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Theoretical prediction of the vertical electronic spectrum of the C2H radical
Theoretical
SIIIXGKUO
Prediction of the Vertical Electronic Spectrum of the C,H Radical SHIH,
SIGRID
I).
PEYERIMHOFF,
AND ROBERT J. RUEMXER
LehrsfuhlfiirTheoretische Chemie ad Inslitut fiir Physikalische Born,, 83 Bow,
West Germm
Chemie, Urziversiliit
Federal Republic
The vertical transition energies and oscillator strengths from the z&+ ground and ii21T excited states of the ethynyl radical CsH to all higher-lying states resulting from excitation out of r and c into r* and U* valence-shell MO’s, respectively, as well as into 3s and 3p Rydberg species, are calculated by large-scale CI techniques. It is found that the first excited states all result from x + ?r* excitations (the lowest three with quartet character), and not from the 4s + 5~ counterparts favored in the case of isoelectronic CN. This distinction can be explained on the basis of orbital stability differences caused by the effects of hydrogen mixing. The first sis states of the CsH+ ion are also treated, and the correspondence with the various associated Rydberp series is discussed. Dipole moments for the _~‘%+ and _q211 states are also calculated. 1. INTRODUCTION
The ethynyl radical CZH is believed to be one of the most abundant interstellar polq’atomic molecules yet detected (I, 2). It has been investigated by electron spin resonance and optical spectroscopic techniques while trapped in argon matrices at liquid-helium temperatures (3-6). Nevertheless, it has not been identified unambiguousl~- in the gas phase in a terrestrial laboratory, although there is a good indication that it is produced in the vacuum uv photolysis of acetylene (7, S) or in any C-H-O plasma at relatively high (2500-4000 EL) temperatures (Y). The ESR measurements (3, 6) support the results of ab initio calculations (IO), namel!-, that the radical is linear in its (“S+) ground state. The,- also determined the important h!perfine structure of the 1 + 0 rotational transition (87.3 GHz), which turned out to be the main basis for the identification of CsH in a number of galactic sources (I). The optical spectrum of the ethynyl radical is believed to be very similar to that of CX (II). Two weak absorption systems have been observed after photolysis of acetylene trapped in solid argon (6); broad but distinct red bands are found around 10 000 A and are believed to correspond to the AzII +- _T”Z+ transitions, while the assignment for the violet system around 3000 A is less certain; the latter species ma! well involve a bent upper state so that these bands might not have any real counterpart in isoelectronic CN. A radiative lifetime of T = 6.2 psec has been measured (7) for the 3000 A s!ystem of C&H* (in emission). No further details are known about the optical spectrum, however. Since recent ab initio calculations have been quite successful in predicting optical transitions in small polyatomic molecules such as H20, H&O, C2H,, C4Hs, HO?, or 0, 167
Cwyright @ 1977by Academic Press, Inc. All rights of reproduction in any form reserved.
168
SHIH, PEYERIMHOFF
AND BUENKER
to within an accuracy of approximately 0.2 eV in energy and roughly lo-SO% in oscillator strength (at least forf > 0.001) (22,13), it is the goal of the present paper to use such methods in order to elucidate the optical spectrum of CzH, and thereby aid in identifying CZH molecules produced under gas-phase conditions in the laboratory. 2. CALCULATIONS
2.1. Basis Set and Geometry The A0 basis set used employs Gaussian lobe functions. A set of double-zeta quality consisting of four s and two px, py, and pz groups located at each carbon atom, together with two contracted s functions on the hydrogen atom, is chosen, analogously to previous work (10). This basis is augmented to better account for polarization effects by including bond s and pa functions between the carbon atoms with exponents of 1.40 and 0.50, respectively, in addition to a set of px, py, and pz species (UJ= 0.735824) on hydrogen. The lobe separations are constructed in the usual manner by the relation l= O.O3ai-1. In order to describe possible Rydberg characteristics of upper excited states, a set of long-range s and px, py, pz AO’s with exponents 0.017 is located at the center of the CC bond; thus a total of 32 contracted functions are employed in the present calculations. The equilibrium geometry which has been reported in SCF calculations by Bar&n (10) for the 2Z+ ground state (. . . l?r”Sa), namely, CC = 2.274 bohr (1.203 A) and CH = 2.008 bohr (1.063 A), is employed in the calculations for the vertical electronic spectrum. In agreement with the predictions of qualitative MO theory (14), the CC bond length of CZH is expected to be somewhat larger than in the corresponding state of isoelectronic CN (1.1718 A), primarily because the upper 5a MO in diatomic AB systems is more AB bonding than in HAB systems, in which it also has a marked A-H bonding character (15). The situation is especially obvious in the comparison between HCN (1.153 A) an d 1 ‘t s isoelectronic partner N2 (1.094 A), for which the SJ is doubly occupied in each case; there is no definite experimental value available for the internuclear distances of C2H, however. An assumed C-C bond of 1.204 A yields a J = 1 -+ 0 rotational transition frequency of 88.4 GHz, while a second attempt with 1.218 A gives a value of 86.3 GHz; the measured quantity is 87.3 GHz (I), i.e., somewhere in between. A neutron powder-diffraction study of the related ionic species NaC2H indicates a C-C equilibrium distance of 1.27 A for this system (and a C-H bond of 1.07 A) (16), an unusually large CC value which has been rationalized elsewhere (16). Results of CI calculations will be discussed in a later section. 2.2. Important Electronic States It is well known that in first-row diatomic molecules the 3a, and lrr, MO’s are quite close in energy, hence the two low-energy states in C2 (‘2 ,+, QU with partial occupation of these MO’s), for example, or the ?Z+ and 2~ states in CN, which are separated by only 1.13 eV. The situation is expected to be quite analogous in CZH, with a 2Zf (. . . l?r45a) ground state and a very low-lying Q(. . . 1~~5~~) excited state, as has indeed been indicated on the basis of SCF calculations (10). For the study of the excited states this situation leads to the complication that excitations out of both MO’s, the l?r,-like (1~) and 3o,-like (5~) species, have to be taken into account even when interest is
VERTICAL ~~~~~
1
Low-lying the
excited
lowest
ELECTRONIC
states
available
of C~H
SPECTRUM
resulting
unoccupied
from
transitions
(The lowest
species.
OF CtH out
of
169 1~ and
40 --c 50 excitation
50 into is also
included.)
2L+ 2"
4o21n45a 4021n41n*
"ala"ce long-range
4o21n43po
2cc
long-range
4021n43pn
21
long-range
401x4502
2x+
valence
2ll 4,2,-
4,2L+
'4,2
4a21n35c3s
4021n25023s 4a21n25c23po
prefer
because
“exclusive general out
the
long-range long-ranqe 2*
4,2,4.2z-
long-ranqe
n.
lor.q-range
latter
2&
long-range
’ =A 2 ) 4,2Tr 6.
term
"long-ranse"
terIn is usually
character".
of the orbital
presence
long-range
“alen.
Zz+
use of the the
of valence appeara"ce
'
2,+ z,,i
4021n25a23pn
"ale"Ce
Zfl
2+2I4,ZzL ,4,2 A,Z,i:, 2F,211 , l,, 4,2rl
4021"25D21n*
authors
'Zn
2-1 Zz- 2 i, ,A
4,2L+
4021n3503pn
"Wdberq"
valence
(2) 4,26
4.2;'
4o21n35a3pa
rule
i;;,
2E+
4021n35o2
The
Charactera'
"ale"==
4021n47s
4a21r3501n*
a)
Probable
z=tate
Configuration
rather
than
interpret&
In the present
context
charge
contours
of a significant
density
al"ou"t of valence
the pore
as carryi"? lonq-range
notation
the u"wa"teA
connotation
simalv
in ouestin" character
conoantionrl
but
refer? certainlv
to the does
not
ttlrrsl".
focused only on the lowest-energy states. Among the low-lying levels available for occupation in electronic transitions are the l?r* (la,-like MO) and the long-range (or first member of Rydberg series) 3s, 3pa, and 3~s MO?. Excitations from the highest occupied to these unoccupied levels lead to the large number of states enumerated in Table 1. In comparison to isoelectronic CN, in which similar states are espected, the situation is even more complicated in the present case, since CzH in a number of its excited states does not favor a linear geometry anymore, especially when the in-plane component of the la* MO becomes occupied. All in all, a rather complex spectrum for the CgH molecule must be expected. 2.3. Treatment of Electronic States From among the large number of states (49 total) given in Table 1 only seven can be treated by the standard Roothaan-SCF method; the corresponding results are contained in Table 2. The total SCF energy is somewhat lower than that obtained earlier (10) Table
2
SCF
enerqies
of
some
of the
low-lying
states
of C2H
(cc = 2.274
bohr,
Configuration
State
ln450
2x+
(Z)
-76.12988
ln3502
21
I%
-76.12113
0.24
ln42r
2 lI(5a+l**)
-75.76160
10.02
4r-
-75.05096
7.59
2( 2;*
-75.8044rl
0.R6
2x-
-75.84666
7.71
ln2502L" (6,.5
TC typf.‘)
Energy
(hartree)
bE
(ev) 0.0
Cl1 = 2.008
bob=).
