) o.\ $ c.)'\O N a..l O' O tn ct\ -f, c-r cF.

e'.i \ci oo oi Cj -'j c.; ,.j oo od- H * i N N N N N C . I

OC;c.l

\ v l nc i s o oc! 61 6l

vlcoc.l

O \ O O S tc o c q ( - l l r ) : \ O * F -..i \o od oi o o.i + od- * * C \ C . ] N N

q ns @N c.l

cni

f ,

=

. F

d

zq)

(n

q,)

;z

q-ikq)

{)oo

r )Ir \

th

F

X

c)

E

o'ra

oc\l()()

€

-z

o

q

N

o(.)O

o

a

H

b0

d

a()q

()

(.)

d.

- r j

> €( J ( J

- a a

v ( D

cg bO

A ( lq <t r v )

.s >.

O E€ olv (6F O

ri

(nf r l

oN{)

(4f r l

!

168 M.Eharaet al.

^ T j -- :

T F rr t h t t t i l

e u i b b x c \ br t s E i E s ic o o o I r j c i ^ c a - - f ,- T t s - - b i - t - \| | ' I r S b I c { ^

5 5 B s 5 * € 5 i * 5 : F s; ' q n x { l } ' I S G e p i : l" 1 n o n " ? : R H 3 c i " . t . \ x , io o + o o ' , ? ^ u P + o ^ ; ( 1 *l : - + : - t * € + r n : ^ r T \ i ' N

/ ^ t ^ t ? ^ b . : - ^ h A ( / v

T H T R T ] 9 I N O I i s < - I N ; O 9 ^h * t s F L h ' . H ! + c . o & S o - Q ^ + : ^ q. b S , \ ̂ 9 6 i ? : d : 5 G ' d L r - v b ̂ y ( )R : ' b : - b H E i e S E I I b : - . . r b + :

ci | 0O I OO cr l acQ r l r ) 0O i = CO + CO a I '

T H T H T I - - i

o l H T T n - r + b' b $ ' H S o x o o i c S ' o ' b c r - ' o S ' H x ' o S

| - . c o - $ l - * . r r ) Q < N . * f - t - O A \ O N . - h $O \ : \ O : + < J ' - O \ ' : $ : 6 l c . l ' i * t : c q l r ) l n ' jcq O $ O rn co cn v O ca O .a \O O + O <1- ci * Oo I o + o o i o + c i I o i I i + i i o +

h h r i hN d d N

h h t i h h

O o o

A - i

h h^lF

(t.l O\ o.l ci \f,* c O C . l o ( \ i

- i A A A A

oo * c.l c! c..l so l c a o o t n l r ) c o

- - ^ l

O O O O O O

O \ O $ i r a ) O O \ O t r ) C \ o O O \ W OO \ \ O c o c o o o C \ o O | r ) \ O O \ / . ) o o c . )- j c ' i c d + + d r 7 1 \ o . d r = S S o < tco ca co co co ao ca co co cq c.) co co

nr/)ca)

co)

cl(--co

nlr)c.)

c.jca

v?cocO

\cnca

ca;c.)

peak IV six 2X states were calculated and the intensity of these states were

mainly due to the final-state interaction with the (5o)-r state; total pole strengthwas calculated to be 0.48. For the peak V and its shoulder in the higher en-ergy region about - 42 eY 1251, ten 2^D states with the intensity larger than 0.01

c.)O

r .=

' -d

bo

d

6

a

o

v)

>,

()

U)rr'l

oC.l0)

(ar r l

i-i

.i

z

>|H

X

o

€

0.)

