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Interpretation of the core electron excitation spectra of hydride molecules and the properties of hydride radicals
Chemical Physics II (1975) 217-228 Q North-Holland Publishing Company
INTERPRETATION OF THE CORE ELECTRON EXClTATION SPECTRA OF HYDRlDE MOLECULES AND THE PROPERTIES OF HYDRLDE RADICALS W.HE. SCHWARZ Lefrrsrufdfir Theoretische
Cfwmie der ChiversitZt,
Wegefer Strasse
12,53
Boml. Germurzy
Received 15 May 1975 Revised manuscript received 11 July 1975 The XUV absorption spectra of HCI, H2S, PH3, SiJ&, and CH4 (from Hayes and Brown, and Chun) and the elzctron energy loss spectra of HzO, NH3, CH4 (recently recorded by Wight and Brian) are discussed. The peaks are assigned and their enerf$es, widths and intensities are explained. Core electron binding ener$es are derived. From the meassured peak enereics and band widths oredictions are made on the wossible existence and on some properties of the mo!ecular hydride radiks ArH, ClHz, SH3. PH,, FHz, OHJ, and NI$. -
1. Introduction
2.Z+l -Analogy and qualitative
The XUV absorption spectra of HCI, H2S, PH,, and SiH4 in the 100-200 eV region, corresponding to the excitation of 2pelectrons of the heavy atom, with an interpretation of the measured fine structure, have recently been published by Hayes and Brown (11. The aim of this note is to provide a more reliable assignment of the absorption bands and to draw further physical information from them. To this end, the following ideas will serve as basis for argumentation: (1) the “Z+l-analogy” [2,4] ; (2) qualitative LCAO MO schemes within the, united and separated atoms approaches together with Hartree-Fock-Roothaan calculations on PH:, Sq, CLH;, ArH+, and R+; (3) the Franck-Condon principle applied to the widths of the absorption bands. These will allow us to.calculate core electron binding energies (which are now in agreement with known ESCA values), and to predict some properties of the corresponding neutral molecular radicals PH, , SH, , CIH;, and ArH. In a similar manner the K-shell XUV absorption spectrum of CH, (Chun [3a]) and the Kshell electron energy loss spectra of CH4, NH3, and H20 (Wight cd Brian [3b]) will be analyzed to yield data onNHG.H30, and H2F.
In order to get an understanding of the experimental spectra of the second row hydrides, shown in fig. 1, a qualitative MO picture is first considered. If an electron is excited from a deep lying non-bonding core level, e.g., the Si 2p A0 in SiH,, the effect of the electron hole near the nucleus on the higher occupied valence MOs and on the excited orbit& will be nearly the same as that of a nucleus, the charge of which is increased by one (“Z+l-analogy”, [2,4]). For example, the Rydberg orbitals of core excited Si*H, (core excitations are indicated by a star) will be very similar to those of PH,. The main difference between Si*H4 and PH4 is, that there is an open shell in the core of the former molecule which will result in exchange splittings. However, ab initio calculations by Deutsch and Kunz [S] on Si*H, have shown, that the influence of this exchange interaction on the term values may be neglected even for the transition of a core electrcn to the lowest excited orbital.. For a crude picture of the excited orbitals .of the hydrides, Hayes and Brown [l] used the united atom model, which was also the physical basis of the-singlecenter calculations of Deutsch [5] on Si*H,+. The united atom of its Z+l-analogue PH4 is K. As PH4 is highly synun&-ic this approach seems Tuite suitable. However, it should be noted that the protons in PH4 are not fully shieIded;so that-a&the excited Rydberg
_’
excited MO picture
218
W.H.E. Schwon/Cbore
elecrmtz excirurion spectra of hydride molecules
orbitals will lie enetgeticaliy lower in.PH, than in K. Furthermore, the d-type orbitals will be strongly split by the tetrahedral field of the protons, with the t2 species being the lower one. The non-tetrahedral hydride malecules, however, arc so strongly asymmetric that the united atom picture of Hayes [ 11 seems rather unsuitable for a discussion of the lower excited MOs. The LCAO of the separated atoms should be a better starting point here.
In AH,, the ir Ills AOs will mix with the 3s and 3p AOs of the heavy atom to form tz occupied (I bonding orhitals and n empty u* antibonding orbitals. In this picture the Rydbcrg orbitals will lie above these antibonding MOs, the former being energetically higher than those of the corresponding atom. The experimental spectra of fig. 1 have then been assigned according to this MO picture.
1021
IS,&
..
1710
1618
1616
ev
17,2.
IOL,
zL2
240
F&g. 1. Absorption c10ss Sections of LII ~,i excitations for q&gas
after
Nakamura [6]
2,LL
106,
246
and fai rhe isaekhoni~
-
lv
ire
ev
100,
2,50-
second IOW
IlY+idc male&les a.f&eiHay& and &o&n [L] . : :
,:
..
, .I.
_:..
-..,
.
.
.
.
‘.
.-.
.
:.,. _:
y:
.I
.:::..
.:
:. -,
.‘.
:
.,,,
W.H.E. SCIWCZPZ/GJ~~elecrrmt
excitation spectraof hydride molecules
219
Table 1 Energy values for or and K (in eV) One electron state
%rtual orbital energy of K+
SCF energy or K below IP
Experimental energy
Experimental energy of
of K below IP a)
core excited AI* below
4s
-3.96
-3.93
-4.35
4P
-2.59
-2.60
-2.13
5s
-1.65
3d 5P 6s
-1.52 -1.24 -0.86
4d
-0.83
a) From C.E. Moore, Atomic
1Pb)
-1.51
Energy
Levels
I (NBS,
-4.11
-1.73 -1.67 -1.2R -0.94
-i&l -1.7
-0.94
-0.9
-0.92
Washington, 1949).
b) Nakamura et al. [ 6I.
3. Ah initio calculations row hydrides
of the spectra of the second
ror inherent
in the SCF method,
of the core-valence
of the reorganization To obtain
a sounder
basis for this qualitative pichave been performed. As we are interested in states with one electron outside a closed valence shell, the SCF approximation should be adequate_ However, there exists no simple way to obtain higher excited states of given symmetry withln the SCF method. Therefore we proceeded as follows. As an example we discuss .%r. The Z+l-analogue of core excited Ar* in K. According to Koopmans’ theorem good estimates for the energies of the ground and the normal excited states of K with reference to the ionization limit are given by the virtual orbital energies of K+. There i; no principal difficulty to obtain several virt~ral orbital energies of the same symmetry by only one SCF calculation. This approach may be called the Analogous Ionic Core Virtual Orbital Method. In table 1 we compare the virtual orbital energies of Kf with the total SCF energies of K with reference to EsCF (K”)_ Indeed the difference is only of the order of 10m2 eV. The experimental term values* of K are obviously lower because_of the correlation er-
ture, ab initio calculations
*
By term value of an excited state we mean the difference between its energy and the energy of the corresponding
ionizationlimit (Robin [Ml).
electron effect.
that is to say because
polarization,
and because
The term values of 2p-
Ar* obtained from the XW absorption spectrum of Nakamura [6] arc shown in the last column of table 1. They correlate nicely with the virtual SCF excited
orbital energies of EC+. In a similar manner, we expect the XW term values of HCl to SiH4 to show the same pattern as the virtual orbital energies of HAr+ to PG. Therefore we performed Hartree-Fock-Roothaan calculations on the closed shell molecular ions HAr+, Cl%, and PH: by means of the Buenker-Peyerirnhoff program package. The basis functions have been taken from Roos and Siegbalm [7], to which were added one s-type bond lobe per bond and several diffuse orbitals of s, p, and d-type on the heavy atom. The following contractions have been used: s(6,2, .5* l), p(4,5* l), d(3* or 4*1) for the heavy atom, and s(3,2rl) for the hydrogens. We used g&Sian lobe functions wit!1 centerlobe separations of O.O3/&for p-type orbit&, and 0.12/d for d-type ones. The smallest orbital exponents E used were 0.001. As we are interested in the vertical excitaticn energies of HCl to Sib, the cdculations have been performed for the corresponding experimental equilibrium geometries of these molecules. The virtual orbital energies obtained in this way are given in table 2. In order to justify the orbital cor-
relations indicated in table 2 we refer to the orbital plots showri
in figs. 2 and 3.