SHIH, PEYERIMHOFF
170 Table
3
SCF
energies
of the
low-lying
AND BUENKER
positive
Ionizationa)
State
504.
lx+
4021"4
fl_'
3, 1,
4021"350
lb 3r-
4021"2502
i n-s "4
50
Configuration
ions
of C~H.
E,ErTy
(hartree)
-75.60784
With
respect
to the C2n
(ev)
14.20
-75.76330
9.9,
-75.70861
11.46
-75.68130 -75.72698
10.96 12.20 --
l1* a)
dE
ground
stitte 2r+ .
(“Yzf: - 76.1066 hartree) by virtue of the inclusion of polarization functions. The previous ?Z+--% splitting is increased from 0.13 to 0.24 eV in the present treatment. On the other hand, it is clear that a CI calculation is necessary to obtain a reliable value for this quantity. The results for the +‘-+ 5u, 3s states of Table 2 can be expected to be fairly close to those for the first member of the ‘/r+ 12s Rydberg series (not obtainable in the SCF treatment), since the 7r--+ 5a excitation energy is so low. The analogous information can also be inferred from Table 3, which presents the SCF results for the various ionic species. On the other hand, if the differences in correlation energies for these ionic states are not drastically different, the indication from Table 3 is that Rydberg states originating from the 5a MO lie considerably higher in energy than most of those involving transitions out of the l?r species. No estimate can be extracted from the SCF results for the important ?r-+ ?r* states nor for the 4a-+ 5~ excitation. All in all it is seen that little information regarding the electronic spectrum of C2H can be obtained from the SCF treatment alone, and that a multiconfigurational treatment is essential for this purpose. The general CI procedure employed in this work is the same as has been used for the treatment of a good number of other molecules (12,13) ; details are described elsewhere (17). The configuration space treated consists of all single- and double-excitation species with respect to all the configurations contributing more than approximately 17o in the final CI expansion. In this way it is expected that none of the key higher-excitation configurations is neglected, while a large number of unimportant high-excitation species do not actually have to be processed. According to previous experience such a treatment is quite close to a full CI within the A0 basis given. The MO basis employed in a given case consists of either appropriate SCF MO’s obtained from the states given in Table 2, or is obtained from a natural orbital transformation (through diagonalization of a large-threshold, moderately large configuration space CI density matrix). This information will be given together with the results to be discussed in the next section. The actual CI calculations are carried through in CzUsymmetry, SOthat Zf and A states (as well as Z- and A or II and 4 species) often result from the same secular equation. The size of the total configuration space thus generated falls in the range of 5000 to 100,000; the secular equations actually solved generally possess orders between 2000 and 6000 (at a selection threshold of 20 rhartree). 3. RESULTS
Ok’ THE
CI CALCULATIOSS
The dominant terms in the CI expansions calculated for the various states are collected in Tables 4a-c; the ordering of states is the same as that used in Table 1. In practically
VERTICr\L ELECTRONIC
SPECTRUM
171
OF C?H
all cases the MO basis is chosen such that the leading terms amount to at least 9052 on a lc;!* basis (i.e., co > 0.95).’ If some configurations contributing more than 17;) are not contained in the set of reference configurations, i.e., are not used explicitly to generate the final configuration space, this fact is also indicated in Table 4. In such cases the calculated CI energy is expected to be somewhat too high compared to the other results (by roughly 0.14.3 eV, judging from previous experience). The calculated energies for the various states treated are given in Table 5,* along with the calculated oscillator strengths for transitions to the ground state _y*Z+ and to the low-lying AI’11 species3 The oscillator strengths are calculated via both the dipole length and velocity operator in each instance; since agreement is uniformly quite close, as has been found in many prior calculations on this level for other molecules (13), onI!. a single value is reported in Table 5.
3.1. T’alerzce-Shell States As has been assumed throughout, the lowest valence excitation is to the ?II state, which is placed by the CI calculations (at the nuclear geometry emplo>-ed) 0.96 eV above the ground-state energy (much higher than in the SCF treatment (Table 2)), thereby underscoring the significant difference between ground- and excited-state correlation energies in this instance. The nest lowest valence-shell states all arise from r -+ s* excitations (Wln5al~* configurations) with the quartet components a1waj.s l!.ing well below the corresponding doublet analogs. Although this situation is different from that in isoelectronic CN, it is exactly what one would expect from the &Hz+ ion, which is also isoelectronic with C2H. In &Ha, the lowest excited states are QU+, $A%, and ?ZU-, in this order (18, 19), followed by the corresponding singlet states of identical electron configuration in reverse (??&--, lAu, ‘Z,+) ordering. Removal of an electron would split each of the three triplets into two states each, of quartet and doublet multiplicity, respectively, presumably with all quartets lying below the respective doublets, just as is observed in Table 5. Similarly, the doublet states corresponding to the singlet ?r -+ ** C?H2 states are considerably higher, with %+ lying much above the others, in close analogy to the situation for the QU+ valence-shell species in &Hz.* The fact that in CZH the ?r-+ x* transitions occur at lower energy than the m-+ (T* (4~ + 5u) species, contrary to the case for CN, can be explained quite simply in terms of orbital stabilities: the lu MO is stabilized in C2H just as is 2u, in CsH2 as a result 1 States of like symmetry are treated in the same secular equation only if they show mixing with one another, i.e., if they have the same constituents. Thus all (a, r*) states of a given (Abelian) symmetrl-, for example, are obtained from the same secular equation, while all (T, 3pr) species are likewise obtained from a common CI, which is distinct from its (r, T*) counterpart (see Table 4a.). 2 In most cases, A states are calculated in both .I, and &-ISsymmetry of the CsL.point group, together with the corresponding S+ and x;- species of like symmetry. The discrepancies in corresponding total energies, resulting from the use of a tlil‘ferent selection method, or sometimes also a different MO I)asis, xrtl generally smaller than 0.05 eV.
J‘I’hr f wlues are calculated separately for the individual components of degenerate ~I~untlirlg to the lower CX, symmetry; the combined value is then given in the table.
species
corw
4 The ordering of the higher-lying ‘A, Ye, and W states in CZH compared to the respective ‘XU-, ‘A,, ‘\‘,+ multiplcts probably results from the effects of interacting with lower states of like symmetry iu GH.
172 the CI expansions lying cate
O' and the
percentage
natural
MO
state
d states
orbital
of C2H:
on a
Icf12 basis.
NO haaia
Basis
of the
the numbers
given
(in SOW
il
Expansion
(50,3s) No
Of
CWPS
!a employed.)
21a)
(402n450)+2.2(n,n*)+2.4(n2,n'
(n,n')
lowindi-
(5o,3s)+17.l(n25u235)
72.8
NO
2r+
91.3
(n,n*)+8.6(4o,50)
93.6
(n,n*)
91.6
(n,n*)
34.1
(4o,So)+35.6(3o,5o)+lO.6(n,n*)
+r7.2c30,n,50n*l 1 b)
88.8 X SCF MO i-J
i 88.7 ! 87.8 87.7
4t-
SCF E10\93.2 184.5
(n,n*) Of
NO
(r,"*)+
91.6
4z+
2.0(n3,n*3)+1.4(n2 i:
,n*
(n,n*)
i 93.8 92.2
(T.3PV)
92.1
ln.lpn)
2
)1b)
(,;,+15.0(n~,o~j+2.13(T~,n*~) _ 1~ SCF
Givenin
for
are
the
40~1*~50
guration b) The
Table
terms
set
Most
cate
MO
in brackets
P- states the
is not
NO
of
2x-
X SC0 MO 4L
2I+
in the
of C2H:
to that
Basis
(r,n*)
terms
1%. The
the
to the
actual
contained
ground
confi-
in the
CI expansions
numbers given 2 on (L /cii basis. The
percentage
2z-
2t2z-
cases
than
respect
however.
important
analogous
2z-
in some
more with
set
species.
lying
state
is always
configuration;
is indicated
4b
contributing
excitation
configuration
of reference
[6.36(ln4)+3.05(n3n*)Ih'
1 83.81(n2502)+1.2(n2,n*2i+
general
notation state
no
the
in Table
4a.
Expansion
94.6
(w,n*)
I 91.6
1n.n')
88.9
(n.3pn)
I 87.8
(n,3pn)
SCF HO
93.5
(,25023S)
Of
'L+
93.3
(",ll*)
of 4?.+
91.9
(n,3pn)
93.2
(0250235)
93.4
(n25o2)
4r-
(n,n*lNO
4L-
(n,3pn)NO
4L-
4x-
31-
'Z- SCF MO
SCF "0
of the
low-
always
indi-
notation
is
VERTICAL 4c
Table
ELECTRONIC
important
Most
lying
n and
to the
percentage
analogous
2!! 2, 2, 2l 211 2II ZE 2,
In,“*)
terms
P states
to that
in the
CI expansion
in C2H;
on a
/CiI
in Table
of
the numbers
2 basis.
173
OF GH the
given
The
lowestrefer
notation
is
4a.
