- Email: [email protected]
SCF discrete-variational Xα calculations of the NH4Cl Auger spectrum
CHEMICAL
PHYSICS
I. IntrodIIctioIl
\ugc~ spc’~-Iros~c~p~ JII\csII~.IIJ~I
oI‘Il1~
15
wideI>’
&x-Ironic
used
structure
3s J Illefhod
for
of nlolccules,
.\llhdS Jld c~lIII~WJlIdS (111 SlldXCs 11 ]_ %\VCVeT, the ~w~prmiiwt 01 Auger bpcctn veryuitenneedsquite III\ uh’d
~YJh1~~11~111~~
111~Ihc1ds.
Some
cskuk!tions
c.mIed WI and they WCIC able to describe Iirx4~qm .ind lint structures of Auger spectra quanIII.III\C~! . In p.IIIImlJr. .Ib Initio calcuiarions of Augc~ cnCIpies JS differences of the initial- and fin,& ‘~I.IJL! Ik11.drnerpm glvc good agrecnient with e.\periIllen 13 61. I Io\seVer. Ihe clnpioywx~t of ab initio 1J1~1hld~ IS IcsI~Icrcd Iu ~~11 niolecules for computaIICIIIJI 15.~boJJ5. CbJJlg Iiie srniicInpIric~1 approxh of JL’IIIIISOI~17.51 me nny c.~kul~Ic Auger transitiori ~SI~;ICS I;lr qu~fc’ Iic0y mulcculrs. Unfortunately. I~IIS.IpprL).xh m]IIIrcs knowledge of the energy of the hQ hole mIc’~.Ic’tJorI and c.\perimental ionization p~re1ir1;115 (II’) \\liich ni~y not be known in every case. .\ c~lIllpJOIllISC be~\ve~n db initio Inethods and
II.I\LT l1w11
~~lllI-~Jll~lirlCJ~
.J~qmlJcheS
is represented
by
1983
nectcd wirb calculations of energies and intensities of the Auger transitions within the Xa model are yet to be answered. In this work the self-consistent discrete-variational Xa Inethod(DVh1) 1151 is applied to calculations of the KVV hueshape for solid NH,Cl_ A new formalim 1o determine the singlet-triplet splitting of the Auger transition energies is suggested.
2. Calculations
of the Auger energies and line&apes
The kinetic energy of an Auger electron is equal to the difference of total energies for an initial state with a vacancy on the inner shell and a final state with fwo vac3ncies on valence NOS.
(1)
the
~IicIllo~is ~vtliclJ e~nploy the local eschange potentials, c g _\a. l~~~cntly SOIW applications of such methods N err’ Icportrd. for example. LCXO Xa to O2 [9] and It> SdJd ~YNO; 1lo]. SW Sa IO CF4 11 I], Co [I?] .ml .~t~ms 1131. ,1nt1 lo La-,‘33 in a cluster model 11-i I. I IuWvcx. sonw inctllodologicsl questions con-
70
75 hlarch
LETTERS
where $‘i are occupation numbers of the ith spinorbitals with spin oi participating in the transition and X is the final electronic configuration. For systems whose ground state is a closed shell, and NH,Cl in particular, the electronic configuration of the final state with two vacancies on valence MOs 0 0092614/83/0000-0000/S
03.00 0 1983 North-Holland
may be either singlet or triplet.
Because in +&e aingle-
determinant spin-polarized approximation of the wavefunction, spin and orbital angular momentum
G?t33 _
=O,n~~=O);
=E(II~
=0)-E,,,,
,
then average energies of singlet (S) and triplet (T) multiplets according to this sum rule are equal to ET@“2 = 0 ,n$ =0)= Es@
Ea2_
,
-4%pY3
(2)
(3)
-
From eqs. (l)-(3) for Auger energies of S and T states we obtain the following expressions:
(4) K&3 = 2&$a
-K&3
-
,n3 =1)-E(r~l=1,tr2=0,n3=0)
+-.&+e.&
= -e&
(7)
with an accuracy up to the third terms of (6). Here e&are orbital energies detemrined for TS. Estimations of the Auger energies using (4) and (5) require in the common case two spin-polarized calculations for every transition with occupation numbers determined by the corresponding configuration of configuraholes. The calculation on a clfla~~P-a~~~a tion gives immediately the triplet component of the Auger transition K 53 = -ey
= 0 , n$ = 0) = ET - 2(ET - Eaza3)
=2Gzp3
algebra E(rtl=0,n2=1
multiplet splitting cannot be treated uambiguously, we use in calculations of multiplet energies the sum rule [ 161. In this approach the energies of singlet and triplet states are averages of all states (with unknown weights in a common case) which arise from the given electronic configuration. if we define E o2 + = E(n;’
25 March 1983
CHEMICAL PHYSICS LETTERS
Volume 96, number 1
+e7Q +&J .