WJf.E. 3cliwarzfCore electron exciration spectm of hydride molecules
220 Table 2
Calculated virtual orbital encrp’es (in e\3 System
K+
R(A-H) iI1 a,,
AtH’
ClH;
PHi
2.4s
2.5
2.9
K’
1ypc of orbital
0’
Type of orbital
-
-S.80
0
-3.96
-2.85
D
-2.36
43:
-2.59
-2.52 -2.32
R D
-2.39 bl -2.36 aI
a,
-2.32 -1.65
-1.290
-1.52
-1530 -1.48rr -1.466
3d
5P
-1.24
4. Comments on the aGgrnnent second tow hydrides
of the spectra
near fururc.
me&ureme~tr
-l&Sal
-1.65
5s
-2.1at*
-2.59
4P
al tz
b,
-l.ClOal
-0.91
a,
-0.88
6s
-1.57al -1.SZa2
-1.63
e
-1.52
-1.42bl -1.43 a, -1.36b2
3%
-1.19
tz
-0.88
4%
-1.17 b, -1.15 al -1_13b,
-1.06
tl
-1.24
5P
of the
The first transit&s in the molecules give rise to very broad bands m the spectra (see fig. 1). As the initial orbitals of the one electron excitations are nonbonding 2p core orbit&, the final orbitals must be strongly antibonding, that is antibonding valence orbitals u*, but not Rydberg orbit&, which are mainly nonbonding. Nevertheless Brown [l] and also Robi [15] have assigned this structure at least partly to Rydberg excitations.,However, whereas the higher Rydberg tran&orrz of P&Is and Sil-&are fully smeared out in the solid state spectra, there is only slight cbnge of shape of thefirst broad band on soIidIfIcation~, inrlicating that the first upper states do not possess considerable Rydberg character. Going from HCl to Sill?-, the corresponding ei-
* The cazresponding
4s 3dt-u*
-3.80 -2.85
4s
5s
-3.96 -1.52
-4.84a, -4.36 b2
will be published in the
perimental u* term values decrease from 6.2 eV to 4.2/3.1 eV (see table 3). This trend is reproduced by the calculated u” orbital energies, which decrease from 5.80 eV to 3.80/2.85 eV (see table 2) The calculated values are about 10% smaller than the experimental ones. This seems reasonable, because the appreciable polarization of the molecular cores by ‘&e excited electron (i.e., the core-excited electron correlation) is not taken into account in the SCF approximation. The experimental term values of the first sharp transitions from 2p to nonbonding orbit& also decrease from 3.15 eV in HCI to 1.9 eV in SiH4 (see table 3). These energy values roughly agree with the calc_ulated orbital energies of the lowest s-type Rydberg orbitals, 2.85 eV in ArHC and l-68 eV in P@ ‘(see table 2). As we used a moderately large basis set, we .do not believe this agreement to be fortuitous and ca&ed by a basis defect, but take it as a proof for the assignment of the first-sharp brie as a 2p + Rydberg s transition; We also do not believe .&thatcorrelation
1VH.E. Schwan/Core Table 3 Experimental
edc~ron excitation
term values of 2p-tore excited molecules
SpeCtrn
o/hJdrL&?
221
mOkCIAkS
(in eV) and quantum defect 6
Ar*
HClf.‘
H+*
P*Hs
Si*H,
M
Type of orbital
4s 5s 6s 7s
4.11 1 Xi4 0.92 0.58
6.2 3.15 1.5 0.8 0.5
5.7 2.75 1.25 0.75
5.1 2.45 1.05 0.65 0.45
4.2 1.9 0.95 0.6 0.4
4.11 1.64 0.92 0.58 0.40
4s 5s
6
2.15
1.9
1.75
15 or 2.5
2.25
2.15
6
4P
2.35
3.0
2.8
5P
1.4
6~
1.2 0.7
4P 5P 6~
6
1.6
1.85
1.8
6
(6.2) 1.6 1.6
5.1
4.4 2.0 I 1.6
Type of orbi taI
o*
a*
-
36
1.1
4d
0.9
0.9
1.0
1.0
Sd
0.6
0.55
0.6
0.6
6
0.15
0.1
0.3
0.3
1.9
differences and reorganization effects between the ion and the excited neutral states, which are neglected in our calculational method, will have any significant influence on the term values of these Rydberg states with closed valence shell.. The magnitude of the u* and Rydberg s term values demand some special comment. In HCl the Rydberg term value of 3.15 eV is typical for a 4s orbital [15]. In SiH,, however, ~(0”) = 4.2 eV lies in the range of 4s term values, whereas the lowest Rydberg term value of 1.9 eV corresponds to 5s. According to our calculations the p- and d-type Rydberg MOs do not strongly mix with the antibonding valence hlOs. Therefore their term values are 1 as usual [Is] very similar for all these molecules, and their quantum defects take the values typical for p- and d-Rydbergs. However, the lowest IJ* valence orbital incorporates some s-Rydberg character as it rises in energy from HCl to SiH,. This mixing of valence and Ryd-
._
:;.
.;
1.7
3d
0.9
4d
0.6
5d
0.4
6d
0.15 6
bital lies even so high above the 4p that it is better called 5’s, the o*al and 4s-Rydberg “conjugate orbital pair” be@ represented by only one mixed orbital in this molecule. For more details on this problem see ref. [S] _ The picture given here is somewhat different from what is usually accepted for voknce to Rydberg excitations [ 15 ] , especi+y for molecules from. the first row of the periodic table. One main difference between core and valence excitations is the fgllowing: in the u + o” singlet states “the electron spins do not act to correlate the wavefunction” (Robin, ref. [15]), leading to a destabilization by the uu* exchange integral, +K, *. As a consequence the u -+ CT*sir&et states, contrary- to their triplet congeners, often lie -above the ionization limit, and the lowest aexcited singlet states are of predominant Rydberg character. However, in the core + o* singlet states the c’ optical electron is Fermi-correlated witll,the closed o-shell, and the energy expression contains the term -K,,, ,
: :
-0.2 0.3
7s 8s
p-type ones. In SiH, the lowest s-type Rydberg or-
berg orbitak results in rather unusual term values: in H$3 and PH, the s-type orbit& lie slightly above the
._
3.1 1.9 I 1 1.3 0.95 I { 0.7 0.6 I I 05
63
:
I
-6
-3
0
.3
6
-6. --;pJ~____--I
-3
-6
0
3
,_______-__-------T
:
r
P
3
.6
orbital of U* #ype. E = Mid eV.
,.
..
: :-.;,,
_.
:
,a:
I ,*’
_i’
‘1. _j
_‘S-
.-b) S&ond~o orbital of 4rRydberg type with some p admix-., ttik (c + 2.85 eV), c).Tiid orbital.of 4p-kydb+;type.(thc :-fo&thiow& virtual hbitij, r : 2132 eV., -.
‘..
‘i.\
;
c
fig;2:Contour diaggr&~~of virtml.orbit& in _&W. Fti ewes: pdsititie wavefunction; broken cmes: negative wave-
function,-a> Lowest vi&l
;
I\ ‘. :
:
-6-
6
0
‘3
6.
Fig. 3. Contour diagrams~of virtual orbitals in PH; . (e) &Itons in the plane, (0) protons above or below the plane. a) Lowest nrtual orbital of a*a 1 or 4s Rydberg type e = 3.80 eV- b) Second lowest orbital of cr.-t* character, E = 2.85.eV. c) -Third lowest virtual orbital (second tl ok) of 4p.Rydkrg type,e
=
3.18 ev.
._ .. . . .‘:.
..
‘.
..-.
: -_ :
IV.i-I.E. Scf~warz/Co~e
Table 4 2p-Ionization
potentials
and spin-orbit
AI
HCI
248.52 f 0.05 (248.60 +_0.05) [9]
201.4 + 0.2 (207.22) =)
IP (2P,,2)
250.56 f 0.05 (250.70 +_0.05) [9]
209.0 +_0.2
tiso
2.03 i 0.01 (2.11 * 0.02) [lo] (CaIC.)
2.05
specrmof hydride molecules
excirariorr
223
splittings in eV (ESCA values given in parentheses)
IP (2P,,,)
MS0
electrm
1.6* 0.1 (1.6+0.05)
170.4 r 0.2 (170x * 0.2) [ 121 171.6 * 0.2 (171.4kO.2) 1.2to.1 <1.20~0.02)
Ill]
I.55
SiHa
PHs
H2.5
106.8 + 0.1 (107.09~0.1)
137.0 = OfI5 (136.87) a) 137.9*0.15
1121 [12]
1.17
0.9 f 0.05 (0.8 + 0.05)
[13]
107.4 + 0.1 (107.7) 0.65 + 0.05
1111
(q.m-+0.05) [ 11 I 0.61
0.84
a) W. Jolly, unpublished.
ment of the spectrum by Hayes and Brown, relying on the calculation of Deutsch, differs considerably from ours. Also their extrapolated IP values differ from those in table 4, especially in the case of HZ!? their values of 17111 and 172.2 + 0.3 eV are larger than ours or the ESCA results [ 121 by about 3/4 eV. Our calculation and assignment is also in actordance* *with a recent highly resolved Sls absorptior! spectrum of H2S (La Villa, ref. [ 14]), from which one obtains ~(a~) = -6.0 eV, e(b2) = -5.0 eV, I =-3.0eV,~(Sp)=-1.4eV,andIP(Sls)=2478.3 eV. The vibrational width of the 1s + al transition is about 1 .l eV, slightly larger than that of the 2p + al transition.
as in the case of the u + u* triplets, which do not show the preference of Rydberg character. Therefore we should not wonder too much, that ‘.n special cases the s-Rydberg term values are considerably different for core and valence excitations, especially as due to their strong penetration the ns orbitals often show term values far off the “normal” values [ 151. Extrapolating the Rydberg series according to these assignments, we obtain 2p ionization limits which are compared with recent ESCA results in table 4. In addition, our 2p312-2p112 ionization energy differences, AEm, are compared with HartreeFock estimates of the 2p spin-orbit splittings. The agreement is satisfactory in both cases, and seems to support our assignment. At this point, the calculation of Deutsch and Kunz on Si*H4 [S] should be discussed. Unfortunately a direct comparison of their results with ours is not possible, since they have only calculated the total energies of several 2pcore excited states of SiH4, but not the corresponding ionization limit, which is the zero reference energy of our calculations. Nevertheless two discrepancies may be noted: (1) According to our calculation there exists a t2 MO of p-type with E = -2.18 eV between the two lowest t2 MOs of d-type with E = -2.85 and -1 .lV eV, respectively. The corresponding t2(p) state has not been found by Deutsch. (2) The energy differences between the two lo--est excited orbit& of at, t,(d) and e-species are 2.12, 1.66, and 0.9 eV, respectively (see table 2), which are in good agreement with the expertinelltal term differences: 2.3, 1.8, and 0.95 eV (see table 3). Deutsch, however, calculates much larger v&es: 3.0,2.4, and 1.8 eV. It is therefore not surprising Ltit the assign-
:.
