J. Phys. Chem. 1995,99, 9755-9761
9755
A Theoretical Investigation of CSO Peter Botschwina" and Jdrg Flugge? Institut f i r Physikalische Chemie, Universitat Gottingen, Tammannstr. 6, 0-37077 Gottingen, Germany
Peter Sebald Fachbereich Chemie der Universitat Kaiserslautem, E. Schrodingerstr., 0-67663 Kaiserslautem, Germany Received: January 23, 1995; In Final Form: March 30, 1995@
Large-scale coupled cluster calculations have been carried out for G O . The equilibrium geometry is linear with bond lengths (in order of chemical formula) of 1.2802, 1.2928, 1.2622, 1.2840, and 1.1554 A. The equilibrium dipole moment is predicted to be 4.06 D, with the negative end at the terminal carbon site. The v1 band at 2290 cm-I has a large IR intensity of 3813 km/mol. Vertical ionization energies of 9.97 and 10.43 eV are predicted for the first c7 and n ionization, respectively.
Introduction
Details of Calculations
Quite recently, the rotational spectra of carbon chain molecules with an oxygen end atom, C,O, have been measured up to n = 9.l.* Such species are of considerable interest to interstellar cloud chemistry, but also-due to interesting binding and electrical and optical properties-of substantial general interest. C20(X3Z-) and C30(%lZ+)were already observed in the interstellar medium by means of radio a s t r ~ n o m y . ~Higher -~ members of the series will be more difficult to detect for reasons of abundancy, but with the steady improvement in radioastronomical techniques the prospects for observing C40 or CsO should be quite good. Like the other C,O species with an odd number of carbon atoms, CsO has a singlet ground state. The rotational spectra of as many as seven different isotopomers could be recorded by Ogata et aL2, and a substitution (rs)structure was derived from the rotational constants by means of Kraitchman's equat i o n ~ . ~To, ~our knowledge, only two ab initio studies of CsO have been published so far. Brown et aL8 reported on SCF and MP3 (third-order perturbation theory according to Mdler and Plesset) calculations of the lowest singlet and triplet states in two different isomeric forms. The equilibrium rotational constant of the linear singlet state was calculated to be 1343.1 MHz (MP3/D95** basis), and an empirical estimate of 1354 MHz was given for the ground-state value. The latter one differs from the experimental value2 of 1366.947 09(6) MHz by 1.0%, about 10 times as much as expected by the authors. More recently, DeFrees and McLean9 calculated the equilibrium geometry of C 5 0 at two levels of theory, termed SCF/ 6-31G(d) and MP3/6-31G(d). The latter calculations yield Be = 1358 MHz. An estimate of the ground-state rotational constant based on an empirically corrected geometric structure was reported: Bo = 1360 MHz. It was estimated to be accurate to &2%. Further predictions at the SCF level were made for the harmonic vibrational wavenumbers and the corresponding (relative) infrared intensities8 The calculations with the larger basis set (D95**) yielded the band with second highest wavenumber (v2 in usual notation, Yg in ref 8) to be the strongest whereas that with highest wavenumber was predicted to be only about one-third as strong.