@I
The calculation-k a c1flav~/2%~/2fl configuration yields the energy Kt& = -rzy + &q + $ which is required by (5) to determine the singlet component of a transition_ It is pertinent to emphasize the model character of the TS computations_ The high multiplicity in the Auger energy calculations is due to the mathematical formalism [see (6) and (7)] and not to the physics of the Auger process. For closed-shell ground-state molecules the intensities of the Auger transitions are connected with Coulomb
(9
The spin index in K123 is omitted because the difference between hdoZa3 and K$a o3 does not exceed tenths of one eV according to our calculations. For valence orbitals this index is omitted due to equality ofEazp3 and E8ap3 in the case of closed-shell systems. Now we expand the total statistical Xo energy in a Taylor series in occupation numbers of MOs involved in the Auger process,
(6) and following the Slater transition state(TS) concept [ 171, select a state in the middle of the initial (11~ = 0, I’2 = 1, "3 = 1) and final (n, = 1, “2 = 0, it3 = 0) states. For the TS should be assigned occupation numbers nl = l/2, n2 = 112 and ns = 112. Using the expansion (6) with respect to TS one may deduce after some
where Q and b denote valence MOs involved in the Auger process and Q(E) is the wavefunction of an Auger electron. In the one-center approsimation which has been commonly used [2,5,6] Q(E) is a spherical wave centered at the atom with the primary vacancy (at N in our case)_ @I,,,(e) = RI(~) YI,,, >
(10)
where R](E) is the radial function of a continuum wavefunction and Ylm is the spherical harmonic_ The one-electron MOs are determined in DVhl by the usual LCAO expansion: pi = c
i
c&a-
J
(11) 72
Voluttxe 96. number 1
CHEhflCAL
where X~ are atomic basis functions. In the one-center approximation
where pi are atomic functions centered at an atom with the primary vacancy. The matrix elements in (117) Jlnve been calculated [ 181 using HFS numerical functions. Here we use numerical HF functions which are practically tile same as HFS ones. Notice that the Auger energies given in the tables are calculated within the doubfc-zeta basis of Clenlenti [20]. Auger energies obtairwd within tile HF basis slightly differ from tile latter ones mainly due to the distinction of calculdtcd energies of the N Is A0 in both bases. The N 1s 11’is 3 11.9 or 406.3 CV against the experimental v&c 403 eV [ 191 of a free atom. Only main Auger lines are calculated witllout taking into account llie processes of shake-up and shake-off types The half-~ idths of a gaussian decomposition of the t?rpcrimental spectrum of NH_+Cl are used wflen plotting the tfleoreticai spectrum.
3. Results and discussion The geometry
of the NJ-J_+Clmolecule
25 hfareh 1983
PHYSICS LFXI-ERS
is taken
partly from the X-ray data on solid NH,CJ 1211, i.e. the point group is C&, R(N-H) = 2.1 au, and from the ab initio calculations of Clementi [22], i-e_ R(H-Cl) = 3-4 au- The hydrogen atoms are assumed to form an undistorted tetrahedron. The cafculations are carried out as within HF using Clementi’s doublezeta f201 functions on N and CLand fs the H. In table 1 we give the IPs, Mulliken charges on atoms and experimental 1Ps of the constituent atoms N, CJ and H, table 2 presents the energies of Auger transitions calculated within the dot&e-zeta basis according to (5) and f7), and the integraf intensities determined by (I f) using the LCAO coefficients of the ground-state wavefunctions within the HF basis. Because the number of fine-structure lines for the main Auger transitions is quite large, seven peaks are selected for comparison with features of the expcrimental spectrum. The theoretical intensities are caJculated to be integral intensities of Auger Iines determining the peaks. In table 3 are given the calculated Auger energies and relative intensities of peaks 1-7 and the experimental v&es obtained by a Gauss decomposition of the experimental spectrum. The latter is recorded for polycrystalline N&Cl using the Mg I& We_ A more detailed description has been published elsewhere [23]. The spectrum after substraction of the back-
l‘&lc I The
wIct11~~d
1%. MuIlAen
ctuqe+
on
Itzoms of NH~CI. and rhe experimental
IPs of N. H and Cl atoms (in eV)
Experimental IFS a)
bfcJ double-zeta - ._.--------7.8
8.2
7-9
17.4 18.9 20.3 19.1
17.2 18.9 20.0
3VI
29.2
2SN
207.0 208.5 264.6 411.9 2832.9
Qll
Qh
---.. 3)
72
- -.. -
horn
ret 119).