84.97(n4n*)+~6.55(n*oZn*)t1.65(~3”*)]
NO
1”4,3pn)
SPECTRUM
,,.g(n43pn)+12.1(n25~23p~)+2.1("23pnn*2)
NO
(n350*),C,
r,n
g2.5(n35~*)r1.3(n502n'2) 56.1(n35~6~)+32.6(n35~70) I 55.5(n35070)+32.3(n35a65)
x" SCF MD
47.3(n35a6~)t40.7(n35070) I 47.8(n35070)+39.6(n35a60) 2n( n 3502)
?m
SCF
90.76(n2502n*) \9Z.0(n25d*n')
MO
?P
1
86.6(n2502n*)'[3.8(n4n')
/
2,
7; 25
notcalculated
ix
211
4,
35a60)+39.4(n35070)
41
39.3(n35060)+49.2(n35a70)
4q 4,
4z-
311
31r SCF
II.0
92.2("35a)+2.2("5%+2)+1.1("*5~~*)
'II
ill SCF
vo
91.1(" 350)+2.1(n5an*2)+1.5(n25an')
a)
The
SW
orbitals
92.7(n25023p")
MO
60 and . The
3s ana
3pa
Tables
4a and
70 are
notation
in most
basis
is otherwise
sets
the
n mixture
same
as
of
in
4b.
of hydrogen mixing (20). This is demonstrated in Table 6, which contains SCF orbital energies obtained from roughly equivalent basis sets. Thus, on the basis of qualitative MO theory, excitations from the lower-energy 4a orbital are expected to be much less favored energetically in CZH than in CN; this is especially true for excitation into the 5~ orbital, which is of higher energy in CZH than in CN (Table 6). In a similar manner, since the r orbital is a purely carbon species in CzH, it is less stable in this environment than in CN, for which it has considerable N atom character; as a result it is not at all surprising that the various 7r+ ?r* states are favored energetically in CSH compared to their counterparts in isoelectronic CN. This trend is carried over to the states of 4u21n25~*1?r*configuration (Table 5), which can be Iooked upon as resulting from n--f rr* excitations out of the 2% state. Again, the energy ordering of these species is easily understood, since these species can be written as products of appropriate K* multiplets (with the usual 3Z-, ‘A, 2+ ordering) with the rr* MO. The lowest two states (“II and ‘II) result from %- X *II, whereas the next two (q and *II) derive from the ‘A X “II coupling. A somewhat unusual feature of the ground-state transitions of C2H is that, apparently, only the lowest intra-valence species (jr211 +- dy22+) shows any appreciable intensity. The f value for the relatively high-lying 4a--t 5u excitation has not been calculated,
174
SHIH, PEYERIMHOFF Table
5
Calculated
vertical
of C2II. The
AND BUENKER
excitation
oscillator
energieg'to
strength
the
lowest
for transitions
states
from
the
upper states to the 2L+ ground state and to the low-lying 2 (Ground state energy is n (1~~50') state are also given. -76.3235
Configuration
hartree.)
Transition
state
-
4021n450
2+z (Xl
AE
(eW
-
-
0.0
not
ca1c.
4021n41"*
5a+ n*
21!
(10.7)
4.21n43*
50-r 3s
2z+
10.95
4a21n43po
5a*
3po
2zf
401r43pn
so+
3pn
2,
11.46
0.011
4021n45a2
40*
50
2I+
(9.6)
not
not
>Il.O
ca1c.
n -r5a
0.96
v *z.*
4.94
0.0035 -
6.22
-
7.32
ca1c.
not
c&c. -
-
6.91
not
0.0006
ca1c.
4021n35a2
not ca1c. 0.005
0.025
4oZln3501n*
2Lf
f *2n
f+2C+
-
0.00002 -
0.024 0.009
*z-
8.13
2A
8.27
2A
8.81
-
0.20
2P-
9.50
-
0.12 _-
i 2z+
not
0.0004
-
talc.
--
.-
-
4ll
8.20
2n
8.48
0.055
0.0002
9.78
0.010
0.008 -
‘n 4n 2n 1 2n 4x+ 46 (
4z-
-
8.92 9.22 10.4" 8.85
0.010
0.13
not ca1c. -
0.06 -
8.91
.-
-
8.95
-
-
I
26
9.12
-
\
2z-
9.13
-
2x+
9.18
0.0002
0.022
10.32
0.0003
0.004
!
2r* 2 2;-
10.46 10.49
=
however, so this result may have to be qualified somewhat. transitions involving the A”% state have been indicated.
0.04 not
talc.
0.008 not ca1c.
By contrast
several strong
3.2. Rydberg Transitions The first members of the various Rydberg transitions are generally seen to lie in the same area (or somewhat higher) than the valence-shell states already discussed. In order to better demonstrate the underlying ordering principle for these species, it is advantageous to compare their respective term values, i.e., their relative location below the corresponding ionization potential; Table 7 contains the necessary information. The heading of the table always contains the various multiplets of the CzH+ ion in a together with the calculated CI ionization potential. given electronic configuration, The term values for the various states originating from a given escitation into the first ?ts or np members are then contained in the main part of the table, and the values are arranged so as to emphasize the ionic limit for higher members of each such Rydberg series,
VERTICAL Table
5,
ELECTRONIC
175
OF CrH
cont.
configuration
Transition
4CY21n25~*1n’
State
AE (eV1 7.35
In t 3~0) (“n,
a)
SPECTRUM
f*
2 + L
f +2n
-
not calculated
These results are obtained at R - 2.274 bohr, which is the SCF ground state bond length. If the actual CI bond length (2.348 bohrl is used, mst AE values are shifted downward by roughly 0.2 eV (see Fig. 1). Values given in parentheses result from relatively poor treatments (in which all dominant configurations are included in the associated reference set).
From a comparison with Table 3 it is seen that the splitting between 311 and ‘11 (~35~) states of C,H+ is practically the same in the SCF and CI approsimations. Apart from this agreement, however, only the qualitative feature, namely, that the positive ion is most stable in such ?r states and least stable in the (n*) species lS+, is carried over from SCF to CI treatment intact. The term values for the 3s states are all calculated to lie within 2.55 and 2.85 eV (20 500 cm-l-23 000 cm-l) for the first two ions; this finding is quite consistent with the general rule (ZI), which puts such Rydberg term values in the 20 000-28 000 cm-l range (most probably 27 000 cm-1).5 Similarly, the term values for all the 3p states are very consistently- obtained to fall between 1.80 and 2.30 eV (15 000 to 19000 cm-‘) for the same ions, again quite normal behavior for Rydberg states of this type. The situation for the various multiplets of CzH+ in the Au2 electronic configuration is somewhat different, with all term values calculated distinctly higher than for the other ions. There does not seem to be an obvious explanation for this feature, however. The calculated oscillator strengths to the ground state are in general largest for the s series, as is to be expected; the magnitude is consistent withf values found for similar states in related molecules. 4. REL.41’10~
TO EXPERIMENT
The longest-wavelength observed band system around 10 000 A in the CrH spectrum From the earlier SCF calculation definitely corresponds to the .I‘%+- A211 transition. (Ill) it is known that ?II has a larger bond length than ‘%+ so that the intensity in suc:f1 GNote that for such calculations underestimated by approximately
it is quite common for term values of II = 3 R?dherg 2500 cm-‘, compared to experiment,
members
to 1,~’
SHIH, PEYERIMHOFF
176 Table
6
Comparison
CNL
MO
2+a E
I
0(4o-2Q
-0.6260
n(ln-1nJ
-0.5161
0(50-3og)
of energies
CNI
2
n)
of higher-lying
in CN,
C2H
and
-
ar.d J. Scheiding,
C2H2.
1 C2112(
C,H(2U) -0.7370
-0.7760
-0.4241
-
-0.4131
-
-0.4507
-0.6835
-0.5209
=-‘IP. Stechert
orbit&s
a
-0.6766
-
AND BUENKER
Diplomarbeit
1974.
Values
zg'b1
-0.7658
are
in hartree.
b) Ref. [201
a transition is expected to be distributed over several CC stretching vibrations. The calculated CC stretch potential curves presented in Fig. 1 show different locations for the 211 and 2E+ minima in both the SCF and CI treatments; the CI values are 2.348 (W) and 2.487 bohr (211), significantly larger than the corresponding SCF quantities of 2.266 bohr (1.20 A) and 2.417 bohr (1.279 A), all values obtained by polynomial fits to the data points calculated. Similarly, the calculated stretching force constant is smaller for the excited state, 11.4 mdyne/A or 1764 cm-’ for 211,while the corresponding ground-state value is 14.5 mdyne/A or 1989 cm-l. The latter result is relatively close to the CC force constant obtained by Atoji (16) for Na+C=CH (13.1 mdyne/A) or to the frequency of 1848 cm-l determined for CZH in argon matrix studies (4, 5); obviously the potential curve is less steep than the corresponding &Hz species (‘ZQ+), which possesses a CC stretching force constant of 15.7 mdyne/A. Although the calculated frequency for the excited C2H state is only in fair agreement with the measured value of ~3’ = 1560 cm-r obtained by trapping C2H in a solid argon matrix (6), the calculated frequency decrease from the ground to the excited state (225 cm-l) is still relatively close to the corresponding experimental value of 288 cm-‘. Again, the SCF quantities are much larger, as is clearly apparent from inspection of Fig. I; these values are 19.3 mdyne/A (2294 cm-l) for the ground and 13.7 mdyne/A (1933 cm-r) for the excited species, reflecting approximately the observed frequency difference. Since the shapes of the two potential curves in Fig. 1 are quite different, their energetic separation varies considerably with CC bond length. Thus the CI vertical transition Table
7
50-r = -------
Term
values
(1")4
(in eV)
1x+,
Ion:
2
50 + 3pn
1
,50) Ion -----
r *
3pa
II *
3s
13.8 ev --
3n#
+ 3pn
41-
,
11.04
2.09
2
_ -
n *
3pn
1*
3s
2 (1_1502) -
obtained
from
CI calculations
__--___---
ev 2x-
In, --
,
1.91
12.43
eV
21.-, 1.94
,
2t+ , 1.86
2I+
46.