Electronic structure calculations for C 5 0 have been performed by various methods: HF-SCF (Hartree-Fock self-consistent field), MP2, CCSD (coupled cluster theory with single and double excitation operatorslo), CCSD(T) (CCSD plus quasiperturbative treatment of the effects of connected triple substitutions' I ) , and CEPA- 1 (coupled electron pair approximationI2). Throughout, the MOLPR094I2 suite of programes was employed; details of the implementation of CCSD and CCSD(T) are described in refs 14 and 15. A basis set of 180 contracted Gaussian-type orbitals (cGTOs), with real spherical harmonics for the angular parts, was employed in most of the calculations. It corresponds to Dunning' sI6 correlation-consistent polarized valence triple-zeta set which is described as (10s,5p,2d,lf) in contraction [4,3,2,1]. Potential Energy Functions and Spectroscopic Constants. Ab initio equilibrium geometries, total energies, equilibrium rotational constants, and harmonic stretching vibrational wavenumbers for the linear electronic ground state of CsO(XIZ+) are given in Table 1. Most credit should be given to the equilibrium bond lengths in the last column (CCSD(T)/all). Although the cc-pVTZ basis set is not expected to be able to quantitatively describe the effects of core and core-valence correlation, it works rather well for equilibrium bond lengths. For example, all-electron CCSD(T) calculations with this basis for the electronic ground states of C2, C3,I7 and C02 overestimate Re by 0.0029, 0.0011, and 0.0033 A, respectively. Inclusion of the effects of connected triple substitutions in the calculations for C 5 0 leads to considerable elongations (by more than 0.010 A with respect to the CCSD results) of the shorter CC equilibrium bond lengths ( R I ,and R34 and the CO equilibrium bond length (R5e). On the other hand, R2e and R3e experience only small changes of 0.0027 and 0.0013 A, respectively. Similar alternating behavior has been previously observed for C5.I8 Here, the effect of connected triple substitutions even changes the ordering of the equilibrium bond lengths. With the exception of Rze, where the effect of connected triples is small, the CEPA-1 equilibrium bond lengths for C 5 0 are intermediate between those obtained by CCSD and CCSD(T). This is a situation we have observed in many other cases. The MP2 equilibrium bond lengths are remarkably close to the CCSD(T) values, but this is not always the case and difficult to anticipate. Connected triple substitutions also significantly lower the
' Present address: National Institute for Advanced Interdisciplinary Research (NAIR), 1-1-4, Higashi Tsukuba, Ibaraka 305, Japan. @Abstractpublished in Advance ACS Abstracts, May 15, 1995. 0022-365419512099-9755$09.00/0
0 1995 American Chemical Society
9756 J. Phys. Chem., Vol. 99, No. 24, 1995
Botschwina et al.
TABLE 1: Ab Initio Equilibrium Geometries, Total Energies, Equilibrium Rotational Constants, and Stretching Harmonic Vibrational Wavenumbers for CsO MP3/D95**O
MP3/6-31G(d)b
SCF
MP2
CCSD
CEPA- 1
CCSD(T)
CCSD(T)/all
1.2859 1.3087 1.2681 1.2993 1.1582
1.278 1.299 1.261 1.291 1.157
1343.1
1358
1.25401 1.28771 1.24116 1.28317 1.12223 0.930066 1398.12 2466.7 2310.8 2094.4 1389.2 703.2
1.28726 1.29862 1.26590 1.28982 1.16580 -0.024824 1350.69 2412.5 2218.4 1871.5 1272.5 647.6
1.27572 1.29592 1.25747 1.28944 1.14912 -0.005420 1365.84 2355.5 2256.1 1953.9 1312.8 666.0
1.28199 1.29406 1.26389 1.28626 1.15679 -0.026854 1360.33 2283.2 2188.6 1902.1 1301.2 660.0
1.28869 1.29863 1.26774 1.29074 1.16106 -0.073466 1350.44 2319.6 2193.3 1873.0 1276.9 648.7
1.28269 1.29208 1.26073 1.28422 1.15718 -0.163414 1363.68
RI, (A) Rze R3e R4e
(4) (4) (4)
R5e (A) V, ( f 2 6 4 hartrees) Be (MHz) W I (cm-I) 0 2 (cm-I) w3 (cm-I) o4(cm-I) wg (cm-I)
Reference 8. Reference 9.
