Ab initio CI study of the electronic spectrum of the interstellar free radical CP

Chemical Physics ELSEVIER

Chemical

Physics 185 ( 1994) 39-45

Ab initio CI study of the electronic spectrum of the interstellar free radical CP Jim-ping

Gu ‘, Robert J. Buenker, Gerhard Hirsch

Bergische Universitdt-Gesamthochschule Wuppertal, Fachbereich 9, Theoretische Chemie, Gaussstrasse 20, D-42097 Wuppertal, Germuny

Received22 December, 1993

Abstract Thirteen electronic states of the interstellar free radical CP have heen studied by ab initio MRD-CI calculations, most of them for the first time. All the doublet and quartet states studied are found to be hound states. The molecular constants of all these states, the first five vibrational levels of the six lowest-lying states and the transition probabilities between these levels are also reported. The calculations indicate that there are three quartet states which lie below the experimentally reported B ‘2 + state but have not yet been observed.

1. Introduction The CP radical is an interstellar species which was detected in the carbon star envelope IRC + 10216 in 1990 by GuBlin et al. [ 11. The B *x+-X *s’ transition of CP was observed in the laboratory by Herzberg as early as in 1930 [ 21. There are quite a few experimental studies for the B *x+-X *C+, B *x+-A *II and A *IIX *Z’ transitions of CP [ 2-71, and the spectroscopic constants for the lowest three doublet states have been determined accurately on the basis of these measurements. Theoretically, empirical methods were used in early studies [ 8-131 in order to determine potential curves, Franck-Condon factors and r-centroids for the CP radical. Later, ab initio calculations were carried out for this system [ 14-181, and properties, including the dipole moment [ 151 and hyperfine constants [ 16,171 of the ground and the first excited A *II states have ’ On leave from: Departmentof Modem Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China. 0301-0104/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIO301-0104 (94)00108-M

been studied. Nevertheless, to date all the experimental studies have been limited to the three lowest-lying doublet states, while the theoretical work has only focused on the X ‘2 + and A *II states. In this paper, we present results of our ab initio multireference single- and double-excitation (MRD-CI) calculations for thirteen low-lying electronic states of the CP radical. The MRD-CI potential curves, vibrational frequencies and other spectroscopic constants for these states are reported, as well as Einstein coefficients and f values between different vibrational levels of some low-lying electronic states. This information should prove valuable for future experimental investigations of the CP radical in the laboratory as well as aiding in the search for this radical in the interstellar environment.

2. Computational

details

The A0 basis employed for tbe carbon atom is the (9s5p) Cartesian Gaussian set contracted to [ %3p]

J. Gu et al. /Chemical Physics185 (1994) 39-45

40

given by Dunning [ 191, augmented by ad polarization function with exponent 0.63 a&’ [ 201, together with one 3s (0.023 aG2) and one 3p (0.021 a;*) Rydberg function [ 21 I. For phosphorous, the primitive ( 12s9p) basis of McLean and Chandler [22] in a [6s5p] contraction has been augmented by a single d polarization function with exponent 0.43 a; 2 [ 201, and 4s (0.020 ai2), 4p (0.017 ug2) and 3d (0.015 ui2) Rydberg functions. Thus a total of 61 contracted functions are employed in the present calculations. Some additional tests have been carried out at a single internuclear distance with a large A0 basis to which an extra d and f function has been added for each atom. Self-consistent field (SCF) calculations have been carried out first to obtain the molecular orbitals which are needed in the ensuing CI calculations. The 61;+ state with the (core) 5~~6a~2~~7a’37~~ configuration has been employed for this purpose. Additional tests have also been carried out with the SCF-MOs of the 2C+ ground state in order to assess the dependence of the final results in this aspect of the theoretical treatment. The CI wavefunctions are generated with the MRDCI approach, including configuration selection and energy extrapolation [23,24] and using the Table CI algorithm [ 25-271. A selection threshold of T= 5.0 pE, is employed throughout. The six lowest molecular orbitals corresponding to the 1s of both phosphorous and carbon and 2s and 2p orbitals of phosphorous are always held doubly occupied, whereas the two highestTable 1 Technical details of the MRD-CI calculations CzV symm.

%*

4& hA, %.*

N,rIN,,

energy orbitals are discarded. Additional technical details of the MRD-CI calculations are listed in Table 1.