2.13
*A,
1.92
2c,
1.97
4n,
2.12
*n,
1.82
'II,
2.03
4n,
2.84
*r,
2.56
2n,
2.65
2.11
______
10"-
3z-'
4n*
2.45
4z-
series
4r+ , 2.19
-z
Rydberg
n, 2.34
lb3
+oI
--n
for various
12.57 --eV zn, 2.25
, 3.50 2z-.
3.36
?%,_l3.7 24‘2.40 2 A,3.38
e" T
:$+ --'-2--n, 2.30
14.0
ev
/ n, 2.21 1zz+, 3.2
VERTICAL
ELECTRONIC
SPECTRUM
E(Har!reel
01; CiH
177
/
-76.12-
.76.28-
-76.30-
-76.32-
I
2.20
I
2.60
2.LO C-C
distance
I
2.80
(bohrl
FIGURE 1
energy (Table 5) calculated at the SW CC equilibrium distance of 2.274 bohr is approsimately 0.25 eV greater than the value obtained by employing the CC bond length determined by the CI treatment itself. Unfortunately, such a discrepancy must be expected for most states given in Table 5 (and hence a correction of AE in this order), since all r---f X* species, for example, are also expected to exhibit a longer equilibrium CC distance than %%?+, and as such their potential curves are also found in the repulsive branch at the R value employed in the vertical spectrum calculations. At the same time, the 04 transition between ,p725+ and A”*II is calculated to be 0.5 eV, with this value being markedly smaller than that estracted from experiments in a solid argon matrix (10 080 A or 1.23 eV). On the other hand, from a qualitative point of view it seems unlikely that this transition just begins at 1.2 eV, since its diatomic analog CN shows a O-O transition for this a + u* species at only 1.13 eV (1 I), and there is good reason to believe that substitution of a CH group for an N atom has a smaller destabilizing effect on the 5s MO (which can be somewhat compensated by the beneficial effects of CH bonding) than for the lower-lying ?r orbital. The orbital energ!results of Table 6 indicate, for example, that the R MO energy increases by nearly 0.10 hartree from CN to CsH, while the corresponding 5a value only goes up by 0.07 hartree. The difference of roughly 0.8 eV cannot be at.tributed quantitative significance, perhaps, but it seems much too large for this effect to be totally absent in the true experimental situation. At the same time, if the CI calculations are correct, the actual 04 transition
178
SHIH, PEYERIMHOFF
AND BUENKER
must be expected at quite large wavelength for an electronic species, perhaps as low as 2.5 000 A (0.5 eV), and hence should be extremely difficult to detect by presently available experimental techniques. In any event, the present CI results indicate that the masimum for this transition should be found in only the 0.7-0.8 eV range of the gas-phase CZH spectrum (18 000-15 000 A), and this result is in significant disagreement with what has been reported in the existing argon matrix studies of this system. The dipole moment (at CC = 2.274 bohr) for the ground state is calculated to be 0.770 D when z’%+ SCF MO’s are employed, and 0.826 D with a 4X:- MO basis. This result supports the value of 0.8 f 0.2 D estimated by Green (22). A large charge transfer occurs upon 2Z++ 211(rr-+ n*) excitation, since the a MO has its charge distributed in an essentially symmetric way between the two carbon atoms in CZH, while the u* MO (doubly occupied after the transition) is primarily localized at the end carbon; hence the calculated *II dipole moment (again at CC = 2.274 bohr) is much larger (3.29 D). The nature of the second observed weak band system (6-8) around 3000 A is still open to question. A number of absorption lines extending from 3.64 to 4.79 eV, with a maximum around 4.5 eV, have been found for C2H in solid argon (6). In addition, an essentially continuous emission from a C2H* in the region from 2.2 to 3 eV (4000-5500 A) (7, 8), with a possible maximum around 2.5 eV, is observed following photolysis of &Hz, whereby a (0, 0) transition is estimated on the basis of kinetic data to lie around 4.11 eV (8). The only low-lying state in this region shown by the calculations is 4Z+ (Table 5) with a vertical energy difference to the ground-state equilibrium geometry of 4.94 eV.6 If this energy can be identified with the absorption maximum around 4.5 eV measured by Graham et al. (6), the various lines at lower energies also obtained in the same experiments should correspond to a progression in each of the CC stretch and *CCH bending vibrations of the excited state, since 4Z+ is expected to have a larger CC bond than rT2Zf, and also to possess a bent nuclear geometry, in contrast to both Ly2Z+ and A”%. The measured lifetime of 6 bsec (f = 0.0003~.0005) (7) could be “2Z + transition. Furthermore, the consistent with the formally spin-forbidden 4Zf-1X emission at lower energies (following photolysis of &HZ) could be simply explained as resulting from transitions between low-energy vibrational levels of the bent upper 4Zf and higher vibrational levels of the linear ground state, thus appearing at longer wavelengths than the absorption lines for C2H in a solid argon matrix at 4 R. The reliability of the derived (0,O) band at 4.11 eV seems to be questionable in light of this discussion, however. The first allowed (but also weak, see Table 5) transition, *Z+ +-fiW at 7.32 eV, seems too high to qualify as being involved in the observed 3000 A emission even if A”‘Jn were the lower state and not X22+ (the transition probability to the former is apparently much higher, however, see Table 5). On the other hand, if emission were to occur from the first few vibrational levels of the upper bent *Z+ state to very high vibrational species of the linear ground or linear A”% state, energies in the 3 eV range might still be possible. In any event, a detailed investigation of the geometry of the ‘x+ and 2~+ r--+ r* upper states as well as the two low-energy -%Y and A’II species 6 Note that the actual CI vertical result may be lower by approximately CI value for the CC bond is employed (see Fig. 1).
0.25 eV once the equilibrium
VERTICAL
ELECTRONIC
SPECTRUM
OF C,H
170
is
clcarlq. necessary, combined with an appropriate vibrational analysis, in order to obtain a more definite assignment for the nature of the second weak absorption band system in CZH. Work in this direction is in progress. At the same time, a more detailed study of the CzH spectrum via experimental techniques would be very desirable. ACKNOWLEDGMENTS The authors wish to thank Professor K. H. Becker and Dr. D. Haaks for numerous helpful discussions; They also wish to express their gratitude to the Deutsche Forschungsgemeinschaft for financial support given to this work. The services and computer time made available by the University of Bonn Computer Center are gratefully acknowledged. RECEIVED: June 29,
1976 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. Y. IO. Il. 1.
13.
1-f. 15. 16. 17. 18. 19. 20. Zf.
22.