5. Discussion
of intensities
and band widths
5.1. Intensity
ratios of the 2~~~~ to 2pI12 excitations
To first order of approximation one would expect this intensity ratio to have the statistical value of 4:2. This is roughly the case for all the excitations with one exceptation: the excitations into the lowest empty orbital of 4s u* character exhibit nearly the inverted intensity ratio, at least in H,S, PH,, and’SiH4 (see fig. 1 and table 5). The “experimerital” values of this table have been obtained by fitting four gaussians of equal width to the experimental spectra. Obviously the numbers have only a qualitative meaning. *However, our results are not consistent with a recent discusssion on X-ray Rydberg spectra by Robin [ 151, nor with an Xacalculation on SiH4 by Sink and Juras [16]. resulted in a wrong order of excited states.
..
.._.
_.:
which
Table 5 Lowest Zp-e&tations
in second
Molecule
row hydrides
“Experimental”
intensity
2p + 0%) HCI H2S PHa -SiH4
ratio
WQP,,,)
1(2p3,2
2p-t
2.o @a! 1-s (e) 2.5 (t2)
Such intensity anomalies, w-hich were also noticed in the spectra of several other molecules [ 171, can be explained, if we take not only the 2p spin-orbit coupIiJ-16but also the excited electron-hole interaction into account. In fig. 4 several intermediate coupling diagrams a:e sketched. The left one should approximately describe the excitation into the lowest emp.‘ty orbital, which is totally symmetric. Two-electron mtemction will raise the intensity of the 2p1,2 excitation, which correlates with a singlet-singlet transition, whereas the first 2p3/? excitation correlales with a spin-forbidden transnion and is weakened therefore. As the spin-orbit coupling is largest in HCI and smallest in SiH,, the intensity ratio is largest for HCI and smallest for SiHq (see table 5). In thtis context it should be noted that the intensities are much more sensitively dependent on the exchange interaction than the transition energies. A 2p u* exchange integral, which is calculated for SiE14 to be as small as 0.1 eV, already reduces the intensity ratio from 2 to 1, whereasthe spin-orbit splitting in the spectrum is nearly unchanged for exchange integAs up to 0.3 eV.
Fig. 4. Intermedi+e coupling diagrams. Corrdlation lines are drawn only for those states which can optically be reached from the totally sym.~Mric ground s~.te. The numbers in the rectangles gke the relative intekities for thdlimiting cases.
: .
. ._..,’
:
_. ;.
.:.:
...‘.-
Calculated half hei$t
1.8 0.8 0.6 0.6
2.0 1.3 1.1 0.9
width at (eV)
o’(d)
2 ‘5
0.8 (al) 0.8 (a) 0.5 (al)
“Experimental” mean width of a single transition (eV)
-:. .:
The u* orbital in HCI has considerable da-characterz (see fig. Za), the intensity contribution of which to the 2~3/2 and 2~112 excitation should be nearly independent from electron interaction, as may be seen from the central diagram of fig. 4. In the case of tetrahedral symmetry, the two-electron interaction even tends to enlarge the intensity ratio of the 2p+ c+t2 transitions to a value greater than two (see right hand diagram of fig. 4). From the measured spectrum one obtains m 26 for Sii& (table 5). For the higher Rydberg states the two-electron interaction is so small that the intensity ratio is near to 2.
The three lowest virtual orbitals of o-species in ArH+ are shown in fig. 2. In the outer region of the molecule, the orbitals look like an s-orbital with dadmixture (2a), a slightly deformed s-orbital (2b), and a p-orbital (2~). However near the heavy nucleus their character is of p, p, and s-type, respectively. Correspondingly the calculated orbital transition moments Qplrlnu} for the three u MOs are comparable in magnitude and roughly agree with the measured oscillator strengths, which are of the order of a.few lo-* per degree of degeneracy. Going from HCl to SiH4, the molecular potential becomes more symmetrical, so that the s-p mixing of the Rydberg orbit& decreases together with a concomitant decrease in’the intensity of the 2p -+ 4p transitions, which are no more detectable in SiH+, partly because ofoverlapping with allowed bands. $ This d&e; not meandiffuse 3d-Rydberg character but corresponds to polari&tion functions in the valence Shea.
W.H.E. Schnrz/Gre
5.3. Vibrational phenomena Because of the antibonding character of the a* potential curves of the lowest apexcited states come out to be strongly repulsive in the region of ground state internuclear distances. Therefore we expect strong vibrational broadening for the 2p + o* transitions. Strictly speaking, vertical excitation into the u* orbit& leads to energies more than 1 eV above the dissociation limit, as sketched in fig. 5. For the width at half height, W, caused by dissociation broadening through one normal mode, we used the following approximate relation derived from the semiclassical Franck-Condon principle: MOs, the calculated
W = (5/3)E’/fi. E’ is the derivative of the difference of the upper and lower potential curves dEJdR, and 1-1and o are the reduced mass and ground state vibrational quanta. Calculated and measured widths (table 5) show the same trend. Using the united atom model one might interpret the Iowest u* orbitafs in SiH4 as nearIy nonbonding Rydberg orbitals; this qualitatively explains the observed trend. For the higher 2p + Rydberg transitions of nonbonding to nonbonding typz we do not expect appreciable vibrational effects. Contrary to the u* excited states, the equilibrium geometry of the Rydberg states (or the ion or Zi1-analogous ion) is near to the ground state geometry, and the calculated E’ values are smaller than those of the 2p --f u* transitions by one order of magnitude. Therefore, only sharp O-O transitions are observed in the Rydberg region. However, as mentioned above, going from HC1 to SiH, results in a1 o*-Rydberg s mixing. The strongest vibrational side bands are therefore expected for the 2p --f ns excitations in SiH,. Indeed, in this case there occurs a small peak in the sharp Rydberg fine structure (indicated by v in fig. l), which we attribute to the excitation of the symmetric (and asymmetric) stretching vibration as already suggested by Brown [l] . Another assignment as vibrationally allowed 2p + 4p transition seems not acceptable, becau?d it would require an unusually low 4p term v&r; of 1.6 eV, contrary to the calculated value of 2.2 eV, which is of reasonable magnitude for 4p. To further support the interpretation as a vibrational side band, we men-
_‘,
225
electron exci:afion spectra of hydride molectdes
tion that the occupied valence shell of a molecule will shrink a little after core excitation because of the in. creased effective nuclear charge. Furthermore it is known that the bond stretching force constants of. several diatomic molecules increase on ionization of an inner ccre electron. Such effects should oe most pronounced in SiH4 with a comparatively soft u&nce shell. Indeed rhe vibrational side band is separated from its parent doublet by 0.31 eV, which is tighrly larger than the corresponding ground state vibrational quantum of 0.27 eV. Even weaker vibrational bands are expected in the Rydberg region of the other molecules. TJnfortunately these spectra are less resolved, and also overlapped in the case of PH3, so that the vibrational bands are not detectable. However, the high energy shoulder of the 2p -+ 4s transition of H,S should be noted, which is higher in energy than the main peak by just - 0.3 eV.
6. The Is excitation
spectra
of !Grst row hydrides
The ordy reliable Xw’absorption spectrum is the one of CH4 recorded by Chun [3a,18]. Recently Wjght and Brian [3b] hsve published and interpreted electron energy loss spectra of CH4, NH3, and H20. Contrary to the second row hydrides, the antibonding valence orbitals of the first row hydrides lie much higher than the lower Rydberg orbit&, at least for ground state equilibrium distances (see, e.g., ref. [19]). Therefore it seems reasonable here to assign the lowest core-excitations to Rydberg transitions, as has been done by Wight and by Bagus I3,18]. The lowest rr = 3 molecular Rydberg orbitals are, however, disturbed by considerab!e admixture of antibonding valence character. The intensity of the first excitation from Is to 3s increases from CH, tc Hz0 in much the same way as Table 6
Experimental term values [3] of first row hydrides (in eV)
Orbital
CHq
NH3
Hz0
NC
3s 3P 4s
3.6 2.6
5.7 3.8,2.6
4P
1.3
5.0 3.4 2.0 1.5
4.9 2.9 1.9 1.4
1.2
-226
IV.H.E. SchwarzjCore
that of the ip -?4p kansition drides. The strongest trkitions
electron
excitarion
in the second row hyare the 1s + 3p ones,
which are considerably split in the case of HZC. ACcording t0 the a&5ignmcrlt of Wight, the 3p-Spbtthg 'shyld be even larger in NH, (AE = 1.3 ev). Espacia!ly because of int+ty reasons this assignment seems not very probable: the second component is weaker by about two orders of magnitude. This could better be interpreted as 1s -+ 4s. Because of the antibonding component of the 3s and 3p-Rydberg orbitals the corresponding transitions show a considerable Gbrational broadening of nearly 1 eV for CH, and HZO_ (It is interesting to note that the CH, Is+ 3p absorption line of Chun [3a] shows a pronounced high energy tail, which is typical for such vibrational broadening.) In the case of NH3 the width amounts to only about half ail eV, which means that the antibonding character of the two lowest Rydberg orbitals is less pronounced here.