3.1. Potential curves Key configurations of different electronic states, together with the values of the squares of their respective CI coefficients have been listed in Table 2, for an internuclear distance of 3.0 a,,. Even with the SCF MOs of the 6z+ state, which have been employed throughout, there is a general tendency away from the conventional situation in which only a single configuration dominates for a given electronic state. The situation is worse for 2C+ SCF-MOs, however, as is most easily seen from the fact that the sums of coefficient squares of reference configurations (Cc;) are uniformally lower (by l-2%) in the corresponding CI calculations as for those on which the %’ orbitals are employed (Table 1) Potential curves for these states have been calculated in the 2.5-5.0 a0 range of internuclear distance and are shown in Fig. 1. The computed molecular constants for these states are listed in Table 3. The corresponding results obtained with the *C+ MO basis are quite similar, especially with regard to T, values (discrepancies of no more than 0.1 eV having been noted for any of the states listed). Computed bond

’ SAFIOT/SAFSEL

5013

922901/11228

7513

1485187/12633

3112

872158/8216

1912

454335 16667

58/l 3212 4/l 22/l

3. Results and discussions

1490309/5388 52194616861 102952/4583 46130714874

C,. notation

xc:

X2’ B2X:’ A% 2% 3% 1 2x_ 1 ‘A 1%’ 14A 1w l?V l%+ 1Q

0.903-0.926 0.905-0.915 0.901-0.923 0.905-0.917 0 905-0.920 0.903-0.911 0.905-0.928 0.908-0.923 0.905-0.919 0.909-0.926 0.903-0.918 0.9 12-0.932 0.901-0.921

’ The number of selected SAFs are given for r= 3.0 a,,, SAFTOT designates the total number of generated, SAFs. N,, and N,, refer to the number of reference configurations and roots treated, respectively.

SAFSBL the number of selected

.I. Gu et al. /Chemical Physics 185 (1994) 39-45 Table 2

Importantconfigurations for the electronic states of CP and respective squares of the coefficients for r= 3.0 a, State

Configuration

c2

X5’

. .50=2n’60=70’

0.64 0.21 0.15 0.48 0.14 0.62 0.26 0.39 0.30 0.25 0.42 0.81 0.11 0.79 0.81 0.78 0.10 0.80 0.92 0.80

BT’

A21-I 2% 3% 12P1 =A 1%’ 14A 1% 1%1 %x+ 1%

. . .5a22?r36a210’3n’ .. .5u22rr46u’lu= . .5u22n36u27u’3n’ .5u22n’6u’7c?3n’ .5u22n’6$7u= ...5u22n26c?7~3n’ .5u22n26~7u23n’ ...5ti2n46ur3n’ ...5u22&6$3n’ ...5u22n26u27~3n’ . ..5u=2~‘6cr=lu’3rrrr’ ..5u?kr36$7u’3n’ . ..5u%‘6u=7u’3~’ . .5u??,ir36~7~3rr’ ...5&&&7o23n’ .5u%r16~u23n2 .5u22n36r?7u’3n’ ..5n22~=6u21u’3rr2 ..5u22~26u27u’3rr’8cr’

lengths are also in good agreement in the two treatments ( f 0.01 A, except for very flat potential curves). The results for vibrational frequencies are less consistent, with discrepancies as high as 100-200 cm-’ in some cases, but again the values obtained with the %$+ MOs given in Table 3 would seem to be clearly preferable in view of the more compact representations for the corresponding electronic wavefunctions which they provide. The tests with the larger A0 basis at a single r value of 3.50 a~ (employing %’ MOs) lead to only relatively minor changes in the relative energies of the states listed in Table 3, with a maximum discrepancy of only 0.07 eV. It was therefore decided to carry out the remaining calculations exclusively with the smaller A0 basis and a CI treatment employing %+ SCF-MOs in each case. The ground state of CP has a configuration of (core) 5a26u22&7a1. The calculated equilibrium bond distance is 1.5895 A, which is somewhat larger than the experimental value of 1.56198 A [7]. The first excited state A 211 is formed by IWJ excitation. The T, value of 7225.3 cm-’ (0.896 eV) computed for this state may be compared with the experimental value of 6972.5 cm- ’ [ 71. Spin-orbit coupling calculations have also been carried out for this state with the aid of