K. D. TUCKER, M. L. KUTNER,AND P. THADDEUS,Astrophys. J. 193, L11.5 (1974). S. M~KRIS ANUA. A. WYLER, Astrophys. J. 150, 877 (1967). E. T. COCHRAN,F. T. ADRIAN, ANDV. A. BOWERS,J. Chem. Phys. 40, 213 (1964). D. E. MILLIGAN, M. E. JACOS, AND L. ABOUAF-MARGUIN,J. Chem. Phys. 46, 4562 (1967). D. E. MILLIGANAND M. E. JACOX, J. Chem. Phys. 51, 1952 (1969). W. R. M. GRAHAM,K. T. DISMKJKE, AND W. WELTNER,JR., J. Chem. Phys. 60, 3817 (1974). K. H. BECKER,D. HAAKS, AND M. SCH~~RGERS, 2. Naturforsch. A 26, 1770 (1971). H. OKABE,J. Chem. Phys. 62, 2782 (1975). D. HEBECKERANDU. HEILE~NN, private communication via Professor V. Vukanovic, Yugoslavia. J. BAKSUHN,Astrophys. Lett. 12, 169 (1972). G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 1950. S. D. PEYER~MHOFF AND R. J. BUEXKER, in “Chemical Spectroscopy and Photochemistry in the Vacuum Ultraviolet” (C. Sandorfy, P. J. Ausloos, and M. B. Robin, Eds.), Reidel, Dordrecht, 1974; S. D. PEYERIMHOFF ANDR. J. BUENE(ER,in “Advances in Quantum Chemistry” (Per-Olov Lowdin, Ed.), Vol. 9, Academic Press, New York, 1975. R. J. BUENKERAND S. D. PEYERIMHOFF,Chem. Phys. Lett. 29, 253 (1974); U. FISCHBACH,R. J. BUENKER,ANDS. D. PEYERIMHOFF,Chem. Phys. 5, 265 (1974); R. J. BUENKERANDS. D. PEYEKIMHOFF,Chem. Phys. 9, 7.5 (1976); Chem. Phys. 8, 56 (1975); Chem. Phys. Lett. 37, 208 (1976); Chem. Phys. 8, 324 (1975); Chem. Phys. Lett. 34, 225 (1975). R. J. BUEN~EKAND S. D. PEYERIMHOFF,Chem. Rev. 74, 127 (1974). See, for example, Fig. 1 of P. J. BRUNA, S. D. PEUEKIMHOFF, END R. J. BUEXER, Chem. Phys. 10, 323 (1975). M. ATOJI,J. C’hem. Phys. 56, 4947 (1972). R. J. BUENF;ERAND S. D. PEYERIMHOFF,Theor. Chim. Ada 35, 33 (1974); 39, 217 (1975). R. J. BUENKEKAND S. D. PEMRIMHOFF,J. Chem. Phys. 48, 354 (1968), especially Appendix 11. W. E. KAMMER,Chem. Phys. Lett. 6, 529 (1970); Ph.D. Thesis, Giessen, 1971. R. J. BUENKER,S. D. PEYERIMHOFF, ANDJ. L. WHITTEN,J. Chem. Phys. 46, 2029 (1967), especially Figs. 3 and 5 therein. C. SAXDORFY,Lecture given at the VII International Conference of Photochemistry, Jerusalem, Israel, August 1973; M. B. ROBIN, “Higher Excited States of Polyatomic Molecules,” Academic Press, New York, 1974. S. GKEEN,given as private communication in Ref. (1).
SIIIXGKUO
Prediction of the Vertical Electronic Spectrum of the C,H Radical SHIH,
SIGRID
I).
PEYERIMHOFF,
AND ROBERT J. RUEMXER
LehrsfuhlfiirTheoretische Chemie ad Inslitut fiir Physikalische Born,, 83 Bow,
West Germm
Chemie, Urziversiliit
Federal Republic
The vertical transition energies and oscillator strengths from the z&+ ground and ii21T excited states of the ethynyl radical CsH to all higher-lying states resulting from excitation out of r and c into r* and U* valence-shell MO’s, respectively, as well as into 3s and 3p Rydberg species, are calculated by large-scale CI techniques. It is found that the first excited states all result from x + ?r* excitations (the lowest three with quartet character), and not from the 4s + 5~ counterparts favored in the case of isoelectronic CN. This distinction can be explained on the basis of orbital stability differences caused by the effects of hydrogen mixing. The first sis states of the CsH+ ion are also treated, and the correspondence with the various associated Rydberp series is discussed. Dipole moments for the _~‘%+ and _q211 states are also calculated. 1. INTRODUCTION
The ethynyl radical CZH is believed to be one of the most abundant interstellar polq’atomic molecules yet detected (I, 2). It has been investigated by electron spin resonance and optical spectroscopic techniques while trapped in argon matrices at liquid-helium temperatures (3-6). Nevertheless, it has not been identified unambiguousl~- in the gas phase in a terrestrial laboratory, although there is a good indication that it is produced in the vacuum uv photolysis of acetylene (7, S) or in any C-H-O plasma at relatively high (2500-4000 EL) temperatures (Y). The ESR measurements (3, 6) support the results of ab initio calculations (IO), namel!-, that the radical is linear in its (“S+) ground state. The,- also determined the important h!perfine structure of the 1 + 0 rotational transition (87.3 GHz), which turned out to be the main basis for the identification of CsH in a number of galactic sources (I). The optical spectrum of the ethynyl radical is believed to be very similar to that of CX (II). Two weak absorption systems have been observed after photolysis of acetylene trapped in solid argon (6); broad but distinct red bands are found around 10 000 A and are believed to correspond to the AzII +- _T”Z+ transitions, while the assignment for the violet system around 3000 A is less certain; the latter species ma! well involve a bent upper state so that these bands might not have any real counterpart in isoelectronic CN. A radiative lifetime of T = 6.2 psec has been measured (7) for the 3000 A s!ystem of C&H* (in emission). No further details are known about the optical spectrum, however. Since recent ab initio calculations have been quite successful in predicting optical transitions in small polyatomic molecules such as H20, H&O, C2H,, C4Hs, HO?, or 0, 167
Cwyright @ 1977by Academic Press, Inc. All rights of reproduction in any form reserved.
168
SHIH, PEYERIMHOFF
AND BUENKER
to within an accuracy of approximately 0.2 eV in energy and roughly lo-SO% in oscillator strength (at least forf > 0.001) (22,13), it is the goal of the present paper to use such methods in order to elucidate the optical spectrum of CzH, and thereby aid in identifying CZH molecules produced under gas-phase conditions in the laboratory. 2. CALCULATIONS
2.1. Basis Set and Geometry The A0 basis set used employs Gaussian lobe functions. A set of double-zeta quality consisting of four s and two px, py, and pz groups located at each carbon atom, together with two contracted s functions on the hydrogen atom, is chosen, analogously to previous work (10). This basis is augmented to better account for polarization effects by including bond s and pa functions between the carbon atoms with exponents of 1.40 and 0.50, respectively, in addition to a set of px, py, and pz species (UJ= 0.735824) on hydrogen. The lobe separations are constructed in the usual manner by the relation l= O.O3ai-1. In order to describe possible Rydberg characteristics of upper excited states, a set of long-range s and px, py, pz AO’s with exponents 0.017 is located at the center of the CC bond; thus a total of 32 contracted functions are employed in the present calculations. The equilibrium geometry which has been reported in SCF calculations by Bar&n (10) for the 2Z+ ground state (. . . l?r”Sa), namely, CC = 2.274 bohr (1.203 A) and CH = 2.008 bohr (1.063 A), is employed in the calculations for the vertical electronic spectrum. In agreement with the predictions of qualitative MO theory (14), the CC bond length of CZH is expected to be somewhat larger than in the corresponding state of isoelectronic CN (1.1718 A), primarily because the upper 5a MO in diatomic AB systems is more AB bonding than in HAB systems, in which it also has a marked A-H bonding character (15). The situation is especially obvious in the comparison between HCN (1.153 A) an d 1 ‘t s isoelectronic partner N2 (1.094 A), for which the SJ is doubly occupied in each case; there is no definite experimental value available for the internuclear distances of C2H, however. An assumed C-C bond of 1.204 A yields a J = 1 -+ 0 rotational transition frequency of 88.4 GHz, while a second attempt with 1.218 A gives a value of 86.3 GHz; the measured quantity is 87.3 GHz (I), i.e., somewhere in between. A neutron powder-diffraction study of the related ionic species NaC2H indicates a C-C equilibrium distance of 1.27 A for this system (and a C-H bond of 1.07 A) (16), an unusually large CC value which has been rationalized elsewhere (16). Results of CI calculations will be discussed in a later section. 2.2. Important Electronic States It is well known that in first-row diatomic molecules the 3a, and lrr, MO’s are quite close in energy, hence the two low-energy states in C2 (‘2 ,+, QU with partial occupation of these MO’s), for example, or the ?Z+ and 2~ states in CN, which are separated by only 1.13 eV. The situation is expected to be quite analogous in CZH, with a 2Zf (. . . l?r45a) ground state and a very low-lying Q(. . . 1~~5~~) excited state, as has indeed been indicated on the basis of SCF calculations (10). For the study of the excited states this situation leads to the complication that excitations out of both MO’s, the l?r,-like (1~) and 3o,-like (5~) species, have to be taken into account even when interest is
VERTICAL ~~~~~
1
Low-lying the
excited
lowest
ELECTRONIC
states
available
of C~H
SPECTRUM
resulting
unoccupied
from
transitions
(The lowest
species.
OF CtH out
of
169 1~ and
40 --c 50 excitation
50 into is also
included.)
2L+ 2"
4o21n45a 4021n41n*
"ala"ce long-range
4o21n43po
2cc
long-range
4021n43pn
21
long-range
401x4502
2x+
valence
2ll 4,2,-
4,2L+
'4,2
4a21n35c3s
4021n25023s 4a21n25c23po
prefer
because
“exclusive general out
the
long-range long-ranqe 2*
4,2,4.2z-
long-ranqe
n.
lor.q-range
latter
2&
long-range
’ =A 2 ) 4,2Tr 6.
term
"long-ranse"
terIn is usually
character".
of the orbital
presence
long-range
“alen.