TABLE 2: Parameters of the CCSD(T) Potential Energy Function for CsO (Stretching Coordinates Only)” PEFterm i i k 1 m PEFterm i j k 1 m 0.339768 -0.362978 0.235600 -0.124 198 0.060728 0.331 359 -0.340889 0.218886 -0.106476 0.049003 0.390639 -0.397335 0.256217 -0.117355 0.068293 0.356671 -0.355557 0.217093 -0.148323 0.073015 0.513532 -0.636774 0.491 393 -0.306653 0.180795 0.021 832 -0.027582 0.009302 -0.017274 0.045 034 -0.020331 0.019037 0.031 332
2 3 4 5 6 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 0 2 3 4 5 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0
0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5
6 0 0 0 0 0 0 0 1 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 0 0 0 1 0 0 1 0
-0.031 589 0.061 092 -0.006256 -0.025510 0.003353 0.000630 -0.003741 -0.002070 0.004907 0.003 790 0.003 767 -0.029507 -0.022296 0.003099 0.004504 -0.005773 -0.008036 -0.018601 -0.012807 0.007773 -0.038773 -0.042321 0.020833 0.004958 -0.000896 0.004000 0.007066 0.003371 0.016256 -0.007 599 0.000566 0.027089
0 0 2 1 2 1 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
0 0
1
2 1 2 1 2 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0
1 2 0 0 0 0 2 1 1 0 0 1 0
0 1 0 2 0 0 1 0 2 0 0 0 0 0 0 0 0 0 2
0 1 1 0 1 1 0 1
0 1 0 0 0 0 1 2 0 0 0 0 0 1 2 0 0 1 2 0 2 1 0 1 0 1 0 1 1 0 1 1
1 1 0 0 0 0 0 0 1 2 1 0 0 0 0 1 2 0 0 2 1 2 0 0 1 0 1 1 0 1 1 1
Valence electrons correlated. PEF terms are given in atomic units; see eq 1 for their definition.
harmonic wavenumbers of the stretching vibrations. Their effect is largest for 123, which is lowered by 81 cm-’ or 4%. Most of the MP2 values given in Table 1 are very close to the CCSD(T) results. In particular, the Be values differ by only 0.25 MHz. The situation is thus similar as in Cg (see table I of ref 18). Among the harmonic stretching vibrational wavenumbers, there is only one case of a larger deviation: W ] (MP2) is larger than W I (CCSD(T)) by 93 cm-I or 4.0%. The ratios wi(SCF)/wi(CCSD(T)) vary over the wide range from 1.054 to 1.118. Single uniform scaling of SCF harmonic wavenumbers would thus be not very accurate for C5O. The parameters of the stretching part of the CCSD(T) potential energy function are given in Table 2. They correspond to a polynomial function of the form Vstretch = v - Ve =
C C~~,,,AR~A&A@AR&ART(1)
ijklm
Here, V, is the total energy at equilibrium and AR, are the changes of the internuclear separations with respect to their equilibrium values. The diagonal parts of this function are displayed in Figure 1. For economical reasons, only the diagonal parts of the bending potential plus the quadratic off-diagonal terms were calculated at the CCSD(T) level. The diagonal parts are shown in Figure 2. Again, we see a pronounced alternation in the shape of the individual potential curves, with V ( a ) and V ( y ) being much more shallow than either V@) or V(6). Here, the angles measure the deviation from linearity; they are numbered according to the chemical formula from left to right. The CCSD(T) quadratic bending PEF terms and the corresponding harmonic bending vibrational wavenumbers are listed in Table 3. The latter are expected to be accurate to 1-2%. A relatively low value of 77 cm-I is predicted for the bending vibration with smallest wavenumber (019). It involves mainly bending of the angle y , which is connected with the smallest force constant (see also Figure 2). The cubic stretch-bend coupling terms have been calculated by CEPA-1; the results are given in Table 4. The full cubic force field is required to calculate the vibration-rotation coupling constants (a)by conventional second-order perturbation theory in normal coordinate space (see, e.g., refs 19-21). The CEPA-1 cubic stretch-bend coupling terms have been combined with the CCSD(T) PEF terms (see Tables 2 and 3) to calculate the a values. They are given in Table 5 , which also contains the results obtained for the centrifugal distorsion constant and the 1-type doubling constants. The sign convention for the small 4: terms which describe the dependence on the rotational quantum number J follows the fundamental paper by Watson.22 The ratio between experimental ground-state and calculated equilibrium quartic centrifugal distorsion constant, D$Di, is 1.36. In order to avoid confusion with dissociation energies, the superscript J has been introduced. The given ratio is a rather sensitive indicator of the degree of “floppiness” of a molecule with linear equilibrium geometry. The above value is larger than in semirigid linear molecules like HC3N, where a value around 1.05 is typical.23 Linear molecules with extremely shallow potentials like C3 have much larger values; however, in the case of the latter molecule, the ratio is 49.38 where @ is calculated from the data of table I of ref 16 (CCSD(T)/255 cGTOs) and the experimental value taken for DA. Equilibrium Geometry of CSOfrom a Mixed Experimental/ Theoretical Procedure. An accurate equilibrium geometry for C50 may be obtained by combination of experimental and ab initio data. The ground-state rotational constants Bo of seven isotopomers are taken from experiment* while the differences AB0 = Be - Bo are calculated from the theoretical vibrationrotation coupling constants (see Table 5 ) by means of the