7. Hydride
radicals
So far, no definitive
information
is known
about
the .hydride mdicals such as PH4,In fig. 5 war have sketched a potential curve diagram for this molecule. The abscissa denote, the asymmetric stretching mode PHS-H: The uppermost curve is tlzat of P$; its well depth is the proton affmity of PH3, known to be 8.1 eV [ZO] . According to the “‘Z-i1 -core analogy model” the states of PH4 resemble the core excited states of Si*H, . The Rydberg states and positive ion of PH,
will have nearly the &me geometry as the ground state of SiH,. Therefore, e.g., the 5s Rydberg state of PH4- will be situated 19 eV vertically below the ionic curve. The two lowest states, o* 4dl and o*t2, howeve_, llave repuisive curves. For vertical excitation, the energy of the lcw&t state of Si*H4 - and PH4 is 4.2 eV b&low the i&kation knit, that is 1.3 eV above the dissociation liinit*. From this and the estimated
sldpe of thk pot&&l
..y _
.I
: .. .: .... : ::
..
a conclusion, that the minimum of the PH, groundstate curve will be near 0 eV. PHd might exist as a loos2 bound PH,-H complex or as a metastable complex, but it should show no significant thermodynamic stability against dissociation. PH4 has recently been
identified by its ESR spectrum, but only as a radical trapped in a krypton matrix [21,28]. From fig. 5 we can also deduce rough estimates of the expected vertical excitation and ionization energies of PH,. These are compiled in table 7, together with estimates for the other molecular radicals. As PH4, also H3S and NH, are possibly weakly stable or metastable with about Emin G + l/2 eV. H, 0 will at most metastable, whereas ClH2, FHZ, and ArH will surely form no stable species. Potential curves for ArH and NH, have been reported elsewhere [4, 221, the former ones agreeing satisfactorily witb cal-
culated curves of Vasudevzm [23] (see ref. [22] ). Existence and some properties of the first row radicals have recently been discussed by Wight and Brion [2d] (see also refs. [4,22] )_ The relevant literature has already been cited there. Our estimates as given in table 7 differ significantly from those of Wight and Brion. E.g.. for NH3 a vertical IP of 5 i eV is predicted here, instead of 3.7 (Wi&t and Brian 1241). The latter value, as well as the theoretically calculated values in the range of 3.74.0 eV [27] refer to the equilibrium geometry of CH4 or NH:, respectively, and are to be interpreted as the vertical electron affinity of NI$. but not as the vertical or adiabatic ionization potential of the neutral radical NHd, which differs in its equilibrium geometry considerably fTOm N$.
I
;I ; 1. CSiHL) 2
..
_f
3.(A) R
..
F&S.Potent&l
energy curves for PH4. The bar on the abscic sa indicates th~:equililhium geometry of SiH4.
: -.
:_-.-
y
.
molecules
cuFre one can draw
* &change COH~C&IIS,which UC of very importance iti some other mol~cbies [4] , arenegligibly small in the underlying c+,(that is:;snialler than 0.1 eV). Hbwever; variation of thf elect&c transition moment with internuclear dkn~= -, might be ~mpor_*+it ic this case and would result in a vei: gc;rl enerw value.which-is about onevibrational quantum higher than the peakcenter. :
:
spectra of hydride
:-
_-
..
._:
‘.
227
electron excitation spectra of hydride mokcuk
W.H.E.Scliwerz/Core Table 7 Estimates for hydride Iadicais A% hoton
affinity of AH,_, in eV 1211
Energy of ZAHn at ground state geometry of z+ t AH, Probable stability
PH4
SH3
ClHz
ArH
NH4
OH3
FH2
8.1
1.4
6.1
4.0
9.0
7.2
5.3
+1.3
+1.1
+1.7
+3.4
+1.0
+1.4
+2.6
unstable
unstable
weakly 01
metastable
weakly or metastable
weakly DT me tnstzble
Adiabatic/vertical IP in cV
516
6/6f
4;/51
fi;/7
First optical excitation energy in eV
1
B 4
1
1;
Lowest vertical
33 4
3; 4,45
4 3;
5$
Our ionization potential for NH, agrees with the experimental 5.9 + 0.5 eV of Melton and Joy [25]. However, Melton’s IP for H30 of 10.9 eV is seriously in error, which seems to indicate that his experiment should not be taken as the fust direct proof for the existence of H30. Our prediction on the stability of H30 fits with a recent H + Hz0 scattering experiment 1261, which did not support the existence of bound H30.
8. Summary Our calculations by an “Analogous Ionic Core Virtual Orbital Method” on the second row hydrides from a reliable basis for the reinterpretation of the 2pexcitation spectra of Hayes and Brown. In HIS and PH3 the Rydberg ns levels are situated near to and above the up levels. Taking electron interaction, spin-orbit coupling, and the slope of the potential curves into account, it is possible to explain the nonstatistical intensity ratios and the widths of the first broad bands - which are assigned to valence orbitals qualitatively with the help if simple model concepts. On these lines we have deduced stabilities, IPs and excitation energies of the hydride molecular radicals. These values can be used as guidelines in experiments for the identification of the radicals. PH4, NH4 and SH, may be (weakly) stable or metastable, whereas H,O seems at best to be metastable;
_
.
5
Acknowledgement At fust I have to thank Professors Peyerimhoff and Buenkcr, whose programs have been used in this investigation. My sincere thanks are due to Dr. Vasudevan for many critical comments which helped significantly improve the manuscript_ I am also gwtefu: to Dr. Sonntag for valuable discussions and to the. Referees for their comments, which inspired me to insert some simple arguments in the manuscript. Furthermore I acknowledge the services and computer time of the University Computing Center (IBM 37c)168). Finally I thank Mrs. Huber-Rutz for typing the manuscript_ References t11 W. Hayes and F.C. Brown, Phys. Rev. A6 (1972) 21. I.31 M. Nakamura et al., Phys. Rev. 178 (1969) 80; see also G.R. Wight and C.E. Brian, J. Electron Spectry. 1 (1973) 457; 4 (1974) 313. 131 a) H.U. Chun, Phys. Letters A30 (1969) 445. b) G.R. Wight and C.E. Brion, J. El. Spcctry. 4 (1974) 25. t41 W.H.E. Schwarz, Angew. Chem. intern. Ed. 13 (1974) 454.
Deutsch and A.B. Kunz, J. Chem. Phys. 59 (1973) 1155. M. N&amlra, hl Sannuma. ‘3. Sate. M. Watanabe, H. Yamashita, Y. Iguchi. A. Ejiri.S. Nakai, S. Yamaguchi, T. Sawwa, Y. Nakni and T. Oshio, Phys. Rev. Letters 21 (1968) 1303.
I51 P.W. 161
.:
:.:
..
unstable
metastable
_.
:.
.
2.28
@..YiE. Schw&/Core
electron
excitation
[j].B. Roos ad P. Siegbahti, Theoret. Chim. Acta 17 (1970) 209. [S] W.H.E. Schwarz. Chem. Phys. 9 (1975) 157. [9] T.D.?homas arrd R.W. Shaw, J. Electron Spectry. 5 (1974)~1081. [lOI U. Gel&, E. Bnsilier. S. Svensso~, T. BerSmark and :K. Siegbahn, J; FIectror. Spxtry. 2 (1974) 4C15. [ll] A. Barrie, I.W. Drummond md C&C. Herd, J. Electron Spectry. 5 (1974) 217. 1121 U. G&us, privite communication (1974). 1131 W.B. Perry and -W.i. Jolly, Chem. Phys. Letters 17 (1972) 611. 1141 R.E. LaVi&, J. Chem. Phys: 62 (1975) 2209. [lS] MB. Robin. Chqn. Phys. Let+s 31 (1475) 140; Higher. Excited States of Polyztbmic Molecules (Academic press, New Yqrk, 1974). [is] -M.L. Sink and G.E. Juras, Chem. Phys. Letters 20 (1973) 474. [I?‘] U. Nielsen, R. Haenscl and W.H.E. Schwa=, 1. Chem. Phys. 51 (1974) 3581. [IS] P.S. Bagus, M. Gauss and R.E: I&%Ua, Chem. Phys. Letters 23 (1973) 13. ,[19) F. Ackermann, H. Lefebvre-Brian and A.L. Roche, Can. J.,P$ys. 50 (1972) 692; KJ. Miller, S.R. hfiekzarek and M. Gauss, J- Chem. Pkys. 51 (1969) 26; R.S. Muen, CIXXI. Phys. Letters 14 (1972) 141.
,.:
.. ..
. .
:. .‘:,
..
:
.‘. :
:. .
:
: .,;._
-. :._ .-.:
..
spectra o/hydrkie
molecules
[ZO] M.A. H&ICY and J.L. Frank&n, J. Phys. Chem. 73 (1969) 4328; J.Chem. Phys. 50 (1969) 2028. J. Long and B. Munson, J. Amer. Chem. Sac. 95 (1973) [2r] [22] [23] [24] [25] 1261 1271
[2B]
??bcDowell, K.A.R. Mitchell and P. Raghur-than, J. Chem. Phys. 57 (1972) 1699. W.H.E. Schwarz, Bet. Sunsenges. 78 (1974) 1206. K. Vasudevan, to be published. G.R. Wight and C.E. Brian, Chem. Phys. Letters 26 (1974) 607. CE. Melton and H.W. Joy, J. Chem. Phys. 46 (1967) 4275. D. Bassi, M. de Paz, A. Pesce and F. Tommarini, Chem. Phys. Letters 26 (1974) 422. C-E. Melton and H.W. Joy. J. Chem. Phys. 48 (1968) 5286; D-M. Bishop, J. Chem. Phys. 48 (1968) 5285; W. Strehl, H. Hartmann. K. Hensen and I!‘. Sarholz, Theorer. Chim. Acts 18 (1970) 290; W.A. Lathan, WJ. Hehre, LA. Cutiss and J.A. Pople, J. Am.Chem. Sot. 93 (1971) 6377. Note added in proof: In the meantime.AAJ. Colussi, J.R. Morton and R.F. Preston, J. Chem. Phys. 62 (1975) 2004, have thoroughly repeated the ESR measurements. Contrary to McDowell et al. [21] they fmd that PH, (trapped in a neopentane matrix) has a nontetmhedral geometry. confirming semi-empirical calculations [21]. This result is in accordance with our ideas.