I ----
QN QCI
-___-.__
I_~-
7.9
0.37 0.30 -0.80 -0.62
13.7 13.2 13.6
3PC1 2px 1SH
199.8 201-4 258.9 406.3 2806.5 0.28 0.70 -0.40 -0.60
2%2,3, 2sfl 1Sh’
kl
Cl
25.3 26.0 206 204 274 403 2827
CHEMICAL PHYSICS UZl-TERS
Volume 46. number 1
25 March 1983
Table 2 The calculated Auger energies (in ev) and integral intensities of the N KVV transitions in NH,Cl Confiiuration
Spin
Kinetic energy
integral intensity
Number of peak
0
336.8
0.590
1
0
347-O 349.6
0.026
1
2
1
345.6 350.4
0.730 I 0.112
Sa;”7ai'
0 1
351.2 352.2
0.528 0.074 I 0.170
6a;* 6a;’ Ze;’
0 0 1
359.7 358.8 360.4
0
1
358.3 361.7
0
361.9
1
362.3
0
362.7 362.9
0
3
1
0 0
1 6a;’ &I;’
0 1
73;’
sa;”
8ai’ 2e;’
8ai2
0
362.8 362.7 362-V
I.020 0.038
1
0.379
0.010
372.0 374.2
0.536 0.020
373.7
0.666
373.6
0.034 O-1 24 j
381.6
0.274
eV to match the first peaks of the
spectra. This shift is due to different phases of NH4CI in the calcnlations and the experiment. After the shift
a close resemblance of both curves is evident. Note that the more traditional approach in calculations for solids is a cluster model within which one should calculate the cl?ster NH4@-. However, as
I
5
0.018 J 0.584
368.1 370.3
ground is presented in fig. 1 together with the theoretical one. The experimental Auger energies are
displaced -9.5
4
6
7
has been noticed f24], a cluster simulating a solid should preferab3y consewe the stoichiometry of the solid. From this point of view the molecule NH&C1is the minimal stoichiometric cluster for solid NH,Cl. Most calculated Auger lines are located near experimental peak positions within limits of experimental errors. The exceptions are peaks 4 and 7 orig-&ating from the 2e- 2 and Sai_ 2 configurations.
agreement for 2e-’
The dis-
may be explained by the one-de73
Volume
96. number
CHEhIICAL
1
T.Me 3 The c\perimcnwl and calculated enersies(in intensirxs for the N KVV i\uger transitions ~-_ . -~- _-__-_ Number
EIhcor
EexP
&or a)
(C’V)
(eV)
(5)
lfheor IS G)
Iexp (%)
1 ,
336.8 34x5 351.2 35s.3 362.7 371.8 3Sl.h
336.S 317 352 362 363 373 379.5
7.7 11 10 ‘2 16 I9 3.7
5.6 13 5.6 41 14 18 2.8
9.2 11 10 20 23 22 4.1
3) fi;s arc hcor and IIS lllr: I \tb LCt$@ coetkicnts
inre_er~lintcnsitirs wlculated using for the ground- and initial-state ~.~\ciuncrionc respccti\ely. The expcrinlental Au_ecrenerSIC<.IIL’zhlftcd h? -9.5 eV.