A Theoretical Investigation of CSO
J. Phys. Chem., Vol. 99, No. 24, 1995 9757
0.08 1
I
I
I
-0.2
-0.1
0
I
I
I
I
0.2
0.3
0.4
0.07
0.06
0.05
-: v
0.04
>
0.03
0.02
0.01
-0.3
0.1 A R (ad.)
0.5
Figure 1. Stretching potential functions for CsO (CCSD(T)/180cGTOs). 0.009
I
I
2
4
I
I
I
I
1
I
I
0.008
0.007 0.006
~
: ’
0.005
v
0.004
0.003 0.002 0.001
0
-.r.
...1
I
I
I
I
1
6
8
10 angle (deg)
12
14
16
18
20
Figure 2. Bending potential functions for CsO (CCSD(T)/180cGTOs).
approximate formula
AB^ x z a j d j 2
(2)
i
where di is a degeneracy factor (1 for stretching, 2 for bending modes). The resulting Be values are then converted to equilibrium moments of inertia from which the equilibrium bond lengths are obtained by least-squares fit. This approach has been successfully applied to a larger number of linear and nonlinear molecule^^^-^^ and usually yields equilibrium bond lengths accurate to 0.001 8, or better.
The equilibrium rotational constants and corresponding equilibrium moments of inertia which were employed in the fit are given in Table 6. The standard deviation of the fit is u = 6 x u A2. The resulting equilibrium bond lengths (in angstroms) are RI, = 1.2802, Rze = 1.2928, R3e = 1.2622, Rde = 1.2840, and Rse = 1.1554. They are believed to be accurate to at least 0.001 A. The differences from the results of the CCSD(T)/all calculations (see Table 1, last column) are smaller than 0.0025 %, and thus lie in the expected range. Somewhat fortuitously, the Be value obtained by CCSD(T)/all almost coincides with the value obtained by combination of theory and
9758 J. Phys. Chem., Vol. 99, No. 24, 1995
Botschwina et al.
TABLE 3: Quadratic Bending Force Constants and Corresponding Harmonic Wavenumbers of CsO (CCSD(T) Results)” term
valueb
term
valueb
a2
0.0142 64 0.063 100 0.01 1 381 0.072 088 0.002 035 -0.002 430 0.000 579
Pr
0.014 053 -0.009 334 0.019 287 549.1 524.6 199.6 77.3
P’ Y2
62
aP ay
ad
Pd
Yd 0 6
w7 WS w9
PEF terms are defined in the same way as for stretching coordinates and are designated by an obvious shorthand notation. Two bending coordinates are defined to have the same sign for a cis-like distortion of the nuclear framework. In atomic units for PEF terms and cm-I for harmonic wavenumbers.
TABLE 4: Cubic Stretch-Bend PEF Terms of C50 (in au)” term
coeff
term
coeff
term
coeff
Rla2 R2a2 R3a2 R4a2 Rja2 Rip2 R2P2 R3P2 R4P2 RjP2 Rly2 R2y2 R3y2
-0.0169 -0.0296 0.0011 0.0015 -0.0034 -0.0065 -0.0415 -0.0453 0.0006 -0.0112 -0.0001 0.0031 -0.0368 -0.0454 0.0156 -0.0005 -0.0053
R3d2 R4d2 Rsd2 RIM R2@ R343 R4ap R5aP Rlay R2ay R3ay R4ay R5ay Rlad R2ad R3ad R4ad
0.0043 -0.0577 -0.0613 0.0213 -0.0087 0.0019 0.0006 -0.0004 0.0013 0.0023 -0.0006 0.0000 0.0012 -0.0022 0.0005 0.0005 0.0006
R5ad RIPy R$y R3Py R4Py R5Py RIPd R$d R3Pd R4Pd RsPd Rlyd R2yd R3yd R4yd Rjyd
-0.0052 0.0015 -0.0038 0.0128 0.0206 -0.0046 0.0009 0.0044 -0.0076 -0.0073 0.0052 0.0061 -0.0069 0.0262 0.0249 -0.0030
R4y2 R5y2 Rid2 R2d2
CEPA-1 results, evaluated at the CCSD(T) equilibrium geometry (see Table 1).