INTERPRETATION OF THE CORE ELECTRON EXClTATION SPECTRA OF HYDRlDE MOLECULES AND THE PROPERTIES OF HYDRLDE RADICALS W.HE. SCHWARZ Lefrrsrufdfir Theoretische
Cfwmie der ChiversitZt,
Wegefer Strasse
12,53
Boml. Germurzy
Received 15 May 1975 Revised manuscript received 11 July 1975 The XUV absorption spectra of HCI, H2S, PH3, SiJ&, and CH4 (from Hayes and Brown, and Chun) and the elzctron energy loss spectra of HzO, NH3, CH4 (recently recorded by Wight and Brian) are discussed. The peaks are assigned and their enerf$es, widths and intensities are explained. Core electron binding ener$es are derived. From the meassured peak enereics and band widths oredictions are made on the wossible existence and on some properties of the mo!ecular hydride radiks ArH, ClHz, SH3. PH,, FHz, OHJ, and NI$. -
1. Introduction
2.Z+l -Analogy and qualitative
The XUV absorption spectra of HCI, H2S, PH,, and SiH4 in the 100-200 eV region, corresponding to the excitation of 2pelectrons of the heavy atom, with an interpretation of the measured fine structure, have recently been published by Hayes and Brown (11. The aim of this note is to provide a more reliable assignment of the absorption bands and to draw further physical information from them. To this end, the following ideas will serve as basis for argumentation: (1) the “Z+l-analogy” [2,4] ; (2) qualitative LCAO MO schemes within the, united and separated atoms approaches together with Hartree-Fock-Roothaan calculations on PH:, Sq, CLH;, ArH+, and R+; (3) the Franck-Condon principle applied to the widths of the absorption bands. These will allow us to.calculate core electron binding energies (which are now in agreement with known ESCA values), and to predict some properties of the corresponding neutral molecular radicals PH, , SH, , CIH;, and ArH. In a similar manner the K-shell XUV absorption spectrum of CH, (Chun [3a]) and the Kshell electron energy loss spectra of CH4, NH3, and H20 (Wight cd Brian [3b]) will be analyzed to yield data onNHG.H30, and H2F.
In order to get an understanding of the experimental spectra of the second row hydrides, shown in fig. 1, a qualitative MO picture is first considered. If an electron is excited from a deep lying non-bonding core level, e.g., the Si 2p A0 in SiH,, the effect of the electron hole near the nucleus on the higher occupied valence MOs and on the excited orbit& will be nearly the same as that of a nucleus, the charge of which is increased by one (“Z+l-analogy”, [2,4]). For example, the Rydberg orbitals of core excited Si*H, (core excitations are indicated by a star) will be very similar to those of PH,. The main difference between Si*H4 and PH4 is, that there is an open shell in the core of the former molecule which will result in exchange splittings. However, ab initio calculations by Deutsch and Kunz [S] on Si*H, have shown, that the influence of this exchange interaction on the term values may be neglected even for the transition of a core electrcn to the lowest excited orbital.. For a crude picture of the excited orbitals .of the hydrides, Hayes and Brown [l] used the united atom model, which was also the physical basis of the-singlecenter calculations of Deutsch [5] on Si*H,+. The united atom of its Z+l-analogue PH4 is K. As PH4 is highly synun&-ic this approach seems Tuite suitable. However, it should be noted that the protons in PH4 are not fully shieIded;so that-a&the excited Rydberg
_’
excited MO picture
218
W.H.E. Schwon/Cbore
elecrmtz excirurion spectra of hydride molecules
orbitals will lie enetgeticaliy lower in.PH, than in K. Furthermore, the d-type orbitals will be strongly split by the tetrahedral field of the protons, with the t2 species being the lower one. The non-tetrahedral hydride malecules, however, arc so strongly asymmetric that the united atom picture of Hayes [ 11 seems rather unsuitable for a discussion of the lower excited MOs. The LCAO of the separated atoms should be a better starting point here.
In AH,, the ir Ills AOs will mix with the 3s and 3p AOs of the heavy atom to form tz occupied (I bonding orhitals and n empty u* antibonding orbitals. In this picture the Rydbcrg orbitals will lie above these antibonding MOs, the former being energetically higher than those of the corresponding atom. The experimental spectra of fig. 1 have then been assigned according to this MO picture.
1021
IS,&
..
1710
1618
1616
ev
17,2.
IOL,
zL2
240
F&g. 1. Absorption c10ss Sections of LII ~,i excitations for q&gas
after
Nakamura [6]
2,LL
106,
246
and fai rhe isaekhoni~
-
lv
ire
ev
100,
2,50-
second IOW
IlY+idc male&les a.f&eiHay& and &o&n [L] . : :
,:
..
, .I.
_:..
-..,
.
.
.
.
‘.
.-.
.
:.,. _:
y:
.I
.:::..
.:
:. -,
.‘.
:
.,,,
W.H.E. SCIWCZPZ/GJ~~elecrrmt
excitation spectraof hydride molecules
219
Table 1 Energy values for or and K (in eV) One electron state
%rtual orbital energy of K+
SCF energy or K below IP
Experimental energy
Experimental energy of
of K below IP a)
core excited AI* below
4s
-3.96
-3.93
-4.35
4P
-2.59
-2.60
-2.13
5s
-1.65
3d 5P 6s
-1.52 -1.24 -0.86
4d
-0.83
a) From C.E. Moore, Atomic
1Pb)
-1.51
Energy
Levels
I (NBS,
-4.11
-1.73 -1.67 -1.2R -0.94
-i&l -1.7
-0.94
-0.9
-0.92
Washington, 1949).
b) Nakamura et al. [ 6I.
3. Ah initio calculations row hydrides
of the spectra of the second
ror inherent
in the SCF method,
of the core-valence
of the reorganization To obtain
a sounder
basis for this qualitative pichave been performed. As we are interested in states with one electron outside a closed valence shell, the SCF approximation should be adequate_ However, there exists no simple way to obtain higher excited states of given symmetry withln the SCF method. Therefore we proceeded as follows. As an example we discuss .%r. The Z+l-analogue of core excited Ar* in K. According to Koopmans’ theorem good estimates for the energies of the ground and the normal excited states of K with reference to the ionization limit are given by the virtual orbital energies of K+. There i; no principal difficulty to obtain several virt~ral orbital energies of the same symmetry by only one SCF calculation. This approach may be called the Analogous Ionic Core Virtual Orbital Method. In table 1 we compare the virtual orbital energies of Kf with the total SCF energies of K with reference to EsCF (K”)_ Indeed the difference is only of the order of 10m2 eV. The experimental term values* of K are obviously lower because_of the correlation er-
ture, ab initio calculations
*
By term value of an excited state we mean the difference between its energy and the energy of the corresponding
ionizationlimit (Robin [Ml).
electron effect.
that is to say because
polarization,
and because
The term values of 2p-
Ar* obtained from the XW absorption spectrum of Nakamura [6] arc shown in the last column of table 1. They correlate nicely with the virtual SCF excited
orbital energies of EC+. In a similar manner, we expect the XW term values of HCl to SiH4 to show the same pattern as the virtual orbital energies of HAr+ to PG. Therefore we performed Hartree-Fock-Roothaan calculations on the closed shell molecular ions HAr+, Cl%, and PH: by means of the Buenker-Peyerirnhoff program package. The basis functions have been taken from Roos and Siegbalm [7], to which were added one s-type bond lobe per bond and several diffuse orbitals of s, p, and d-type on the heavy atom. The following contractions have been used: s(6,2, .5* l), p(4,5* l), d(3* or 4*1) for the heavy atom, and s(3,2rl) for the hydrogens. We used g&Sian lobe functions wit!1 centerlobe separations of O.O3/&for p-type orbit&, and 0.12/d for d-type ones. The smallest orbital exponents E used were 0.001. As we are interested in the vertical excitaticn energies of HCl to Sib, the cdculations have been performed for the corresponding experimental equilibrium geometries of these molecules. The virtual orbital energies obtained in this way are given in table 2. In order to justify the orbital cor-
relations indicated in table 2 we refer to the orbital plots showri
in figs. 2 and 3.
WJf.E. 3cliwarzfCore electron exciration spectm of hydride molecules
220 Table 2
Calculated virtual orbital encrp’es (in e\3 System
K+
R(A-H) iI1 a,,
AtH’
ClH;
PHi
2.4s
2.5
2.9
K’
1ypc of orbital
0’
Type of orbital
-
-S.80
0
-3.96
-2.85
D
-2.36
43:
-2.59
-2.52 -2.32
R D
-2.39 bl -2.36 aI
a,
-2.32 -1.65
-1.290
-1.52
-1530 -1.48rr -1.466
3d
5P
-1.24
4. Comments on the aGgrnnent second tow hydrides
of the spectra
near fururc.