Icrnunxlt approximation used because we do not resolve rhe multlplet structure of this configuration and dccounf for the configurarion interactions. and for S.I~ ’ ir may be connected with a lattice potential inllucnrc. The theoretical inrensities of peaks l-7 are 111a good agreement with experimental ones if one uses t!lc l-C.40 coefficients of the ground-state wave-
function. Thr intensilies were calculated using the Xl0 LCAO coefficients of the initial state wavefunctiorl with a vdcmcy in the K shell of N as well. In the
H--
LE-ITERS
25 March 1983
latter case the contribution
eV) and peak in NbCl
of pc.A
; J 5 6 7
PHYSICS
of p AOs does increase to the influence of the core vacancy field, leading to a considerable relative Increase of amplitude of peak 4. The same trend is observed when calculating the intensities with the use of LCAO coefficients for TS of the 7ai’2e? ’ configuration. Recently [23 ] we have qualitatively assigned the fine structure for the N KVV Auger spectra of NHdX, X = Br and Cl, assuming the approximate equivalency of the NH; and CH4 electronic structures, accounting for their isoelectronic character. The high-energy peaks 7 and 8 were considered to be satellite ones for transitions from the highest valence MOs composed mainly of N AOs. According to results of the DVM calculations the appearance of peaks 7 and 8 (see fig_ 1) is due to a substantial delocaliiation of the N-H-Cl bond owing to hybridization of N 2s, 2p,, the bridge H Is and Cl 3s. 3p, AOs. It is interesting to note that the shape of the other peaks l-6 is similar to that of the carbon Auger lines in CH,. It allows us to connect the intensities of peaks 7 and 8 with the covalency strength of the Cl-NH, bond. due mainly
Acknowledgement The authors wish to express their sincere gratitude to Drs. Ju.M. Shul’ga and A.F. Shestackov for discussion and critical remarks, and to the referee for valuable comments_
References
h--H-_CI
[ 1 ] R. Weissmann and K. hl’uller, Surface Sci. Rep. 105
.-__
307
_. *
327
347
367
387 Et,”
ieVl-
1 lg. 1. 1 he c.dsul~Icd and cxpcrmxnt.d N KVV Auger specII~ of jY14Cl. The positions of theoretical peaks 1-7 are tn.~rkxl x\lth \cr~x.d bxs. Their amplitudes are proportional to Ihc pc.k mrcnsirws. The pe_k to the left is due to admixturc 01 thr 0 KCUcwitarlon ofC1 2p levels.
73
(1981) 251. [ 2 ] H. Siegbahn. L. Asplund and P. Krlfve. Chem. Phi-s. Letters 35 (1975) 330. [3 J 1~. Agren, S. Svcnsson and U-1. Wahlgren. Chem. Phys. Letters 35 (1975) 336. [?I hl.T- Okland, K. Faegri Jr. and R. Mannc, Chem. Phys. Letters40 (1976) 185. 151 K. Faegri Jr. and H.P. Kelly. Phys. Rev_ A19 (1979) 1649. [6] H. Agren. J. Chem. Phys. 75 (1981) 1267. [7] D.R. Jennison, Chem. Phys. Letters 69 (1980) 435. [S] D-R. Jennison, J. Vat. Sci. Technol. 17 (1980) 172. (91 B-1. Dunlap. P.A. hlills and D.E. Ramaker, J_ Chem. Phys. 75 (1981) 300. [IO] F-L. Hutson. D.E. Ramalter, B-1. Dunlap, J-D. Ganjei and J-S. hfurday. J. Chcm. Phys. 76 (1982) 2181.
Volume 96, number 1
CHEMICAL PHYSICS LETTERS
111 J hf. Barber, I.D. Qark and A. ~~~h~ffe, Chem. Phys. Letters 48 (1977) 593. 1121 P.C. Desmukh and R.G. Hayes, Chem. Phys, Letters 88 (1982) 384. 1131 K-D. Sen, 3. Chem. Phys. 73 (1980) 4704. fl4] LA. Topal, privtrte communicatioa [ ISI G-L. Gutsev and A.A. Levi& Chem. Phys. 51 (1980) 459. [i6] T. Ziegler, A. Rauk and E.J. Baerends, Theoret. Chim. Acta 43 (1977) 261. iI71 3-C Slates, The self-consistent field for molecules and solids @lit, Moscow, 1978) ch. 2_ fl8l EJ. McGuire_ Phyr Rev_ 185 (1969) l_
25 March 1983
[ 19 I K. Siegbahn, C. NordIin#& k Fahhnan, R Nordberg, K. Hamrin, J. Hedman,G. Johanssdn,T. Bergmark, S.-E. Karlsson, I. Lindgren and B. Lindberg, ESCA, Atomic, molecular and solid state structures studied by means of electron spectroscopy (MI, Moscow, 1971) table43. I201 E. Clementi. R Matcha and A. Veillard, J. Chem. Phys. 47 (1967) 1865.
1211 Structure Reports 23,295, (221 E. Clementi, J. Chem. Phys. 46 (1967) 3851. (23 1 G-M. hlichailov and Ju.G. Borod’ko, Surface 6 (1982) 85 [in Russian]_ 1241 C Umrigu and D-E. Ellis, Phys. Rev. B21 (1980) 652.