TABLE 5: Centrifugal Distortion Constant, l-Tyle Doubling Constants, and Vibration-Rotation Constants for
cso
25.85 0.287 0.291 0.638 1.60 -0.021 -0.033 -0.392 -3.146
5.06 4.68 3.25 2.32 0.90 -1.19 -1.76 -3.55 -4.49
TABLE 6: Equilibrium Rotational Constants” and Corresponding Equilibrium Moments of Inertia for Different CsO Isotopomers 12- 12- 12- 12- 1213-12-12-12-12-16 12- 13- 12- 12- 1212- 12- 13- 12- 1212- 12- 12- 13- 1212-12-12-12-13-16 12- 12- 12- 12- 12-
16 16 16 16 18
1363.9613 1324.3971 1348.6193 1361.8000 1363.0717 1352.5512 1304.8542
370.5230 381.5917 374.7381 37 1.1 110 370.7648 373.6487 387.3069
a Obtained by combination of experimental Bo and theoretical AB0 values (see eq 2).
experiment. Due to some favorable error compensation, the present CEPA- 1 calculations in which only the valence electrons were correlated yielded only small differences from the mixed experimentalkheoretical equilibrium structure. A similar situation is observed for C5 where CEPA-1 calculations (valence
TABLE 7: Parameters of Electric Dipole Moment Functions for C50 (in au, Stretching Coordinates Only)” i
j
k
l
m
SCF
MP2
CCSD
CCSD(T)
0 1 2 3 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
0 0 0 0 1 2 3 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 1 0 0 1 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 1 0 0
1.1827 -2.2813 0.2284 0.0621 2.8987 -0.2432 -0.2160 -2.8298 0.1781 0.1121 2.7366 -0.2696 -0.0916 -3.4562 0.2388 0.6010 -0.0168 -0.5300 0.1570 -0.7210 0.0767 0.2545 0.1965 0.1172 -0.5160 0.3510
1.8005 -1.2751 0.9278 0.2144 1.5372 0.1972 -0.1627 -1.2909 0.5425 0.0792 1.7446 -0.0075 -0.0326 -2.3495 1.1597 -0.0105 -1.1173 0.2555 -0.1675 -0.3390 -0.5375 0.3192 -0.3132 -0.0195 0.1500 -0.7285
1.6104 -1.7955 0.4615 0.0284 2.3065 -0.0183 -0.2508 -2.0765 0.2530 0.0690 2.2904 -0.1072 -0.1174 -2.8805 0.5346 0.3285 -0.4160 -0.2740 0.0503 -0.5975 -0.1330 0.2825 0.0335 0.1063 -0.3262 -0.0940
1.5962 -1.5987 0.5652 -0.0043 1.8027 -0.0169 -0.3035 -1.6237 0.4131 0.2273 1.8902 -0.0822 -0.1656 -2.5932 0.9489 0.4178 -0.7380 0.0365 -0.0955 -0.3925 -0.3847 0.2246 -0.2263 -0.0012 0.1365 -0.5985
1
0 1 1
a Expanded around the recommended (mixed experimentaUtheoretical) equilibrium geometry from this work.