me&ureme~tr
-l&Sal
-1.65
5s
-2.1at*
-2.59
4P
al tz
b,
-l.ClOal
-0.91
a,
-0.88
6s
-1.57al -1.SZa2
-1.63
e
-1.52
-1.42bl -1.43 a, -1.36b2
3%
-1.19
tz
-0.88
4%
-1.17 b, -1.15 al -1_13b,
-1.06
tl
-1.24
5P
of the
The first transit&s in the molecules give rise to very broad bands m the spectra (see fig. 1). As the initial orbitals of the one electron excitations are nonbonding 2p core orbit&, the final orbitals must be strongly antibonding, that is antibonding valence orbitals u*, but not Rydberg orbit&, which are mainly nonbonding. Nevertheless Brown [l] and also Robi [15] have assigned this structure at least partly to Rydberg excitations.,However, whereas the higher Rydberg tran&orrz of P&Is and Sil-&are fully smeared out in the solid state spectra, there is only slight cbnge of shape of thefirst broad band on soIidIfIcation~, inrlicating that the first upper states do not possess considerable Rydberg character. Going from HCl to Sill?-, the corresponding ei-
* The cazresponding
4s 3dt-u*
-3.80 -2.85
4s
5s
-3.96 -1.52
-4.84a, -4.36 b2
will be published in the
perimental u* term values decrease from 6.2 eV to 4.2/3.1 eV (see table 3). This trend is reproduced by the calculated u” orbital energies, which decrease from 5.80 eV to 3.80/2.85 eV (see table 2) The calculated values are about 10% smaller than the experimental ones. This seems reasonable, because the appreciable polarization of the molecular cores by ‘&e excited electron (i.e., the core-excited electron correlation) is not taken into account in the SCF approximation. The experimental term values of the first sharp transitions from 2p to nonbonding orbit& also decrease from 3.15 eV in HCI to 1.9 eV in SiH4 (see table 3). These energy values roughly agree with the calc_ulated orbital energies of the lowest s-type Rydberg orbitals, 2.85 eV in ArHC and l-68 eV in P@ ‘(see table 2). As we used a moderately large basis set, we .do not believe this agreement to be fortuitous and ca&ed by a basis defect, but take it as a proof for the assignment of the first-sharp brie as a 2p + Rydberg s transition; We also do not believe .&thatcorrelation
1VH.E. Schwan/Core Table 3 Experimental
edc~ron excitation
term values of 2p-tore excited molecules
SpeCtrn
o/hJdrL&?
221
mOkCIAkS
(in eV) and quantum defect 6
Ar*
HClf.‘
H+*
P*Hs
Si*H,
M
Type of orbital
4s 5s 6s 7s
4.11 1 Xi4 0.92 0.58
6.2 3.15 1.5 0.8 0.5
5.7 2.75 1.25 0.75
5.1 2.45 1.05 0.65 0.45
4.2 1.9 0.95 0.6 0.4
4.11 1.64 0.92 0.58 0.40
4s 5s
6
2.15
1.9
1.75
15 or 2.5
2.25
2.15
6
4P
2.35
3.0
2.8
5P
1.4
6~
1.2 0.7
4P 5P 6~
6
1.6
1.85
1.8
6
(6.2) 1.6 1.6
5.1
4.4 2.0 I 1.6
Type of orbi taI
o*
a*
-
36
1.1
4d
0.9
0.9
1.0
1.0
Sd
0.6
0.55
0.6
0.6
6
0.15
0.1
0.3
0.3
1.9
differences and reorganization effects between the ion and the excited neutral states, which are neglected in our calculational method, will have any significant influence on the term values of these Rydberg states with closed valence shell.. The magnitude of the u* and Rydberg s term values demand some special comment. In HCl the Rydberg term value of 3.15 eV is typical for a 4s orbital [15]. In SiH,, however, ~(0”) = 4.2 eV lies in the range of 4s term values, whereas the lowest Rydberg term value of 1.9 eV corresponds to 5s. According to our calculations the p- and d-type Rydberg MOs do not strongly mix with the antibonding valence hlOs. Therefore their term values are 1 as usual [Is] very similar for all these molecules, and their quantum defects take the values typical for p- and d-Rydbergs. However, the lowest IJ* valence orbital incorporates some s-Rydberg character as it rises in energy from HCl to SiH,. This mixing of valence and Ryd-
._
:;.
.;
1.7
3d
0.9
4d
0.6
5d
0.4
6d
0.15 6
bital lies even so high above the 4p that it is better called 5’s, the o*al and 4s-Rydberg “conjugate orbital pair” be@ represented by only one mixed orbital in this molecule. For more details on this problem see ref. [S] _ The picture given here is somewhat different from what is usually accepted for voknce to Rydberg excitations [ 15 ] , especi+y for molecules from. the first row of the periodic table. One main difference between core and valence excitations is the fgllowing: in the u + o” singlet states “the electron spins do not act to correlate the wavefunction” (Robin, ref. [15]), leading to a destabilization by the uu* exchange integral, +K, *. As a consequence the u -+ CT*sir&et states, contrary- to their triplet congeners, often lie -above the ionization limit, and the lowest aexcited singlet states are of predominant Rydberg character. However, in the core + o* singlet states the c’ optical electron is Fermi-correlated witll,the closed o-shell, and the energy expression contains the term -K,,, ,
: :
-0.2 0.3
7s 8s
p-type ones. In SiH, the lowest s-type Rydberg or-
berg orbitak results in rather unusual term values: in H$3 and PH, the s-type orbit& lie slightly above the
._
3.1 1.9 I 1 1.3 0.95 I { 0.7 0.6 I I 05
63
:
I
-6
-3
0
.3
6
-6. --;pJ~____--I
-3
-6
0
3
,_______-__-------T
:
r
P
3
.6
orbital of U* #ype. E = Mid eV.
,.
..
: :-.;,,
_.
:
,a:
I ,*’
_i’
‘1. _j
_‘S-
.-b) S&ond~o orbital of 4rRydberg type with some p admix-., ttik (c + 2.85 eV), c).Tiid orbital.of 4p-kydb+;type.(thc :-fo&thiow& virtual hbitij, r : 2132 eV., -.
‘..
‘i.\
;
c
fig;2:Contour diaggr&~~of virtml.orbit& in _&W. Fti ewes: pdsititie wavefunction; broken cmes: negative wave-
function,-a> Lowest vi&l
;
I\ ‘. :
:
-6-
6
0
‘3
6.
Fig. 3. Contour diagrams~of virtual orbitals in PH; . (e) &Itons in the plane, (0) protons above or below the plane. a) Lowest nrtual orbital of a*a 1 or 4s Rydberg type e = 3.80 eV- b) Second lowest orbital of cr.-t* character, E = 2.85.eV. c) -Third lowest virtual orbital (second tl ok) of 4p.Rydkrg type,e
=
3.18 ev.
._ .. . . .‘:.
..
‘.
..-.
: -_ :
IV.i-I.E. Scf~warz/Co~e
Table 4 2p-Ionization
potentials
and spin-orbit
AI
HCI
248.52 f 0.05 (248.60 +_0.05) [9]
201.4 + 0.2 (207.22) =)
IP (2P,,2)
250.56 f 0.05 (250.70 +_0.05) [9]
209.0 +_0.2
tiso
2.03 i 0.01 (2.11 * 0.02) [lo] (CaIC.)
2.05
specrmof hydride molecules
excirariorr
223
splittings in eV (ESCA values given in parentheses)
IP (2P,,,)
MS0
electrm
1.6* 0.1 (1.6+0.05)
170.4 r 0.2 (170x * 0.2) [ 121 171.6 * 0.2 (171.4kO.2) 1.2to.1 <1.20~0.02)
Ill]
I.55
SiHa
PHs
H2.5
106.8 + 0.1 (107.09~0.1)
137.0 = OfI5 (136.87) a) 137.9*0.15
1121 [12]
1.17
0.9 f 0.05 (0.8 + 0.05)
[13]
107.4 + 0.1 (107.7) 0.65 + 0.05
1111
(q.m-+0.05) [ 11 I 0.61
0.84
a) W. Jolly, unpublished.
ment of the spectrum by Hayes and Brown, relying on the calculation of Deutsch, differs considerably from ours. Also their extrapolated IP values differ from those in table 4, especially in the case of HZ!? their values of 17111 and 172.2 + 0.3 eV are larger than ours or the ESCA results [ 121 by about 3/4 eV. Our calculation and assignment is also in actordance* *with a recent highly resolved Sls absorptior! spectrum of H2S (La Villa, ref. [ 14]), from which one obtains ~(a~) = -6.0 eV, e(b2) = -5.0 eV, I =-3.0eV,~(Sp)=-1.4eV,andIP(Sls)=2478.3 eV. The vibrational width of the 1s + al transition is about 1 .l eV, slightly larger than that of the 2p + al transition.
as in the case of the u + u* triplets, which do not show the preference of Rydberg character. Therefore we should not wonder too much, that ‘.n special cases the s-Rydberg term values are considerably different for core and valence excitations, especially as due to their strong penetration the ns orbitals often show term values far off the “normal” values [ 151. Extrapolating the Rydberg series according to these assignments, we obtain 2p ionization limits which are compared with recent ESCA results in table 4. In addition, our 2p312-2p112 ionization energy differences, AEm, are compared with HartreeFock estimates of the 2p spin-orbit splittings. The agreement is satisfactory in both cases, and seems to support our assignment. At this point, the calculation of Deutsch and Kunz on Si*H4 [S] should be discussed. Unfortunately a direct comparison of their results with ours is not possible, since they have only calculated the total energies of several 2pcore excited states of SiH4, but not the corresponding ionization limit, which is the zero reference energy of our calculations. Nevertheless two discrepancies may be noted: (1) According to our calculation there exists a t2 MO of p-type with E = -2.18 eV between the two lowest t2 MOs of d-type with E = -2.85 and -1 .lV eV, respectively. The corresponding t2(p) state has not been found by Deutsch. (2) The energy differences between the two lo--est excited orbit& of at, t,(d) and e-species are 2.12, 1.66, and 0.9 eV, respectively (see table 2), which are in good agreement with the expertinelltal term differences: 2.3, 1.8, and 0.95 eV (see table 3). Deutsch, however, calculates much larger v&es: 3.0,2.4, and 1.8 eV. It is therefore not surprising Ltit the assign-
:.