PHYSICS
I. IntrodIIctioIl
\ugc~ spc’~-Iros~c~p~ JII\csII~.IIJ~I
oI‘Il1~
15
wideI>’
&x-Ironic
used
structure
3s J Illefhod
for
of nlolccules,
.\llhdS Jld c~lIII~WJlIdS (111 SlldXCs 11 ]_ %\VCVeT, the ~w~prmiiwt 01 Auger bpcctn veryuitenneedsquite III\ uh’d
~YJh1~~11~111~~
111~Ihc1ds.
Some
cskuk!tions
c.mIed WI and they WCIC able to describe Iirx4~qm .ind lint structures of Auger spectra quanIII.III\C~! . In p.IIIImlJr. .Ib Initio calcuiarions of Augc~ cnCIpies JS differences of the initial- and fin,& ‘~I.IJL! Ik11.drnerpm glvc good agrecnient with e.\periIllen 13 61. I Io\seVer. Ihe clnpioywx~t of ab initio 1J1~1hld~ IS IcsI~Icrcd Iu ~~11 niolecules for computaIICIIIJI 15.~boJJ5. CbJJlg Iiie srniicInpIric~1 approxh of JL’IIIIISOI~17.51 me nny c.~kul~Ic Auger transitiori ~SI~;ICS I;lr qu~fc’ Iic0y mulcculrs. Unfortunately. I~IIS.IpprL).xh m]IIIrcs knowledge of the energy of the hQ hole mIc’~.Ic’tJorI and c.\perimental ionization p~re1ir1;115 (II’) \\liich ni~y not be known in every case. .\ c~lIllpJOIllISC be~\ve~n db initio Inethods and
II.I\LT l1w11
~~lllI-~Jll~lirlCJ~
.J~qmlJcheS
is represented
by
1983
nectcd wirb calculations of energies and intensities of the Auger transitions within the Xa model are yet to be answered. In this work the self-consistent discrete-variational Xa Inethod(DVh1) 1151 is applied to calculations of the KVV hueshape for solid NH,Cl_ A new formalim 1o determine the singlet-triplet splitting of the Auger transition energies is suggested.
2. Calculations
of the Auger energies and line&apes
The kinetic energy of an Auger electron is equal to the difference of total energies for an initial state with a vacancy on the inner shell and a final state with fwo vac3ncies on valence NOS.
(1)
the
~IicIllo~is ~vtliclJ e~nploy the local eschange potentials, c g _\a. l~~~cntly SOIW applications of such methods N err’ Icportrd. for example. LCXO Xa to O2 [9] and It> SdJd ~YNO; 1lo]. SW Sa IO CF4 11 I], Co [I?] .ml .~t~ms 1131. ,1nt1 lo La-,‘33 in a cluster model 11-i I. I IuWvcx. sonw inctllodologicsl questions con-
70
75 hlarch
LETTERS
where $‘i are occupation numbers of the ith spinorbitals with spin oi participating in the transition and X is the final electronic configuration. For systems whose ground state is a closed shell, and NH,Cl in particular, the electronic configuration of the final state with two vacancies on valence MOs 0 0092614/83/0000-0000/S
03.00 0 1983 North-Holland
may be either singlet or triplet.
Because in +&e aingle-
determinant spin-polarized approximation of the wavefunction, spin and orbital angular momentum
G?t33 _
=O,n~~=O);
=E(II~
=0)-E,,,,
,
then average energies of singlet (S) and triplet (T) multiplets according to this sum rule are equal to ET@“2 = 0 ,n$ =0)= Es@
Ea2_
,
-4%pY3
(2)
(3)
-
From eqs. (l)-(3) for Auger energies of S and T states we obtain the following expressions:
(4) K&3 = 2&$a
-K&3
-
,n3 =1)-E(r~l=1,tr2=0,n3=0)
+-.&+e.&
= -e&
(7)
with an accuracy up to the third terms of (6). Here e&are orbital energies detemrined for TS. Estimations of the Auger energies using (4) and (5) require in the common case two spin-polarized calculations for every transition with occupation numbers determined by the corresponding configuration of configuraholes. The calculation on a clfla~~P-a~~~a tion gives immediately the triplet component of the Auger transition K 53 = -ey
= 0 , n$ = 0) = ET - 2(ET - Eaza3)
=2Gzp3
algebra E(rtl=0,n2=1
multiplet splitting cannot be treated uambiguously, we use in calculations of multiplet energies the sum rule [ 161. In this approach the energies of singlet and triplet states are averages of all states (with unknown weights in a common case) which arise from the given electronic configuration. if we define E o2 + = E(n;’
25 March 1983
CHEMICAL PHYSICS LETTERS
Volume 96, number 1
+e7Q +&J .