0)c.l()O

k(.)d

0)bo

r )I

r \

U)

(J

N

F

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . 169

tr-N

g.l

c.lc.]

$$

^ : - j -^ i l t s ^ ' ^

l lr b S . R u i , \ E ' ' n FP r - - l ' - ^ * F - b

' i o l R S Hp H k p H o c \ : o i r . o

F t r : c " i c " i s - - ' r l B t s lc . ) - i d 1 - : t - F . C O c a

i ' H ' ! ' !

o - o " s \ ; ' i ' SH s . & N : r D 3 5 . p ^ \ Va 5 5 ; ; i = < 1 9 = 1 9 " 1P n - " 1 n A " ? o n H 9 o

I r ' r ^ r \ |j e v v r _ r : . , . _ _ : _ rY + + - . 1 - I | - l - ^ e R e -- L ' - I a n I -

t t _ r l

: - T T I i ' * i T H : - r r a . bI t \ h h F \ H l l r - - U l F -

€ i S . S r E € r , \ 8 E S tH ; t s t s i _ = r H i I : e j l e s !

C i , ^ d ^ C O C Q d | $ # | C q I C f ) r

| | | | | | b T T H T H f RH b H b H H * D x x C 9 * 9 o Q )

# . \ f . N . $ . N . N * o l N . * . c a C . . l l r ) t n O \v v v v r r v ; v ; v _\ O $ O \ - N r n t r ) j c o O " l * " i r ) ' :ca cq s s \n co cq o cq co o co o ci oi i o o o i i + i i l i l d r

hLir \ F l

\ o ** c i

A A

hh h h h hd d d

\O O\ t-- Cq OO tr)O \ C \ l r n o O ( \ l *- - A ! A

0Q e) c..l \O O, \O t-- $ n N\ O O N o O I - - o o o o C - l N O .o i o i i - - ; - : - j G i c j c . ic a $ $ S s f $ . t $ $ . +

ooco

c.]v2

la?@c.)

ca

I

were assigned. The double ionization threshold of NzO has been determinedby the double-charge-transfer (DCT) spectroscopy 154,551 and photoion- pho-toion coincidence spectroscopy (PIPICO) [55]: triplet states of N2O2+ weremeasured at35.7,38.8, 41.8, and 43.1 eV [54].

cnO

o=-

'r-1

bo-

-6J

o

(n

q

()d

n<I

k0)

C)oo

Ur \

U)

Fj

> ' !! s %I H

X o r

9 \6 ( UFi .{

(t.cl t!

dz

C)NC)

a,)

F.i

C)

al

170 M.Eharaet al.

3.2 HN3

The ground-state electronic structure of HN3 is (core)6(4a'1215a'1216a')2(7a')2(la")z(8a')279a'7212a" )2. The valence-ionization spectrum of HN3 up to about35 eV, whose energy region corresponds to peaks I- III of N2O were studied.For this pu{pose, 80 and 60 states were calculated for A' and A" symme-try, respectively. The number of single, double, and triple R-operators weresummarized in Table 1; SAC-CI dimensions were 102154 and7794I for A'and A" states, respectively. Fig.2 shows the valence-ionization spectrum ofHN3 calculated by the SAC-CI general-R method in comparison with the He IUPS [32]. Unfortunately, there is no experimental spectrum for the inner-valence region of HN3 except for solid phase. Table 3 summarizes the IPs,monopole intensities, and main configurations of the outer- and inner-valencepeaks, whose intensities are greater than 0.01.

The theoretical spectrum by the SAC-CI general-R method reproducedthe peak positions and shape of the experimental spectrum. Six peaks exist

(a) He I UPS

HNszf,

u.tF

ozul

=

20I D

1 0

rlg. z. valence lonrzatlonmethod.