5. Discussion
of intensities
and band widths
5.1. Intensity
ratios of the 2~~~~ to 2pI12 excitations
To first order of approximation one would expect this intensity ratio to have the statistical value of 4:2. This is roughly the case for all the excitations with one exceptation: the excitations into the lowest empty orbital of 4s u* character exhibit nearly the inverted intensity ratio, at least in H,S, PH,, and’SiH4 (see fig. 1 and table 5). The “experimerital” values of this table have been obtained by fitting four gaussians of equal width to the experimental spectra. Obviously the numbers have only a qualitative meaning. *However, our results are not consistent with a recent discusssion on X-ray Rydberg spectra by Robin [ 151, nor with an Xacalculation on SiH4 by Sink and Juras [16]. resulted in a wrong order of excited states.
..
.._.
_.:
which
Table 5 Lowest Zp-e&tations
in second
Molecule
row hydrides
“Experimental”
intensity
2p + 0%) HCI H2S PHa -SiH4
ratio
WQP,,,)
1(2p3,2
2p-t
2.o @a! 1-s (e) 2.5 (t2)
Such intensity anomalies, w-hich were also noticed in the spectra of several other molecules [ 171, can be explained, if we take not only the 2p spin-orbit coupIiJ-16but also the excited electron-hole interaction into account. In fig. 4 several intermediate coupling diagrams a:e sketched. The left one should approximately describe the excitation into the lowest emp.‘ty orbital, which is totally symmetric. Two-electron mtemction will raise the intensity of the 2p1,2 excitation, which correlates with a singlet-singlet transition, whereas the first 2p3/? excitation correlales with a spin-forbidden transnion and is weakened therefore. As the spin-orbit coupling is largest in HCI and smallest in SiH,, the intensity ratio is largest for HCI and smallest for SiHq (see table 5). In thtis context it should be noted that the intensities are much more sensitively dependent on the exchange interaction than the transition energies. A 2p u* exchange integral, which is calculated for SiE14 to be as small as 0.1 eV, already reduces the intensity ratio from 2 to 1, whereasthe spin-orbit splitting in the spectrum is nearly unchanged for exchange integAs up to 0.3 eV.
Fig. 4. Intermedi+e coupling diagrams. Corrdlation lines are drawn only for those states which can optically be reached from the totally sym.~Mric ground s~.te. The numbers in the rectangles gke the relative intekities for thdlimiting cases.
: .
. ._..,’
:
_. ;.
.:.:
...‘.-
Calculated half hei$t
1.8 0.8 0.6 0.6
2.0 1.3 1.1 0.9
width at (eV)
o’(d)
2 ‘5
0.8 (al) 0.8 (a) 0.5 (al)
“Experimental” mean width of a single transition (eV)
-:. .:
The u* orbital in HCI has considerable da-characterz (see fig. Za), the intensity contribution of which to the 2~3/2 and 2~112 excitation should be nearly independent from electron interaction, as may be seen from the central diagram of fig. 4. In the case of tetrahedral symmetry, the two-electron interaction even tends to enlarge the intensity ratio of the 2p+ c+t2 transitions to a value greater than two (see right hand diagram of fig. 4). From the measured spectrum one obtains m 26 for Sii& (table 5). For the higher Rydberg states the two-electron interaction is so small that the intensity ratio is near to 2.
The three lowest virtual orbitals of o-species in ArH+ are shown in fig. 2. In the outer region of the molecule, the orbitals look like an s-orbital with dadmixture (2a), a slightly deformed s-orbital (2b), and a p-orbital (2~). However near the heavy nucleus their character is of p, p, and s-type, respectively. Correspondingly the calculated orbital transition moments Qplrlnu} for the three u MOs are comparable in magnitude and roughly agree with the measured oscillator strengths, which are of the order of a.few lo-* per degree of degeneracy. Going from HCl to SiH4, the molecular potential becomes more symmetrical, so that the s-p mixing of the Rydberg orbit& decreases together with a concomitant decrease in’the intensity of the 2p -+ 4p transitions, which are no more detectable in SiH+, partly because ofoverlapping with allowed bands. $ This d&e; not meandiffuse 3d-Rydberg character but corresponds to polari&tion functions in the valence Shea.
W.H.E. Schnrz/Gre
5.3. Vibrational phenomena Because of the antibonding character of the a* potential curves of the lowest apexcited states come out to be strongly repulsive in the region of ground state internuclear distances. Therefore we expect strong vibrational broadening for the 2p + o* transitions. Strictly speaking, vertical excitation into the u* orbit& leads to energies more than 1 eV above the dissociation limit, as sketched in fig. 5. For the width at half height, W, caused by dissociation broadening through one normal mode, we used the following approximate relation derived from the semiclassical Franck-Condon principle: MOs, the calculated
W = (5/3)E’/fi. E’ is the derivative of the difference of the upper and lower potential curves dEJdR, and 1-1and o are the reduced mass and ground state vibrational quanta. Calculated and measured widths (table 5) show the same trend. Using the united atom model one might interpret the Iowest u* orbitafs in SiH4 as nearIy nonbonding Rydberg orbitals; this qualitatively explains the observed trend. For the higher 2p + Rydberg transitions of nonbonding to nonbonding typz we do not expect appreciable vibrational effects. Contrary to the u* excited states, the equilibrium geometry of the Rydberg states (or the ion or Zi1-analogous ion) is near to the ground state geometry, and the calculated E’ values are smaller than those of the 2p --f u* transitions by one order of magnitude. Therefore, only sharp O-O transitions are observed in the Rydberg region. However, as mentioned above, going from HC1 to SiH, results in a1 o*-Rydberg s mixing. The strongest vibrational side bands are therefore expected for the 2p --f ns excitations in SiH,. Indeed, in this case there occurs a small peak in the sharp Rydberg fine structure (indicated by v in fig. l), which we attribute to the excitation of the symmetric (and asymmetric) stretching vibration as already suggested by Brown [l] . Another assignment as vibrationally allowed 2p + 4p transition seems not acceptable, becau?d it would require an unusually low 4p term v&r; of 1.6 eV, contrary to the calculated value of 2.2 eV, which is of reasonable magnitude for 4p. To further support the interpretation as a vibrational side band, we men-
_‘,
225
electron exci:afion spectra of hydride molectdes
tion that the occupied valence shell of a molecule will shrink a little after core excitation because of the in. creased effective nuclear charge. Furthermore it is known that the bond stretching force constants of. several diatomic molecules increase on ionization of an inner ccre electron. Such effects should oe most pronounced in SiH4 with a comparatively soft u&nce shell. Indeed rhe vibrational side band is separated from its parent doublet by 0.31 eV, which is tighrly larger than the corresponding ground state vibrational quantum of 0.27 eV. Even weaker vibrational bands are expected in the Rydberg region of the other molecules. TJnfortunately these spectra are less resolved, and also overlapped in the case of PH3, so that the vibrational bands are not detectable. However, the high energy shoulder of the 2p -+ 4s transition of H,S should be noted, which is higher in energy than the main peak by just - 0.3 eV.
6. The Is excitation
spectra
of !Grst row hydrides
The ordy reliable Xw’absorption spectrum is the one of CH4 recorded by Chun [3a,18]. Recently Wjght and Brian [3b] hsve published and interpreted electron energy loss spectra of CH4, NH3, and H20. Contrary to the second row hydrides, the antibonding valence orbitals of the first row hydrides lie much higher than the lower Rydberg orbit&, at least for ground state equilibrium distances (see, e.g., ref. [19]). Therefore it seems reasonable here to assign the lowest core-excitations to Rydberg transitions, as has been done by Wight and by Bagus I3,18]. The lowest rr = 3 molecular Rydberg orbitals are, however, disturbed by considerab!e admixture of antibonding valence character. The intensity of the first excitation from Is to 3s increases from CH, tc Hz0 in much the same way as Table 6
Experimental term values [3] of first row hydrides (in eV)
Orbital
CHq
NH3
Hz0
NC
3s 3P 4s
3.6 2.6
5.7 3.8,2.6
4P
1.3
5.0 3.4 2.0 1.5
4.9 2.9 1.9 1.4
1.2
-226
IV.H.E. SchwarzjCore
that of the ip -?4p kansition drides. The strongest trkitions
electron
excitarion
in the second row hyare the 1s + 3p ones,
which are considerably split in the case of HZC. ACcording t0 the a&5ignmcrlt of Wight, the 3p-Spbtthg 'shyld be even larger in NH, (AE = 1.3 ev). Espacia!ly because of int+ty reasons this assignment seems not very probable: the second component is weaker by about two orders of magnitude. This could better be interpreted as 1s -+ 4s. Because of the antibonding component of the 3s and 3p-Rydberg orbitals the corresponding transitions show a considerable Gbrational broadening of nearly 1 eV for CH, and HZO_ (It is interesting to note that the CH, Is+ 3p absorption line of Chun [3a] shows a pronounced high energy tail, which is typical for such vibrational broadening.) In the case of NH3 the width amounts to only about half ail eV, which means that the antibonding character of the two lowest Rydberg orbitals is less pronounced here.