@I
The calculation-k a c1flav~/2%~/2fl configuration yields the energy Kt& = -rzy + &q + $ which is required by (5) to determine the singlet component of a transition_ It is pertinent to emphasize the model character of the TS computations_ The high multiplicity in the Auger energy calculations is due to the mathematical formalism [see (6) and (7)] and not to the physics of the Auger process. For closed-shell ground-state molecules the intensities of the Auger transitions are connected with Coulomb
(9
The spin index in K123 is omitted because the difference between hdoZa3 and K$a o3 does not exceed tenths of one eV according to our calculations. For valence orbitals this index is omitted due to equality ofEazp3 and E8ap3 in the case of closed-shell systems. Now we expand the total statistical Xo energy in a Taylor series in occupation numbers of MOs involved in the Auger process,
(6) and following the Slater transition state(TS) concept [ 171, select a state in the middle of the initial (11~ = 0, I’2 = 1, "3 = 1) and final (n, = 1, “2 = 0, it3 = 0) states. For the TS should be assigned occupation numbers nl = l/2, n2 = 112 and ns = 112. Using the expansion (6) with respect to TS one may deduce after some
where Q and b denote valence MOs involved in the Auger process and Q(E) is the wavefunction of an Auger electron. In the one-center approsimation which has been commonly used [2,5,6] Q(E) is a spherical wave centered at the atom with the primary vacancy (at N in our case)_ @I,,,(e) = RI(~) YI,,, >
(10)
where R](E) is the radial function of a continuum wavefunction and Ylm is the spherical harmonic_ The one-electron MOs are determined in DVhl by the usual LCAO expansion: pi = c
i
c&a-
J
(11) 72
Voluttxe 96. number 1
CHEhflCAL
where X~ are atomic basis functions. In the one-center approximation
where pi are atomic functions centered at an atom with the primary vacancy. The matrix elements in (117) Jlnve been calculated [ 181 using HFS numerical functions. Here we use numerical HF functions which are practically tile same as HFS ones. Notice that the Auger energies given in the tables are calculated within the doubfc-zeta basis of Clenlenti [20]. Auger energies obtairwd within tile HF basis slightly differ from tile latter ones mainly due to the distinction of calculdtcd energies of the N Is A0 in both bases. The N 1s 11’is 3 11.9 or 406.3 CV against the experimental v&c 403 eV [ 191 of a free atom. Only main Auger lines are calculated witllout taking into account llie processes of shake-up and shake-off types The half-~ idths of a gaussian decomposition of the t?rpcrimental spectrum of NH_+Cl are used wflen plotting the tfleoreticai spectrum.
3. Results and discussion The geometry
of the NJ-J_+Clmolecule
25 hfareh 1983
PHYSICS LFXI-ERS
is taken
partly from the X-ray data on solid NH,CJ 1211, i.e. the point group is C&, R(N-H) = 2.1 au, and from the ab initio calculations of Clementi [22], i-e_ R(H-Cl) = 3-4 au- The hydrogen atoms are assumed to form an undistorted tetrahedron. The cafculations are carried out as within HF using Clementi’s doublezeta f201 functions on N and CLand fs the H. In table 1 we give the IPs, Mulliken charges on atoms and experimental 1Ps of the constituent atoms N, CJ and H, table 2 presents the energies of Auger transitions calculated within the dot&e-zeta basis according to (5) and f7), and the integraf intensities determined by (I f) using the LCAO coefficients of the ground-state wavefunctions within the HF basis. Because the number of fine-structure lines for the main Auger transitions is quite large, seven peaks are selected for comparison with features of the expcrimental spectrum. The theoretical intensities are caJculated to be integral intensities of Auger Iines determining the peaks. In table 3 are given the calculated Auger energies and relative intensities of peaks 1-7 and the experimental v&es obtained by a Gauss decomposition of the experimental spectrum. The latter is recorded for polycrystalline N&Cl using the Mg I& We_ A more detailed description has been published elsewhere [23]. The spectrum after substraction of the back-
l‘&lc I The
wIct11~~d
1%. MuIlAen
ctuqe+
on
Itzoms of NH~CI. and rhe experimental
IPs of N. H and Cl atoms (in eV)
Experimental IFS a)
bfcJ double-zeta - ._.--------7.8
8.2
7-9
17.4 18.9 20.3 19.1
17.2 18.9 20.0
3VI
29.2
2SN
207.0 208.5 264.6 411.9 2832.9
Qll
Qh
---.. 3)
72
- -.. -
horn
ret 119).