BINDING ENERGY (eV)

spectra of HN3 by (a) He I UPS [32] and (b) SAC-CI general-R

(b) SAC-CI general-R

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . l 7 l

TR

\-

Ta- -. ._

r N-: -: .c\. :-*

cr 6r :Jt l ^ !i \

Q A ; \N N | - q jc.r trl :--

-s i-

co cn I c.)_ i ; i- r

Y d ! ^ \t l

a - A 'N - *

" i = = ; 1 of 1 ^ . s ? +\ i ^ ._ .c. i

_1_ :_

S ! c \ I N { : - ! ^e ; i A F : \ - s iu ? l n 9 ' 1 6 , ( J sc o t i + l : , \

l r . o r - S -' t - t - . 1 - ^ H \

- ^ : - I ^ , I J c ' li * t _i r t l - l B l B t B l\ \ \ \ \ - N - t R . - - - R . o \ . r \N o \ o o # 1 : X r : X o \ ) ( d

v v v : j = v l j

O O\ c..l ta) i o|\ \. I-- \,O \ ( } \ t t - \ O r . ) O t O \ O O O \o i i i o + o l i l i

coA

f t

v-

-

l<

oo

o

O

CN

ha

CJ

qI

HC)

o

r \r ' )

(a

fr(JN

{)-(.)

()

q

!

oo

63d

fi

q

O

n xE 9

()

X e

O r

9 l i

> ;

X ' c nF. o.r

.o >,

( ) Y

t s ( J

d vN o' e z

;= Frr

Q ) q

.r! -i.:

in the outer-valence region of the He I UPS [32]. There is a correspondenceof the electronic structure between HN3 and NzO, however, large differencehas been found between their valence-ionization spectra as shown in Fig. Iand 2. The peaks 1 and 2 arc ronization from the 2a" and 9a' orbitals, re-spectively, and they correspond to the peak X of NzO. They were calculatedat 10.45 and 12.10eV with the energy separation of 1.55eV in good agree-ment with the experiment. The peak} was experimentally observed as a broadpeak, which should be attributed to the vibrational structvre. 2a" orbital isa non-bonding MO localized on N(1) and N(3) atoms, while 9a' orbital is delo-

{

t > t - - r n o a o o c a \ O O \ F -\ O r n \ o o r ) O \ O \ b bc o o o t r - $ c O c O * O O;. /i A -i -i -i -i -i ,-:

t a ) c ) $ o o o t / ) I r ) o . l \ oS * @ C O O \ C O O O C . T \ O

O c.i .r; .O rO r.- r-- d od-

c o @ c o o lF- c'.1 lr) O,i oj ,r; \o

\(--

z

U)

D()

Fr<

172 M.Eharaet al.

r - I a- : - j . -^^I l S I ^ I * i , ^ , ^' N N l - : - ' l l

S ' i : A l A ' o ' . . ' l r :\ = A t l i i i . \ s \ . - d9 T ; f - = \ J " s S \ \ : s S :

T i r i - . . r - c d c ' , c - =

: _ S i o . \ ; _ . ' o f I r : - i I; i x c n \ N ^ s = S N v _ s _ q . s

t s t s

Y i 6 ' g G i s 5 9 : > s l : : 9 3I ? : ; n ; d f q ? s S g gY - r ; . ! r d + O C O O O O il : - | c i i I i l | | - L l _ ^ | | r

^ t - Y

- i - i ^ : - - . - ^ ' ^ ^ ^ ^ rl - - h r - T -! ^ \ i _ : ; r . s l - i I

- S - i I i

N s r N ; T ' \ \ I 5 s 5 d 5 s s s3 : 3 t . - d \ \ - ; \ : '

r - r ' : : I, - . o r = S r = S S S i i S ir l - : : - - : T -

l.* t* s i* L_ : .\ t_ 1_ N ._ l_ l_ s l* t.. l_s s F g € = - r d e a " d J d E ; d & g3 f l d ; S ; ; $ e J € 3 8 3 : i S S 3d o l o i l l i o + i o o i l d o i

cnA

f t

k

oo

t

()

U)

>'a

q)

n<I

Lo(.)bo

r ' lIr )