7. Hydride
radicals
So far, no definitive
information
is known
about
the .hydride mdicals such as PH4,In fig. 5 war have sketched a potential curve diagram for this molecule. The abscissa denote, the asymmetric stretching mode PHS-H: The uppermost curve is tlzat of P$; its well depth is the proton affmity of PH3, known to be 8.1 eV [ZO] . According to the “‘Z-i1 -core analogy model” the states of PH4 resemble the core excited states of Si*H, . The Rydberg states and positive ion of PH,
will have nearly the &me geometry as the ground state of SiH,. Therefore, e.g., the 5s Rydberg state of PH4- will be situated 19 eV vertically below the ionic curve. The two lowest states, o* 4dl and o*t2, howeve_, llave repuisive curves. For vertical excitation, the energy of the lcw&t state of Si*H4 - and PH4 is 4.2 eV b&low the i&kation knit, that is 1.3 eV above the dissociation liinit*. From this and the estimated
sldpe of thk pot&&l
..y _
.I
: .. .: .... : ::
..
a conclusion, that the minimum of the PH, groundstate curve will be near 0 eV. PHd might exist as a loos2 bound PH,-H complex or as a metastable complex, but it should show no significant thermodynamic stability against dissociation. PH4 has recently been
identified by its ESR spectrum, but only as a radical trapped in a krypton matrix [21,28]. From fig. 5 we can also deduce rough estimates of the expected vertical excitation and ionization energies of PH,. These are compiled in table 7, together with estimates for the other molecular radicals. As PH4, also H3S and NH, are possibly weakly stable or metastable with about Emin G + l/2 eV. H, 0 will at most metastable, whereas ClH2, FHZ, and ArH will surely form no stable species. Potential curves for ArH and NH, have been reported elsewhere [4, 221, the former ones agreeing satisfactorily witb cal-
culated curves of Vasudevzm [23] (see ref. [22] ). Existence and some properties of the first row radicals have recently been discussed by Wight and Brion [2d] (see also refs. [4,22] )_ The relevant literature has already been cited there. Our estimates as given in table 7 differ significantly from those of Wight and Brion. E.g.. for NH3 a vertical IP of 5 i eV is predicted here, instead of 3.7 (Wi&t and Brian 1241). The latter value, as well as the theoretically calculated values in the range of 3.74.0 eV [27] refer to the equilibrium geometry of CH4 or NH:, respectively, and are to be interpreted as the vertical electron affinity of NI$. but not as the vertical or adiabatic ionization potential of the neutral radical NHd, which differs in its equilibrium geometry considerably fTOm N$.
I
;I ; 1. CSiHL) 2
..
_f
3.(A) R
..
F&S.Potent&l
energy curves for PH4. The bar on the abscic sa indicates th~:equililhium geometry of SiH4.
: -.
:_-.-
y
.
molecules
cuFre one can draw
* &change COH~C&IIS,which UC of very importance iti some other mol~cbies [4] , arenegligibly small in the underlying c+,(that is:;snialler than 0.1 eV). Hbwever; variation of thf elect&c transition moment with internuclear dkn~= -, might be ~mpor_*+it ic this case and would result in a vei: gc;rl enerw value.which-is about onevibrational quantum higher than the peakcenter. :
:
spectra of hydride
:-
_-
..
._:
‘.
227
electron excitation spectra of hydride mokcuk
W.H.E.Scliwerz/Core Table 7 Estimates for hydride Iadicais A% hoton
affinity of AH,_, in eV 1211
Energy of ZAHn at ground state geometry of z+ t AH, Probable stability
PH4
SH3
ClHz
ArH
NH4
OH3
FH2
8.1
1.4
6.1
4.0
9.0
7.2
5.3
+1.3
+1.1
+1.7
+3.4
+1.0
+1.4
+2.6
unstable
unstable
weakly 01
metastable
weakly or metastable
weakly DT me tnstzble
Adiabatic/vertical IP in cV
516
6/6f
4;/51
fi;/7
First optical excitation energy in eV
1
B 4
1
1;
Lowest vertical
33 4
3; 4,45
4 3;
5$
Our ionization potential for NH, agrees with the experimental 5.9 + 0.5 eV of Melton and Joy [25]. However, Melton’s IP for H30 of 10.9 eV is seriously in error, which seems to indicate that his experiment should not be taken as the fust direct proof for the existence of H30. Our prediction on the stability of H30 fits with a recent H + Hz0 scattering experiment 1261, which did not support the existence of bound H30.
8. Summary Our calculations by an “Analogous Ionic Core Virtual Orbital Method” on the second row hydrides from a reliable basis for the reinterpretation of the 2pexcitation spectra of Hayes and Brown. In HIS and PH3 the Rydberg ns levels are situated near to and above the up levels. Taking electron interaction, spin-orbit coupling, and the slope of the potential curves into account, it is possible to explain the nonstatistical intensity ratios and the widths of the first broad bands - which are assigned to valence orbitals qualitatively with the help if simple model concepts. On these lines we have deduced stabilities, IPs and excitation energies of the hydride molecular radicals. These values can be used as guidelines in experiments for the identification of the radicals. PH4, NH4 and SH, may be (weakly) stable or metastable, whereas H,O seems at best to be metastable;
_
.
5
Acknowledgement At fust I have to thank Professors Peyerimhoff and Buenkcr, whose programs have been used in this investigation. My sincere thanks are due to Dr. Vasudevan for many critical comments which helped significantly improve the manuscript_ I am also gwtefu: to Dr. Sonntag for valuable discussions and to the. Referees for their comments, which inspired me to insert some simple arguments in the manuscript. Furthermore I acknowledge the services and computer time of the University Computing Center (IBM 37c)168). Finally I thank Mrs. Huber-Rutz for typing the manuscript_ References t11 W. Hayes and F.C. Brown, Phys. Rev. A6 (1972) 21. I.31 M. Nakamura et al., Phys. Rev. 178 (1969) 80; see also G.R. Wight and C.E. Brian, J. Electron Spectry. 1 (1973) 457; 4 (1974) 313. 131 a) H.U. Chun, Phys. Letters A30 (1969) 445. b) G.R. Wight and C.E. Brion, J. El. Spcctry. 4 (1974) 25. t41 W.H.E. Schwarz, Angew. Chem. intern. Ed. 13 (1974) 454.
Deutsch and A.B. Kunz, J. Chem. Phys. 59 (1973) 1155. M. N&amlra, hl Sannuma. ‘3. Sate. M. Watanabe, H. Yamashita, Y. Iguchi. A. Ejiri.S. Nakai, S. Yamaguchi, T. Sawwa, Y. Nakni and T. Oshio, Phys. Rev. Letters 21 (1968) 1303.
I51 P.W. 161
.:
:.:
..
unstable
metastable
_.
:.
.
2.28
@..YiE. Schw&/Core
electron
excitation
[j].B. Roos ad P. Siegbahti, Theoret. Chim. Acta 17 (1970) 209. [S] W.H.E. Schwarz. Chem. Phys. 9 (1975) 157. [9] T.D.?homas arrd R.W. Shaw, J. Electron Spectry. 5 (1974)~1081. [lOI U. Gel&, E. Bnsilier. S. Svensso~, T. BerSmark and :K. Siegbahn, J; FIectror. Spxtry. 2 (1974) 4C15. [ll] A. Barrie, I.W. Drummond md C&C. Herd, J. Electron Spectry. 5 (1974) 217. 1121 U. G&us, privite communication (1974). 1131 W.B. Perry and -W.i. Jolly, Chem. Phys. Letters 17 (1972) 611. 1141 R.E. LaVi&, J. Chem. Phys: 62 (1975) 2209. [lS] MB. Robin. Chqn. Phys. Let+s 31 (1475) 140; Higher. Excited States of Polyztbmic Molecules (Academic press, New Yqrk, 1974). [is] -M.L. Sink and G.E. Juras, Chem. Phys. Letters 20 (1973) 474. [I?‘] U. Nielsen, R. Haenscl and W.H.E. Schwa=, 1. Chem. Phys. 51 (1974) 3581. [IS] P.S. Bagus, M. Gauss and R.E: I&%Ua, Chem. Phys. Letters 23 (1973) 13. ,[19) F. Ackermann, H. Lefebvre-Brian and A.L. Roche, Can. J.,P$ys. 50 (1972) 692; KJ. Miller, S.R. hfiekzarek and M. Gauss, J- Chem. Pkys. 51 (1969) 26; R.S. Muen, CIXXI. Phys. Letters 14 (1972) 141.
,.:
.. ..
. .
:. .‘:,
..
:
.‘. :
:. .
:
: .,;._
-. :._ .-.:
..
spectra o/hydrkie
molecules
[ZO] M.A. H&ICY and J.L. Frank&n, J. Phys. Chem. 73 (1969) 4328; J.Chem. Phys. 50 (1969) 2028. J. Long and B. Munson, J. Amer. Chem. Sac. 95 (1973) [2r] [22] [23] [24] [25] 1261 1271
[2B]
??bcDowell, K.A.R. Mitchell and P. Raghur-than, J. Chem. Phys. 57 (1972) 1699. W.H.E. Schwarz, Bet. Sunsenges. 78 (1974) 1206. K. Vasudevan, to be published. G.R. Wight and C.E. Brian, Chem. Phys. Letters 26 (1974) 607. CE. Melton and H.W. Joy, J. Chem. Phys. 46 (1967) 4275. D. Bassi, M. de Paz, A. Pesce and F. Tommarini, Chem. Phys. Letters 26 (1974) 422. C-E. Melton and H.W. Joy. J. Chem. Phys. 48 (1968) 5286; D-M. Bishop, J. Chem. Phys. 48 (1968) 5285; W. Strehl, H. Hartmann. K. Hensen and I!‘. Sarholz, Theorer. Chim. Acts 18 (1970) 290; W.A. Lathan, WJ. Hehre, LA. Cutiss and J.A. Pople, J. Am.Chem. Sot. 93 (1971) 6377. Note added in proof: In the meantime.AAJ. Colussi, J.R. Morton and R.F. Preston, J. Chem. Phys. 62 (1975) 2004, have thoroughly repeated the ESR measurements. Contrary to McDowell et al. [21] they fmd that PH, (trapped in a neopentane matrix) has a nontetmhedral geometry. confirming semi-empirical calculations [21]. This result is in accordance with our ideas.