I ----
QN QCI
-___-.__
I_~-
7.9
0.37 0.30 -0.80 -0.62
13.7 13.2 13.6
3PC1 2px 1SH
199.8 201-4 258.9 406.3 2806.5 0.28 0.70 -0.40 -0.60
2%2,3, 2sfl 1Sh’
kl
Cl
25.3 26.0 206 204 274 403 2827
CHEMICAL PHYSICS UZl-TERS
Volume 46. number 1
25 March 1983
Table 2 The calculated Auger energies (in ev) and integral intensities of the N KVV transitions in NH,Cl Confiiuration
Spin
Kinetic energy
integral intensity
Number of peak
0
336.8
0.590
1
0
347-O 349.6
0.026
1
2
1
345.6 350.4
0.730 I 0.112
Sa;”7ai'
0 1
351.2 352.2
0.528 0.074 I 0.170
6a;* 6a;’ Ze;’
0 0 1
359.7 358.8 360.4
0
1
358.3 361.7
0
361.9
1
362.3
0
362.7 362.9
0
3
1
0 0
1 6a;’ &I;’
0 1
73;’
sa;”
8ai’ 2e;’
8ai2
0
362.8 362.7 362-V
I.020 0.038
1
0.379
0.010
372.0 374.2
0.536 0.020
373.7
0.666
373.6
0.034 O-1 24 j
381.6
0.274
eV to match the first peaks of the
spectra. This shift is due to different phases of NH4CI in the calcnlations and the experiment. After the shift
a close resemblance of both curves is evident. Note that the more traditional approach in calculations for solids is a cluster model within which one should calculate the cl?ster NH4@-. However, as
I
5
0.018 J 0.584
368.1 370.3
ground is presented in fig. 1 together with the theoretical one. The experimental Auger energies are
displaced -9.5
4
6
7
has been noticed f24], a cluster simulating a solid should preferab3y consewe the stoichiometry of the solid. From this point of view the molecule NH&C1is the minimal stoichiometric cluster for solid NH,Cl. Most calculated Auger lines are located near experimental peak positions within limits of experimental errors. The exceptions are peaks 4 and 7 orig-&ating from the 2e- 2 and Sai_ 2 configurations.
agreement for 2e-’
The dis-
may be explained by the one-de73
Volume
96. number
CHEhIICAL
1
T.Me 3 The c\perimcnwl and calculated enersies(in intensirxs for the N KVV i\uger transitions ~-_ . -~- _-__-_ Number
EIhcor
EexP
&or a)
(C’V)
(eV)
(5)
lfheor IS G)
Iexp (%)
1 ,
336.8 34x5 351.2 35s.3 362.7 371.8 3Sl.h
336.S 317 352 362 363 373 379.5
7.7 11 10 ‘2 16 I9 3.7
5.6 13 5.6 41 14 18 2.8
9.2 11 10 20 23 22 4.1
3) fi;s arc hcor and IIS lllr: I \tb LCt$@ coetkicnts
inre_er~lintcnsitirs wlculated using for the ground- and initial-state ~.~\ciuncrionc respccti\ely. The expcrinlental Au_ecrenerSIC<.IIL’zhlftcd h? -9.5 eV.