Zz+
use of the the
of valence appeara"ce
'
2,+ z,,i
4021n25a23pn
"ale"Ce
Zfl
2+2I4,ZzL ,4,2 A,Z,i:, 2F,211 , l,, 4,2rl
4021"25D21n*
authors
'Zn
2-1 Zz- 2 i, ,A
4,2L+
4021n3503pn
"Wdberq"
valence
(2) 4,26
4.2;'
4o21n35a3pa
rule
i;;,
2E+
4021n35o2
The
Charactera'
"ale"==
4021n47s
4a21r3501n*
a)
Probable
z=tate
Configuration
rather
than
interpret&
In the present
context
charge
contours
of a significant
density
al"ou"t of valence
the pore
as carryi"? lonq-range
notation
the u"wa"teA
connotation
simalv
in ouestin" character
conoantionrl
but
refer? certainlv
to the does
not
ttlrrsl".
focused only on the lowest-energy states. Among the low-lying levels available for occupation in electronic transitions are the l?r* (la,-like MO) and the long-range (or first member of Rydberg series) 3s, 3pa, and 3~s MO?. Excitations from the highest occupied to these unoccupied levels lead to the large number of states enumerated in Table 1. In comparison to isoelectronic CN, in which similar states are espected, the situation is even more complicated in the present case, since CzH in a number of its excited states does not favor a linear geometry anymore, especially when the in-plane component of the la* MO becomes occupied. All in all, a rather complex spectrum for the CgH molecule must be expected. 2.3. Treatment of Electronic States From among the large number of states (49 total) given in Table 1 only seven can be treated by the standard Roothaan-SCF method; the corresponding results are contained in Table 2. The total SCF energy is somewhat lower than that obtained earlier (10) Table
2
SCF
enerqies
of
some
of the
low-lying
states
of C2H
(cc = 2.274
bohr,
Configuration
State
ln450
2x+
(Z)
-76.12988
ln3502
21
I%
-76.12113
0.24
ln42r
2 lI(5a+l**)
-75.76160
10.02
4r-
-75.05096
7.59
2( 2;*
-75.8044rl
0.R6
2x-
-75.84666
7.71
ln2502L" (6,.5
TC typf.‘)
Energy
(hartree)
bE
(ev) 0.0
Cl1 = 2.008
bob=).
SHIH, PEYERIMHOFF
170 Table
3
SCF
energies
of the
low-lying
AND BUENKER
positive
Ionizationa)
State
504.
lx+
4021"4
fl_'
3, 1,
4021"350
lb 3r-
4021"2502
i n-s "4
50
Configuration
ions
of C~H.
E,ErTy
(hartree)
-75.60784
With
respect
to the C2n
(ev)
14.20
-75.76330
9.9,
-75.70861
11.46
-75.68130 -75.72698
10.96 12.20 --
l1* a)
dE
ground
stitte 2r+ .
(“Yzf: - 76.1066 hartree) by virtue of the inclusion of polarization functions. The previous ?Z+--% splitting is increased from 0.13 to 0.24 eV in the present treatment. On the other hand, it is clear that a CI calculation is necessary to obtain a reliable value for this quantity. The results for the +‘-+ 5u, 3s states of Table 2 can be expected to be fairly close to those for the first member of the ‘/r+ 12s Rydberg series (not obtainable in the SCF treatment), since the 7r--+ 5a excitation energy is so low. The analogous information can also be inferred from Table 3, which presents the SCF results for the various ionic species. On the other hand, if the differences in correlation energies for these ionic states are not drastically different, the indication from Table 3 is that Rydberg states originating from the 5a MO lie considerably higher in energy than most of those involving transitions out of the l?r species. No estimate can be extracted from the SCF results for the important ?r-+ ?r* states nor for the 4a-+ 5~ excitation. All in all it is seen that little information regarding the electronic spectrum of C2H can be obtained from the SCF treatment alone, and that a multiconfigurational treatment is essential for this purpose. The general CI procedure employed in this work is the same as has been used for the treatment of a good number of other molecules (12,13) ; details are described elsewhere (17). The configuration space treated consists of all single- and double-excitation species with respect to all the configurations contributing more than approximately 17o in the final CI expansion. In this way it is expected that none of the key higher-excitation configurations is neglected, while a large number of unimportant high-excitation species do not actually have to be processed. According to previous experience such a treatment is quite close to a full CI within the A0 basis given. The MO basis employed in a given case consists of either appropriate SCF MO’s obtained from the states given in Table 2, or is obtained from a natural orbital transformation (through diagonalization of a large-threshold, moderately large configuration space CI density matrix). This information will be given together with the results to be discussed in the next section. The actual CI calculations are carried through in CzUsymmetry, SOthat Zf and A states (as well as Z- and A or II and 4 species) often result from the same secular equation. The size of the total configuration space thus generated falls in the range of 5000 to 100,000; the secular equations actually solved generally possess orders between 2000 and 6000 (at a selection threshold of 20 rhartree). 3. RESULTS
Ok’ THE
CI CALCULATIOSS
The dominant terms in the CI expansions calculated for the various states are collected in Tables 4a-c; the ordering of states is the same as that used in Table 1. In practically
VERTICr\L ELECTRONIC
SPECTRUM
171
OF C?H
all cases the MO basis is chosen such that the leading terms amount to at least 9052 on a lc;!* basis (i.e., co > 0.95).’ If some configurations contributing more than 17;) are not contained in the set of reference configurations, i.e., are not used explicitly to generate the final configuration space, this fact is also indicated in Table 4. In such cases the calculated CI energy is expected to be somewhat too high compared to the other results (by roughly 0.14.3 eV, judging from previous experience). The calculated energies for the various states treated are given in Table 5,* along with the calculated oscillator strengths for transitions to the ground state _y*Z+ and to the low-lying AI’11 species3 The oscillator strengths are calculated via both the dipole length and velocity operator in each instance; since agreement is uniformly quite close, as has been found in many prior calculations on this level for other molecules (13), onI!. a single value is reported in Table 5.
3.1. T’alerzce-Shell States As has been assumed throughout, the lowest valence excitation is to the ?II state, which is placed by the CI calculations (at the nuclear geometry emplo>-ed) 0.96 eV above the ground-state energy (much higher than in the SCF treatment (Table 2)), thereby underscoring the significant difference between ground- and excited-state correlation energies in this instance. The nest lowest valence-shell states all arise from r -+ s* excitations (Wln5al~* configurations) with the quartet components a1waj.s l!.ing well below the corresponding doublet analogs. Although this situation is different from that in isoelectronic CN, it is exactly what one would expect from the &Hz+ ion, which is also isoelectronic with C2H. In &Ha, the lowest excited states are QU+, $A%, and ?ZU-, in this order (18, 19), followed by the corresponding singlet states of identical electron configuration in reverse (??&--, lAu, ‘Z,+) ordering. Removal of an electron would split each of the three triplets into two states each, of quartet and doublet multiplicity, respectively, presumably with all quartets lying below the respective doublets, just as is observed in Table 5. Similarly, the doublet states corresponding to the singlet ?r -+ ** C?H2 states are considerably higher, with %+ lying much above the others, in close analogy to the situation for the QU+ valence-shell species in &Hz.* The fact that in CZH the ?r-+ x* transitions occur at lower energy than the m-+ (T* (4~ + 5u) species, contrary to the case for CN, can be explained quite simply in terms of orbital stabilities: the lu MO is stabilized in C2H just as is 2u, in CsH2 as a result 1 States of like symmetry are treated in the same secular equation only if they show mixing with one another, i.e., if they have the same constituents. Thus all (a, r*) states of a given (Abelian) symmetrl-, for example, are obtained from the same secular equation, while all (T, 3pr) species are likewise obtained from a common CI, which is distinct from its (r, T*) counterpart (see Table 4a.). 2 In most cases, A states are calculated in both .I, and &-ISsymmetry of the CsL.point group, together with the corresponding S+ and x;- species of like symmetry. The discrepancies in corresponding total energies, resulting from the use of a tlil‘ferent selection method, or sometimes also a different MO I)asis, xrtl generally smaller than 0.05 eV.
J‘I’hr f wlues are calculated separately for the individual components of degenerate ~I~untlirlg to the lower CX, symmetry; the combined value is then given in the table.
species
corw
4 The ordering of the higher-lying ‘A, Ye, and W states in CZH compared to the respective ‘XU-, ‘A,, ‘\‘,+ multiplcts probably results from the effects of interacting with lower states of like symmetry iu GH.
172 the CI expansions lying cate
O' and the
percentage
natural
MO
state
d states
orbital
of C2H:
on a
Icf12 basis.
NO haaia
Basis
of the
the numbers
given
(in SOW
il
Expansion
(50,3s) No
Of
CWPS
!a employed.)
21a)
(402n450)+2.2(n,n*)+2.4(n2,n'
(n,n')
lowindi-
(5o,3s)+17.l(n25u235)
72.8
NO
2r+
91.3
(n,n*)+8.6(4o,50)
93.6
(n,n*)
91.6
(n,n*)
34.1
(4o,So)+35.6(3o,5o)+lO.6(n,n*)
+r7.2c30,n,50n*l 1 b)
88.8 X SCF MO i-J
i 88.7 ! 87.8 87.7
4t-
SCF E10\93.2 184.5
(n,n*) Of
NO
(r,"*)+
91.6
4z+
2.0(n3,n*3)+1.4(n2 i:
,n*
(n,n*)
i 93.8 92.2
(T.3PV)
92.1
ln.lpn)
2
)1b)
(,;,+15.0(n~,o~j+2.13(T~,n*~) _ 1~ SCF
Givenin
for
are
the
40~1*~50
guration b) The
Table
terms
set
Most
cate
MO
in brackets
P- states the
is not
NO
of
2x-
X SC0 MO 4L
2I+
in the
of C2H:
to that
Basis
(r,n*)
terms
1%. The
the
to the
actual
contained
ground
confi-
in the
CI expansions
numbers given 2 on (L /cii basis. The
percentage
2z-
2t2z-
cases
than
respect
however.
important
analogous
2z-
in some
more with
set
species.
lying
state
is always
configuration;
is indicated
4b
contributing
excitation
configuration
of reference
[6.36(ln4)+3.05(n3n*)Ih'
1 83.81(n2502)+1.2(n2,n*2i+
general
notation state
no
the
in Table
4a.