electrons correlated) with a basis set of 150 cGTOs3’ yielded differences of only -0.0006 and 0.0013 8, compared to the results of much more extended CCSD(T)/all calculations with a basis set of 275 cGTOs.I8 The following substitution structure of C 5 0 has been obtained by Ogata et al.:2 R I , = 1.2736(10) A, R Z = ~ 1.2947(21) A, R3s = 1.2881(38) A, R4s = 1.2552(30) A, andR5, = 1.1562(11) A, with error bars in terms of the least significant digit being given in parentheses. The differences in R I ,R2, and R5 compared to our accurate equilibrium structure are well within the limits of usual differences between substitution and equilibrium structures (which are not the same!). The differences of 0.0219 and -0.0288 8, in R3 and R4 are unusually large, however. As noted by Ogata et al., the center-of-mass condition is poorly fulfilled for their substitution structure. Determination of the z coordinate of C(4j by the first-moment condition Cimizi = 0 leads to R(C(&4) = 1.2668(53) A and R(C(4&)) = 1.2765(45) A, in much closer agreement with our equilibrium structure. Electric Dipole Moment Functions. The dependence of the electric dipole moment on the stretching coordinates was investigated by means of a more flexible basis set which includes s and p functions from the “augmented” sets of Kendall et al.38 and thus comprises 204 cGTOs. Except for SCF, where the Hellmann-Feynman theorem applies, it was calculated as an energy derivative, Le., as the first derivative of the energy with respect to a homogeneous electric field at zero field strength. The electric dipole moment function (EDMF) was expanded around the mixed experimentdtheoretical equilibrium geometry of this work and fitted by a polynomial function in an analogous way as the total energy. The EDMF terms from the least squares fits of the results from four different methods are listed in Table 7. Plots of the diagonal CCSD(T) curves are shown in Figure 3. According to our experience with other molecules (see, e.g., refs 39 and 40), the CCSD(T) equilibrium dipole moment of he = 4.057 D (negative end at terminal carbon site) should be accurate to ca. 0.01 D. Correlation effects on this quantity are substantial; they lead to an increase by 35%. MP2 overestimates
A Theoretical Investigation of CSO 2.6
-
2.4
-'...,,
2.2
-
J. Phys. Chem., Vol. 99, No. 24, 1995 9759 I
CI
I
I
I
I
(W
Figure 3. Variation
by as much as 0.52 D or 13%. The effect of connected triples on pe is very small. Previous SCF values for pe are 3.088 and 3.37 DS9 DeFrees and McLean9 made an estimate of the ground-state dipole moment by scaling their pe value with a factor taken over from C3O and arrived at po = 4.4 D. This value appears to be too high. We believe that zero-point vibrational effects will produce a po value which is smaller than peand recommend po = 3.9 & 0.1 D. Wavenumbers and Absolute IR Intensities of Stretching Vibrational Transitions. Making use of the analytical potential energy function from Table 2, we have calculated vibrational term energies and wave functions by representing the approximate vibrational Hamiltonian
,De
TABLE 8: Harmonic and Anharmonic Wavenumbers and IR Intensities for stretching Vibrations of CS@ band ij (cm-') A, ( k d m o l ) (DH) (DH) ~3 (DH) ~4 (DH) w (DH) WI ~2
V5 v4 v3
v2 VI v3
+ v5
2V%
+v5 + v5 v 3 + V%
v2 VI
+ "stretch
(3)
v2 + v 4 VI
in a sufficiently large basis of harmonic oscillator product functions.23 The CCSD(T) electric dipole moment function from Table 7 is then used to calculate absolute IR intensities for transitions arising from the vibrational ground state by means of the formula
+v4
2V3 v2 VI
+ v3
+ v3
2v2 2Vl (I
23 19.6 2193.3 1873.1 1276.9 648.7 643.0 1263.7 1850.3 2166.1 2290.3 2491.7 2525.5 2806.5 2929.7 3109.1 3422.1 3546.1 3692.0 4003.5 4131.9 4321.4 4566.3
Abbreviation DH stands for double-harmonic approximation.
(4)
(5)
-
Here, VR is the wavenumber of the transition 0 f and p p is the corresponding transition dipole moment. The fundamental constants appearing in (4) have their usual meaning. The results are given in Table 8. It includes the fundamental transitions plus those overtones and combination tones up to 2 ~ for 1 which intensities of more than 1 km/mol have been calculated. In contrast to the previous SCF calculations of Brown et al.,s we find the V I band with origin at 2290 cm" to be clearly the strongest. Its absolute intensity of 3811 km/mol is very big and comparable to the value of 3999 km/mol we have recently obtained for the V I band of C S S . ~ 'The high intensity may be rationalized within the double harmonic approximation within which it is given by the expression
3989.6 672.8 484.5 0.234 0.003 0.008 0.161 482.2 643.9 3812.6 1.1 14.5 21.4 57.3 3.1 21.7 17.7 12.7 1.7 2.0 4.5 4.3
The relevant normal coordinate derivative is
with the L matrix elements being given in Table 9. All five contributions in eq 6 have the same sign, with the last three being the important ones. There are two further strong bands: Y:!at 2166 cm-I with an intensity of 644 km/mol and v3 at 1850 cm-' with A3 = 483 km/mol. The remaining fundamentals v4 and ~5 are very weak.