Icrnunxlt approximation used because we do not resolve rhe multlplet structure of this configuration and dccounf for the configurarion interactions. and for S.I~ ’ ir may be connected with a lattice potential inllucnrc. The theoretical inrensities of peaks l-7 are 111a good agreement with experimental ones if one uses t!lc l-C.40 coefficients of the ground-state wave-
function. Thr intensilies were calculated using the Xl0 LCAO coefficients of the initial state wavefunctiorl with a vdcmcy in the K shell of N as well. In the
H--
LE-ITERS
25 March 1983
latter case the contribution
eV) and peak in NbCl
of pc.A
; J 5 6 7
PHYSICS
of p AOs does increase to the influence of the core vacancy field, leading to a considerable relative Increase of amplitude of peak 4. The same trend is observed when calculating the intensities with the use of LCAO coefficients for TS of the 7ai’2e? ’ configuration. Recently [23 ] we have qualitatively assigned the fine structure for the N KVV Auger spectra of NHdX, X = Br and Cl, assuming the approximate equivalency of the NH; and CH4 electronic structures, accounting for their isoelectronic character. The high-energy peaks 7 and 8 were considered to be satellite ones for transitions from the highest valence MOs composed mainly of N AOs. According to results of the DVM calculations the appearance of peaks 7 and 8 (see fig_ 1) is due to a substantial delocaliiation of the N-H-Cl bond owing to hybridization of N 2s, 2p,, the bridge H Is and Cl 3s. 3p, AOs. It is interesting to note that the shape of the other peaks l-6 is similar to that of the carbon Auger lines in CH,. It allows us to connect the intensities of peaks 7 and 8 with the covalency strength of the Cl-NH, bond. due mainly
Acknowledgement The authors wish to express their sincere gratitude to Drs. Ju.M. Shul’ga and A.F. Shestackov for discussion and critical remarks, and to the referee for valuable comments_
References
h--H-_CI
[ 1 ] R. Weissmann and K. hl’uller, Surface Sci. Rep. 105
.-__
307
_. *
327
347
367
387 Et,”
ieVl-
1 lg. 1. 1 he c.dsul~Icd and cxpcrmxnt.d N KVV Auger specII~ of jY14Cl. The positions of theoretical peaks 1-7 are tn.~rkxl x\lth \cr~x.d bxs. Their amplitudes are proportional to Ihc pc.k mrcnsirws. The pe_k to the left is due to admixturc 01 thr 0 KCUcwitarlon ofC1 2p levels.
73
(1981) 251. [ 2 ] H. Siegbahn. L. Asplund and P. Krlfve. Chem. Phi-s. Letters 35 (1975) 330. [3 J 1~. Agren, S. Svcnsson and U-1. Wahlgren. Chem. Phys. Letters 35 (1975) 336. [?I hl.T- Okland, K. Faegri Jr. and R. Mannc, Chem. Phys. Letters40 (1976) 185. 151 K. Faegri Jr. and H.P. Kelly. Phys. Rev_ A19 (1979) 1649. [6] H. Agren. J. Chem. Phys. 75 (1981) 1267. [7] D.R. Jennison, Chem. Phys. Letters 69 (1980) 435. [S] D-R. Jennison, J. Vat. Sci. Technol. 17 (1980) 172. (91 B-1. Dunlap. P.A. hlills and D.E. Ramaker, J_ Chem. Phys. 75 (1981) 300. [IO] F-L. Hutson. D.E. Ramalter, B-1. Dunlap, J-D. Ganjei and J-S. hfurday. J. Chcm. Phys. 76 (1982) 2181.
Volume 96, number 1
CHEMICAL PHYSICS LETTERS
111 J hf. Barber, I.D. Qark and A. ~~~h~ffe, Chem. Phys. Letters 48 (1977) 593. 1121 P.C. Desmukh and R.G. Hayes, Chem. Phys, Letters 88 (1982) 384. 1131 K-D. Sen, 3. Chem. Phys. 73 (1980) 4704. fl4] LA. Topal, privtrte communicatioa [ ISI G-L. Gutsev and A.A. Levi& Chem. Phys. 51 (1980) 459. [i6] T. Ziegler, A. Rauk and E.J. Baerends, Theoret. Chim. Acta 43 (1977) 261. iI71 3-C Slates, The self-consistent field for molecules and solids @lit, Moscow, 1978) ch. 2_ fl8l EJ. McGuire_ Phyr Rev_ 185 (1969) l_
25 March 1983
[ 19 I K. Siegbahn, C. NordIin#& k Fahhnan, R Nordberg, K. Hamrin, J. Hedman,G. Johanssdn,T. Bergmark, S.-E. Karlsson, I. Lindgren and B. Lindberg, ESCA, Atomic, molecular and solid state structures studied by means of electron spectroscopy (MI, Moscow, 1971) table43. I201 E. Clementi. R Matcha and A. Veillard, J. Chem. Phys. 47 (1967) 1865.
1211 Structure Reports 23,295, (221 E. Clementi, J. Chem. Phys. 46 (1967) 3851. (23 1 G-M. hlichailov and Ju.G. Borod’ko, Surface 6 (1982) 85 [in Russian]_ 1241 C Umrigu and D-E. Ellis, Phys. Rev. B21 (1980) 652.