Expansion
94.6
(w,n*)
I 91.6
1n.n')
88.9
(n.3pn)
I 87.8
(n,3pn)
SCF HO
93.5
(,25023S)
Of
'L+
93.3
(",ll*)
of 4?.+
91.9
(n,3pn)
93.2
(0250235)
93.4
(n25o2)
4r-
(n,n*lNO
4L-
(n,3pn)NO
4L-
4x-
31-
'Z- SCF MO
SCF "0
of the
low-
always
indi-
notation
is
VERTICAL 4c
Table
ELECTRONIC
important
Most
lying
n and
to the
percentage
analogous
2!! 2, 2, 2l 211 2II ZE 2,
In,“*)
terms
P states
to that
in the
CI expansion
in C2H;
on a
/CiI
in Table
of
the numbers
2 basis.
173
OF GH the
given
The
lowestrefer
notation
is
4a.
84.97(n4n*)+~6.55(n*oZn*)t1.65(~3”*)]
NO
1”4,3pn)
SPECTRUM
,,.g(n43pn)+12.1(n25~23p~)+2.1("23pnn*2)
NO
(n350*),C,
r,n
g2.5(n35~*)r1.3(n502n'2) 56.1(n35~6~)+32.6(n35~70) I 55.5(n35070)+32.3(n35a65)
x" SCF MD
47.3(n35a6~)t40.7(n35070) I 47.8(n35070)+39.6(n35a60) 2n( n 3502)
?m
SCF
90.76(n2502n*) \9Z.0(n25d*n')
MO
?P
1
86.6(n2502n*)'[3.8(n4n')
/
2,
7; 25
notcalculated
ix
211
4,
35a60)+39.4(n35070)
41
39.3(n35060)+49.2(n35a70)
4q 4,
4z-
311
31r SCF
II.0
92.2("35a)+2.2("5%+2)+1.1("*5~~*)
'II
ill SCF
vo
91.1(" 350)+2.1(n5an*2)+1.5(n25an')
a)
The
SW
orbitals
92.7(n25023p")
MO
60 and . The
3s ana
3pa
Tables
4a and
70 are
notation
in most
basis
is otherwise
sets
the
n mixture
same
as
of
in
4b.
of hydrogen mixing (20). This is demonstrated in Table 6, which contains SCF orbital energies obtained from roughly equivalent basis sets. Thus, on the basis of qualitative MO theory, excitations from the lower-energy 4a orbital are expected to be much less favored energetically in CZH than in CN; this is especially true for excitation into the 5~ orbital, which is of higher energy in CZH than in CN (Table 6). In a similar manner, since the r orbital is a purely carbon species in CzH, it is less stable in this environment than in CN, for which it has considerable N atom character; as a result it is not at all surprising that the various 7r+ ?r* states are favored energetically in CSH compared to their counterparts in isoelectronic CN. This trend is carried over to the states of 4u21n25~*1?r*configuration (Table 5), which can be Iooked upon as resulting from n--f rr* excitations out of the 2% state. Again, the energy ordering of these species is easily understood, since these species can be written as products of appropriate K* multiplets (with the usual 3Z-, ‘A, 2+ ordering) with the rr* MO. The lowest two states (“II and ‘II) result from %- X *II, whereas the next two (q and *II) derive from the ‘A X “II coupling. A somewhat unusual feature of the ground-state transitions of C2H is that, apparently, only the lowest intra-valence species (jr211 +- dy22+) shows any appreciable intensity. The f value for the relatively high-lying 4a--t 5u excitation has not been calculated,
174
SHIH, PEYERIMHOFF Table
5
Calculated
vertical
of C2II. The
AND BUENKER
excitation
oscillator
energieg'to
strength
the
lowest
for transitions
states
from
the
upper states to the 2L+ ground state and to the low-lying 2 (Ground state energy is n (1~~50') state are also given. -76.3235
Configuration
hartree.)
Transition
state
-
4021n450
2+z (Xl
AE
(eW
-
-
0.0
not
ca1c.
4021n41"*
5a+ n*
21!
(10.7)
4.21n43*
50-r 3s
2z+
10.95
4a21n43po
5a*
3po
2zf
401r43pn
so+
3pn
2,
11.46
0.011
4021n45a2
40*
50
2I+
(9.6)
not
not
>Il.O
ca1c.
n -r5a
0.96
v *z.*
4.94
0.0035 -
6.22
-
7.32
ca1c.
not
c&c. -
-
6.91
not
0.0006
ca1c.
4021n35a2
not ca1c. 0.005
0.025
4oZln3501n*
2Lf
f *2n
f+2C+
-
0.00002 -
0.024 0.009
*z-
8.13
2A
8.27
2A
8.81
-
0.20
2P-
9.50
-
0.12 _-
i 2z+
not
0.0004
-
talc.
--
.-
-
4ll
8.20
2n
8.48
0.055
0.0002
9.78
0.010
0.008 -
‘n 4n 2n 1 2n 4x+ 46 (
4z-
-
8.92 9.22 10.4" 8.85
0.010
0.13
not ca1c. -
0.06 -
8.91
.-
-
8.95
-
-
I
26
9.12
-
\
2z-
9.13
-
2x+
9.18
0.0002
0.022
10.32
0.0003
0.004
!
2r* 2 2;-
10.46 10.49
=
however, so this result may have to be qualified somewhat. transitions involving the A”% state have been indicated.
0.04 not
talc.
0.008 not ca1c.
By contrast
several strong
3.2. Rydberg Transitions The first members of the various Rydberg transitions are generally seen to lie in the same area (or somewhat higher) than the valence-shell states already discussed. In order to better demonstrate the underlying ordering principle for these species, it is advantageous to compare their respective term values, i.e., their relative location below the corresponding ionization potential; Table 7 contains the necessary information. The heading of the table always contains the various multiplets of the CzH+ ion in a together with the calculated CI ionization potential. given electronic configuration, The term values for the various states originating from a given escitation into the first ?ts or np members are then contained in the main part of the table, and the values are arranged so as to emphasize the ionic limit for higher members of each such Rydberg series,
VERTICAL Table
5,
ELECTRONIC
175
OF CrH
cont.
configuration
Transition
4CY21n25~*1n’
State
AE (eV1 7.35
In t 3~0) (“n,
a)
SPECTRUM
f*
2 + L
f +2n
-
not calculated
These results are obtained at R - 2.274 bohr, which is the SCF ground state bond length. If the actual CI bond length (2.348 bohrl is used, mst AE values are shifted downward by roughly 0.2 eV (see Fig. 1). Values given in parentheses result from relatively poor treatments (in which all dominant configurations are included in the associated reference set).
From a comparison with Table 3 it is seen that the splitting between 311 and ‘11 (~35~) states of C,H+ is practically the same in the SCF and CI approsimations. Apart from this agreement, however, only the qualitative feature, namely, that the positive ion is most stable in such ?r states and least stable in the (n*) species lS+, is carried over from SCF to CI treatment intact. The term values for the 3s states are all calculated to lie within 2.55 and 2.85 eV (20 500 cm-l-23 000 cm-l) for the first two ions; this finding is quite consistent with the general rule (ZI), which puts such Rydberg term values in the 20 000-28 000 cm-l range (most probably 27 000 cm-1).5 Similarly, the term values for all the 3p states are very consistently- obtained to fall between 1.80 and 2.30 eV (15 000 to 19000 cm-‘) for the same ions, again quite normal behavior for Rydberg states of this type. The situation for the various multiplets of CzH+ in the Au2 electronic configuration is somewhat different, with all term values calculated distinctly higher than for the other ions. There does not seem to be an obvious explanation for this feature, however. The calculated oscillator strengths to the ground state are in general largest for the s series, as is to be expected; the magnitude is consistent withf values found for similar states in related molecules. 4. REL.41’10~
TO EXPERIMENT
The longest-wavelength observed band system around 10 000 A in the CrH spectrum From the earlier SCF calculation definitely corresponds to the .I‘%+- A211 transition. (Ill) it is known that ?II has a larger bond length than ‘%+ so that the intensity in suc:f1 GNote that for such calculations underestimated by approximately
it is quite common for term values of II = 3 R?dherg 2500 cm-‘, compared to experiment,
members
to 1,~’
SHIH, PEYERIMHOFF
176 Table
6
Comparison
CNL
MO
2+a E
I
0(4o-2Q
-0.6260
n(ln-1nJ
-0.5161
0(50-3og)
of energies
CNI
2
n)
of higher-lying
in CN,
C2H
and
-
ar.d J. Scheiding,
C2H2.