Botschwina et al.
9760 J. Phys. Chem., Vol. 99, No. 24, 1995 TABLE 9: L Matrix for Stretching Vibrations of CsO (CCSD(T)/180cGTOSY QZ
Qi
AR 1 AR2 A& AR4 ARs a
0.005 502 7 -0.007 993 8 0.005 444 9 0.001 133 6 -0.004 028 8
0.000 2 12 5 -0.002 454 3 0.006 072 9 -0.008 554 5 0.006 396 7
Q3
Q4
0.006 826 2 -0.002 367 3 -0.004 641 9 0.000 986 8 0.004 139 2
-0.003 643 4 -0.003 5 5 1 6 0.000 423 9 0.003 595 7 0.002 272 6
Qj
-0.001 -0.001 -0.001 -0.001 -0.000
110 8 813 0 782 3 750 2 752 1
Matrix elements are given in atomic units.
0.3
0.25
0.2
-
->
0.15
0.1
0.05
0
1.5
2
2.5
3
Figure 4. Potential curves for the dissociation process CsO(X'Z+)
3.5
-
Similarly as has been found previously for C30,25the intensity ratio A(~vI)/A(YI) is unusually small. While a very small intensity of 0.17 krdmol has been calculated for the v4 band at 1264 cm-I, its first overtone at 2526 cm-' is stronger by 2 orders of magnitude. This is due to intensity borrowing from the very strong v1 band whose origin is 235 cm-' apart. The normalized vibrational wave function of the state described mainly as 2 ~ has 4 a contribution from the harmonic oscillator product function Il,O,O,O,O) with a coefficient of c = 0.0614. The crude calculation A(2~4) c2 A(YI) = 14.4 W m o l compares remarkably well with the result of 14.6 W m o l given in Table 8. A similar intensity pattern was previously found for C3O, both experimentally and the~retically.~~ Here, the v3 band is extremely weak while its first overtone gains intensity through slight anharmonic interaction with the strong band, with origin calculated to be apart by as much as 348 cm-I. The intensities of the bending vibrations have been calculated by CCSD(T) within the double-harmonic approximation. They are (in km/mol) A(w6) = 26.7, A(w7) = 27.8,A(w8) = 8.7, and A(w9) = 6.0. Bending vibrations of C5O will thus be difficult to observe. The Lowest Dissociation Channel. Under the restriction of linear arrangement of the nuclei, we have investigated the dissociation of C=O , into the energetically lowest-lying fragments, C2(X12,+) and C30(X1X+). This is formally a closedshell process, but we wish to note that, due to the near degeneracy of the 30, and In, orbitals in the vicinity of Re, the singlet ground state of C2 is poorly described by a single Slater determinant. However, CCSD(T) still performs well for spectroscopic constants of this species. For example, CCSD(T)/
R (a.u.)
4
4.5
5
5.5
6
C30(2'Xf) + C>(X'Z:,+).