(n

\ kd N d N

o lr) F- a ta F- N t-- o\ oo oo \o o\ -f,l - = c a \ 9 o . l C \ l - S O ' c a N #I - - O O O O O O O O a O O O: A A -i -i -l -i -i -i -i -{ -l -: .-:

v v 9 v I I I

- t o o o r n o c a o oq n n n q n 9(\.l co co =i- lr) \o F-o i N N N N c . t c . . l

t n . t o \ N \ oOO O\ O\ CO cni i .-i c.i c.ic . . l o l N ( \ N

oi

N @

\ \c.t c!C.i c-l

calized over HN, molecule and has a bonding character. Hence, the equilibriumstructure of (9a')-t is different from the ground state so that the vibrationalstructure should be remarkable for peak 2 and is responsible for the broadpeak.

Peak 3 observed at 15.53 eV was assigned to the (8a')-' state by the PIESexperiment 1321. However, the (la")-l state interacting with (2a"-t3a") wasalso obtained just above (8a')-' state in our calculation, and we attributed thesetwo states to the peak 3. For the next peak 4 observed at 16.92 eV, twinningpeaks of (7a')-t were calculated at 16.98 and 17.35 eV; these states were de-scribed by the linear combination of (7a')-t , 12a"-210a'), and (2a"-211a'). Asthe shoulder of peak 4, peak 5 was measured at l7 .7 eY l32l and this peak wasattributed to the.satellites by the analysis of the collision energy dependenceof partial ionization cross section (CEDPICS) of the PIES [32]. Accordingly,three shake-up states of both A' and A" symmetry were calculated at 11.85,

Fi

oz

()

(n

F

(4

Dq)ts

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . 173

j-

t ls : I L T r i t l oI s 6 S \ \ ! " d ? o. X - \ \ \ a a ' c o r s- .

T i d : : - : j . _ + i j ' , :, \ S \ l * t * l - l - : : r r _i t X = d r : . j B o E S Y S iI n ; Y > i F ; . = c i ' - - x^ c J \ E i l h . r S i S V( \ , ^

Y l : - i e J e e O l C ) a: ^ t - - | | * ^ - l | ^ - l - - f ^

; i ^ . . , : - - - a - a - - j - n - ^ i - : - fY \ - i o T I r | - R I T s l I

- i r *

: i \ l i \ S s : s ' = 1 \ i i iS ; ( \ \ 1 - : t S \ ; \ I = I \ \ S \

c C : '

. ; t l - . j " J r j = j o 5 n l : , _ i i - , : _ \ * ol* N l_ L* l* !* -_ l* .$ |* |_ € l* ._ l_ .\ l_ l_c \ i - G o d G i n d G X r : d d X o d ; i d d X f i dv ; ; ' v v : - v v v =c c ' _ :

O \ t t - ( ' . 1 c O o o ' , i . f , O ' j F - $ ' l

C . . l.o O lt co co $ cq -f O co $ O ,. c{ + O c'., cao + o o o o o i + o o l i o i + i o

c.)O

c

!

oo

d

a

qJ

(n

@

(.)

a<

koobo

OI

U(h

{d d

18.32, and 18.66 eV. Peaks 3 - 5 of HN3 correspond to the peaks A and B ofN2O, however, the assignment of the outer-valence region of HN3 is very char-acteristic due to the strong electron correlations: this picture is very differentfrom the previous experimental l32l and theoretical [33] works. Peak 6 wasattributed to the (6a')-t state in agreement with the experimental assignment.This peak corresponds to the peak C of N2O.