1 C2112(
C,H(2U) -0.7370
-0.7760
-0.4241
-
-0.4131
-
-0.4507
-0.6835
-0.5209
=-‘IP. Stechert
orbit&s
a
-0.6766
-
AND BUENKER
Diplomarbeit
1974.
Values
zg'b1
-0.7658
are
in hartree.
b) Ref. [201
a transition is expected to be distributed over several CC stretching vibrations. The calculated CC stretch potential curves presented in Fig. 1 show different locations for the 211 and 2E+ minima in both the SCF and CI treatments; the CI values are 2.348 (W) and 2.487 bohr (211), significantly larger than the corresponding SCF quantities of 2.266 bohr (1.20 A) and 2.417 bohr (1.279 A), all values obtained by polynomial fits to the data points calculated. Similarly, the calculated stretching force constant is smaller for the excited state, 11.4 mdyne/A or 1764 cm-’ for 211,while the corresponding ground-state value is 14.5 mdyne/A or 1989 cm-l. The latter result is relatively close to the CC force constant obtained by Atoji (16) for Na+C=CH (13.1 mdyne/A) or to the frequency of 1848 cm-l determined for CZH in argon matrix studies (4, 5); obviously the potential curve is less steep than the corresponding &Hz species (‘ZQ+), which possesses a CC stretching force constant of 15.7 mdyne/A. Although the calculated frequency for the excited C2H state is only in fair agreement with the measured value of ~3’ = 1560 cm-r obtained by trapping C2H in a solid argon matrix (6), the calculated frequency decrease from the ground to the excited state (225 cm-l) is still relatively close to the corresponding experimental value of 288 cm-‘. Again, the SCF quantities are much larger, as is clearly apparent from inspection of Fig. I; these values are 19.3 mdyne/A (2294 cm-l) for the ground and 13.7 mdyne/A (1933 cm-r) for the excited species, reflecting approximately the observed frequency difference. Since the shapes of the two potential curves in Fig. 1 are quite different, their energetic separation varies considerably with CC bond length. Thus the CI vertical transition Table
7
50-r = -------
Term
values
(1")4
(in eV)
1x+,
Ion:
2
50 + 3pn
1
,50) Ion -----
r *
3pa
II *
3s
13.8 ev --
3n#
+ 3pn
41-
,
11.04
2.09
2
_ -
n *
3pn
1*
3s
2 (1_1502) -
obtained
from
CI calculations
__--___---
ev 2x-
In, --
,
1.91
12.43
eV
21.-, 1.94
,
2t+ , 1.86
2I+
46.
2.13
*A,
1.92
2c,
1.97
4n,
2.12
*n,
1.82
'II,
2.03
4n,
2.84
*r,
2.56
2n,
2.65
2.11
______
10"-
3z-'
4n*
2.45
4z-
series
4r+ , 2.19
-z
Rydberg
n, 2.34
lb3
+oI
--n
for various
12.57 --eV zn, 2.25
, 3.50 2z-.
3.36
?%,_l3.7 24‘2.40 2 A,3.38
e" T
:$+ --'-2--n, 2.30
14.0
ev
/ n, 2.21 1zz+, 3.2
VERTICAL
ELECTRONIC
SPECTRUM
E(Har!reel
01; CiH
177
/
-76.12-
.76.28-
-76.30-
-76.32-
I
2.20
I
2.60
2.LO C-C
distance
I
2.80
(bohrl
FIGURE 1
energy (Table 5) calculated at the SW CC equilibrium distance of 2.274 bohr is approsimately 0.25 eV greater than the value obtained by employing the CC bond length determined by the CI treatment itself. Unfortunately, such a discrepancy must be expected for most states given in Table 5 (and hence a correction of AE in this order), since all r---f X* species, for example, are also expected to exhibit a longer equilibrium CC distance than %%?+, and as such their potential curves are also found in the repulsive branch at the R value employed in the vertical spectrum calculations. At the same time, the 04 transition between ,p725+ and A”*II is calculated to be 0.5 eV, with this value being markedly smaller than that estracted from experiments in a solid argon matrix (10 080 A or 1.23 eV). On the other hand, from a qualitative point of view it seems unlikely that this transition just begins at 1.2 eV, since its diatomic analog CN shows a O-O transition for this a + u* species at only 1.13 eV (1 I), and there is good reason to believe that substitution of a CH group for an N atom has a smaller destabilizing effect on the 5s MO (which can be somewhat compensated by the beneficial effects of CH bonding) than for the lower-lying ?r orbital. The orbital energ!results of Table 6 indicate, for example, that the R MO energy increases by nearly 0.10 hartree from CN to CsH, while the corresponding 5a value only goes up by 0.07 hartree. The difference of roughly 0.8 eV cannot be at.tributed quantitative significance, perhaps, but it seems much too large for this effect to be totally absent in the true experimental situation. At the same time, if the CI calculations are correct, the actual 04 transition
178
SHIH, PEYERIMHOFF
AND BUENKER
must be expected at quite large wavelength for an electronic species, perhaps as low as 2.5 000 A (0.5 eV), and hence should be extremely difficult to detect by presently available experimental techniques. In any event, the present CI results indicate that the masimum for this transition should be found in only the 0.7-0.8 eV range of the gas-phase CZH spectrum (18 000-15 000 A), and this result is in significant disagreement with what has been reported in the existing argon matrix studies of this system. The dipole moment (at CC = 2.274 bohr) for the ground state is calculated to be 0.770 D when z’%+ SCF MO’s are employed, and 0.826 D with a 4X:- MO basis. This result supports the value of 0.8 f 0.2 D estimated by Green (22). A large charge transfer occurs upon 2Z++ 211(rr-+ n*) excitation, since the a MO has its charge distributed in an essentially symmetric way between the two carbon atoms in CZH, while the u* MO (doubly occupied after the transition) is primarily localized at the end carbon; hence the calculated *II dipole moment (again at CC = 2.274 bohr) is much larger (3.29 D). The nature of the second observed weak band system (6-8) around 3000 A is still open to question. A number of absorption lines extending from 3.64 to 4.79 eV, with a maximum around 4.5 eV, have been found for C2H in solid argon (6). In addition, an essentially continuous emission from a C2H* in the region from 2.2 to 3 eV (4000-5500 A) (7, 8), with a possible maximum around 2.5 eV, is observed following photolysis of &Hz, whereby a (0, 0) transition is estimated on the basis of kinetic data to lie around 4.11 eV (8). The only low-lying state in this region shown by the calculations is 4Z+ (Table 5) with a vertical energy difference to the ground-state equilibrium geometry of 4.94 eV.6 If this energy can be identified with the absorption maximum around 4.5 eV measured by Graham et al. (6), the various lines at lower energies also obtained in the same experiments should correspond to a progression in each of the CC stretch and *CCH bending vibrations of the excited state, since 4Z+ is expected to have a larger CC bond than rT2Zf, and also to possess a bent nuclear geometry, in contrast to both Ly2Z+ and A”%. The measured lifetime of 6 bsec (f = 0.0003~.0005) (7) could be “2Z + transition. Furthermore, the consistent with the formally spin-forbidden 4Zf-1X emission at lower energies (following photolysis of &HZ) could be simply explained as resulting from transitions between low-energy vibrational levels of the bent upper 4Zf and higher vibrational levels of the linear ground state, thus appearing at longer wavelengths than the absorption lines for C2H in a solid argon matrix at 4 R. The reliability of the derived (0,O) band at 4.11 eV seems to be questionable in light of this discussion, however. The first allowed (but also weak, see Table 5) transition, *Z+ +-fiW at 7.32 eV, seems too high to qualify as being involved in the observed 3000 A emission even if A”‘Jn were the lower state and not X22+ (the transition probability to the former is apparently much higher, however, see Table 5). On the other hand, if emission were to occur from the first few vibrational levels of the upper bent *Z+ state to very high vibrational species of the linear ground or linear A”% state, energies in the 3 eV range might still be possible. In any event, a detailed investigation of the geometry of the ‘x+ and 2~+ r--+ r* upper states as well as the two low-energy -%Y and A’II species 6 Note that the actual CI vertical result may be lower by approximately CI value for the CC bond is employed (see Fig. 1).
0.25 eV once the equilibrium
VERTICAL
ELECTRONIC
SPECTRUM
OF C,H
170
is
clcarlq. necessary, combined with an appropriate vibrational analysis, in order to obtain a more definite assignment for the nature of the second weak absorption band system in CZH. Work in this direction is in progress. At the same time, a more detailed study of the CzH spectrum via experimental techniques would be very desirable. ACKNOWLEDGMENTS The authors wish to thank Professor K. H. Becker and Dr. D. Haaks for numerous helpful discussions; They also wish to express their gratitude to the Deutsche Forschungsgemeinschaft for financial support given to this work. The services and computer time made available by the University of Bonn Computer Center are gratefully acknowledged. RECEIVED: June 29,
1976 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. Y. IO. Il. 1.
13.
1-f. 15. 16. 17. 18. 19. 20. Zf.
22.
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