all calculations with the cc-pVQZ basis set (110 cGTOs) underestimate Re by only 0.0004 8, and overestimate w eby 16 cm-'.I8 The present CCSD(T) calculations with the cc-pVTZ basis (valence electrons correlated) overestimate Re by 0.0082 A and underestimate w eby 9.1 cm-I. The potential curves for dissociation into the above fragments as calculated by various methods are shown in Figure 4. Except for the bond length varied CCSD(T) bond lengths of CsO are employed; Le., no geometrical relaxation was taken into account. In the case of CCSD(T), geometry optimization of the fragments leads to an asymptotic energy lowering by 0.00371 hartree or 10.2 kJ/mol. Due to the poor description of the ground state of C2, the SCF calculations substantially overestimate the dissociation energy. MP2 shows spurious behavior in the range 4ao 5 R 5 5 . 5 ~ .As is apparent from the shape of the ZI defined as ZI = Ilt,ll& where tl is the vector of the single excitation amplitudes and Nval the number of valence electrons, this is a range of increasing importance of nondynamical correlation. The equilibrium dissociation energy calculated by CCSD(T) is De = 547.1 kJ/mol. It is smaller than the value for C5" by 50 kJ/mol. The zero-point vibrational contribution, obtained from this and our previous work on C30,25is 15 kJ/mol so that DO = 532 kJ/mol results. The latter value is expected to be accurate to ca. 5 kJ/mol. This error estimate is based on comparable studies for C5 and C30 where larger basis sets (up to full cc-pVQZ) could be employed. We also wish to note that the whole correlation effect on De makes up only ca. 20%. Vertical Ionization Energies. Vertical ionization energies (IE) for transitions to the lowest 21-1and 2,Z+ states of the C50+
A Theoretical Investigation of
J. Phys. Chem., Vol. 99, No. 24, 1995 9761
c50
TABLE 10: Vertical Ionization Energies for CsO (Basis: 234 cGTOs)" method
2z-+
KTb RHF RCCSD RCCSD(T)
12.994 9.499 9.927 9.974
2l-I 10.382 9.338 10.221 10.432
a Calculated at mixed experimentaYtheoretica1 equilibrium geometry (see text). Koopmans' theorem.
radical cation have been calculated by RHF and partially restricted open-shell coupled cluster t h e ~ r y . ' ~The , ~ ~mixed experimentdtheoretical equilibrium geometry for C 5 0 is employed in these calculations which make use of a larger basis set of 234 cGTOs. It is briefly described as spd(vqz) f(vtz) where obvious abbreviations are used for Dunning'~'~ basis sets. The results are given in Table 10. The RCCSD(T) results are expected to be accurate to ca. 0.05 eV. Other variants accounting for the effects of connected triple substitution^'^ lead to practically the same results. Upon inclusion of connected triple substitutions the first two vertical IEs are increased by 0.047 eV (*E+) and 0.21 1 eV (*lI). Both RHF and calculations making use of Koopmans' theorem (KT) yield an incorrect energetic order of the two lowest doublet states of the cation. As is frequently observed, KT works very well for the ionization out of the highest occupied n orbital but severely overestimates the ionization energy for ionization to the lowest *Cf state.
+
Conclusions
The carbon oxide C50, an unsaturated carbene with a linear cumulenic equilibrium structure, has been investigated by largescale coupled cluster calculations. Making use of experimental ground-state rotational constants for seven different isotopomers and theoretical values for the vibration-rotation coupling constants, calculated by second-order perturbation theory in normal coordinate space, an accurate equilibrium geometry (better than 0.001 A accuracy in bond lengths) has been established. C5O is probably the most complex linear molecule (five independent geometrical parameters) for which such an accurate equilibrium structure has been determined to date. A variety of spectroscopic properties have been predicted which should be of help to detect C 5 0 in the infrared region of the spectrum. The V I band with calculated origin at 2290 cm-' is a particularly promising candidate since it has a huge absolute IR intensity of 38 13 "01. The equilibrium dipole moment is predicted to be pe = 4.06 D. Like in CO or C30 the negative end of the dipole is located at the terminal carbon site. MP2 overestimates pe by as much as 13%. The potential curve for dissociation into fragments C2(X 'Eg+) and c @ ( x 'Eg+), a formally Woodward-Hoffmann allowed process, has been investigated by various methods. MP2 yields spurious results at larger separation. The vertical ionization energies of c50 are predicted to be 9.97 and 10.43 eV for ionization into the 2E+ and 211states of the cation, respectively. Koopmans' theorem produces an excellent result for n ionization but performs poorly (3.02 eV error) for the first 0 ionization. Acknowledgment. Thanks are due to Prof. H.-J. Wemer (University of Stuttgart) and Dr. P. J. Knowles (University of Sussex) for providing us with a copy of MOLPR094. Financial support by the Deutsche Forschungsgemeinschaft (through the SFB 357) and the Fonds der Chemischen Industrie is gratefully acknowledged. We thank the Regionale Rechenzentren at Hannover and Kaiserslautern for providing computation time. Thanks are due to Profs. Ogata and Endo for sending us information about their experimental work prior to publication.
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