Above this energy region, no experimental information exists for the gasphase HN3. In our calculation, many correlation peaks were calculated in theinner-valence region and their IPs were relatively lower than correspondingstates of N2O. The shake-up states in the energy region of 22 - 24 eY were as-signed to the satellites of (7a')-t and (la")-l, which correspond to the peak Iof N2O; remarkable A" and A' state were calculated at 22.36 and23.50 eV, re-spectively. The shake-up states with small intensity continue from}7 to 30 eV,whose intensity originates in (6a')-t; these peaks correspond to the peak II of

lr) O O\ Q $ \n F- co O r.) O \f, co $l= n S Cl - Cl CO * N * c-l - O \nO O O O O O O O O O O O = O-i A -i ^i A A ; -i -i ^i -i ^i -{ ;

co \n s tr) (.i c\l .{- o t-- \o $ c.l cn Ir)- \ o c \ q - c . l o q o q q 9 . : ' . q q|,- |.- (-- oo 0O O\ o:\ o}\ O\ O O H d d(..l (t.l N c.l a-l Cn c.i N c\l - - co ca c.l

J

Az

al-

{)'fr

EiC)

-

(fl

c)

174 M.Eharaet al.

a<I

tr()q)

bo

OI

UU)

cqi

f t

v-

k

a(n

ha

o

T:- -s --^I c \ l L i\ ^ \ \ :

^ O \ ; N ^ C \ ( sI ' x ' 8 . : I \ S: u A $ s t : - \S : - . : i S +

! ! I - i

\ ! S ' r - r

. : ^ s s : ; S . x - si 9 . 9 ; c t I Y : e .- - ' i i i - r ss = . o \ l Yd : A c \ + d : :

C v v _ v s 3

S 1 * S ; - 3 + + . -, i ^ ^ ' \ ^ : , ^ , ^ lv - : - : l v S i u - - t- l - - t a . l r - L r i l f

' i * i L s '

T . \ N ! - C + P C 9 o d ' *G l . - S . 5 : - c ; S \ . -.I v- v-

I - : , x! v v v v

N O \ O ' O \ N O r C j O , N

o o \ o $ N o \ ' : @ c a ' :. i - c o $ $ c o O c . t t r ) + \ O Oo o i o i r i i i o i

NzO. For the energy region of 30 - 35 eV, shake-up states of (5a')-r exist andthey correspond to the peak III of N2O.

4. Conclusions

The SAC-CI general-R method has been utilized for calculating the fine theor-etical spectra of the valence-ionizations of N2O and HN3. The peak positionsand shape of the experimental spectra were well reproduced and the detailedassignments of the satellite peaks were proposed.

For N2O, the general-R method gave the continuous satellite peaks in theenergy region of 24 - 43 eY, which reproduced the peaks I - V observed bythe dipole (e,Ze) spectroscopy. Low-lying satellites for which earlier theoretical

\ O a ] r ) c o * O c a S $c j $ - i - c A S c . . l

-i -i -i -i -i -i -i -i -l

C . ) O O * \ O * t - - $ O Oo c . l c n | r ) F - o o o l 0 0 0 0c.i oj c.i c.i o.i c.i cd d c.;ca ca co c.) co co ca co co

€o

d

()?aC)

(h

f-r

()+r

ii

;

zc.lI

Fine Theoretical Spectroscopy Using SAC-CI General-R Method . . . 175

results were criticized by the X-ray PES work l27l were calculated in agree-ment with the experiment; two 2rr shake-up states at the foot of C state, zEand zlr states for the peak L For peaks II - V many 2) satellites were calcu-lated with distributed intensity and no prominent peaks were obtained, whichis different from the previous theoretical works 125,281. Some 2I1 states werecalculated in the peaks I-II I , i .e.25.49,28.34, and 31.90eV, which agreeswith the experimental observations [25,27].

For HN3, new interpretation was proposed for the peaks in the outer-valence region; the peaks 3 - 5 were composed of the mixture of the one- andtwo-electron processes and therefore, split peaks. The satellite spectrum in theinner-valence region which corresponds to the peaks I - III was calculated forwhich no experimental spectrum was reported.

Acknowledgement

We thank Dr. M. Ishida for the discussion on the computational details of thegeneral-R calculations. This study has been supported by the Grant for Cre-ative Scientific Research from the Ministry of Education. Science. Culture. andSports ofJapan.

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