41

effective core potentials and a somewhat simpler theoretical treatment, as will be discussed in the next subsection. To date experimental molecular constants are only available for the three lowest doublet states of CP: X 2Z$+, A 211and B 2x’. In comparison with the experimental values (see Table 3) the calculated equilibrium bond distances for these three states are found to be 0.02-0.03 A too large in each case. Errors in the computed T, values are in the order of 400 cm- ’ (0.05 eV) . The two main sources of error in the calculations are the choice of A0 basis and the neglect of core-valence correlation effects. The accuracy of the present results would still seem to be quite acceptable on this basis. Three quartet states, 1 4x+, 1 411 and 1 4A, are found to lie between the X 2x + and B 2X + states. The computed T, value of the lowest quartet state, 1 4c+, is 2.406 eV. Electric dipole transitions between these E/E)

-0.4

-0.5

-0.6

-0.7

7 2.5

I

3.0

3.5

I

4.0

4.5

r/a0

Fig. 1. Computed potential energy curves (T= 0) of electronic states of CP. In addition to the twelve low-lying states, the 1 en state is also included because it is strongly repulsive towards the lowest dissociation limit. The energy is given with respect to - 378.0 E,,.

42

J. Gu et al. /Chemical

Physics 185 (1994) 3945

Table 3 Calculated and experimental a spectroscopic properties of CP: bond lengths r,, vibrational dipole moments p (calculated at the respective r, of the states)

frequencies

o,, transition energies

T. and electric

state

r, (A)

w, (cm-‘)

T, (ev)

F (e 4

X%’

1.5895 (1.56198) 1.6724 ( 1.65442) 1.7549 1.9119 1.7478 1.7178 ( 1.6894) 1.9044 2.0009 1.7435 1.9217 1.7499 1 7725

1243 (1239.799) 1062 (1062.471) 891 675 882 832 (836.32) 655 525 841 672 798 783

0.0 0.0 0.896 (0.864) 2.406 3 378 3.442 3.565 (3.6078) 4 002 4.041 4.108 4.715 4 773 4.831

- 0.3099

AZII 14Zf 1% 1 4A B%’ 2% 1 ?z+ 1?3% 1% 1 ‘A a The experimental

data (from ref.

- 0.2280 -0.7551 - 0.2158 - 0.5764 - 0.8333 - 0.5068 - 0.2077 -0.7312 - 0.2042 -02216

[ 71 for X ‘2’ and A *H states and from ref. [28] for B %+ state) are given in parentheses.

states and the lower doublets, X *C+ and A 211, are spin-forbidden. These quite low-lying quartet states have apparently never been observed experimentally. It can be seen from Fig. 1 that there are at least two avoided crossings of importance for the 2 ‘II and 3 *II states, occurring in the 3.0-3.2 a0 region. The one near r = 3.2 a0 involves a higher-lying 211species, while that near r= 3.0 a, is between the 2 %I and 3 *II states themselves. Finally, there is one sextet ( 1 ‘?Z+) state which has a T, value of 4.041 eV among the calculated species. The state has a large equilibrium distance of about 2.0 A and a rather shallow potential well. All other computed low-lying doublet and quartet states shown in Fig. 1 are seen to be bound by a fairly substantial margin. We have also calculated the 1 % state, which is strongly repulsive to the lowest dissociation limit C( 3P,) + P( 4S,). For shorter bond distances there are more states lying between the twelve lowest-lying species treated here and the 1 % state. 3.2. Spin-orbit state

- 0 8684

interaction calculation for the A *II

The zero-field splitting for the A *II state has been measuredtobe158.3cm-’ [28].Inthiscase,wehave carried out additional calculations which take the spinorbit interaction into consideration. The same basis set

has been used as above, but the relativistic effective core potentials of Patios and Christiansen [ 291 have been employed in addition. The spin-orbit matrix elements have been calculated at r values from 2.6 to 4.0 a0 between the two components of the A 211 state, as well as between the X ‘2 * ground state and both A ‘II components. A 3 x 3 secular equation has then been solved on this basis upon including the electrostatic and other spin-independent interactions. The *II zero-field splitting thus computed is found to vary relatively slowly with internuclear distance. Its value at the calculated r, value is 159 cm-- ‘, which is in very good agreement with the observed result. 3.3. Vibrational energies of low-lying electronic states and transition probabilities The calculated potential curves have been fit to polynomials and standard numerical techniques [ 30-321 have been employed to compute the corresponding vibrational energies and wavefunctions. The first five vibrational energy levels of the six lowest-lying electronic states are given in Table 4, together with the corresponding experimental values of Ram et al. [ 71. The vibrational frequency w, of the ground state obtained thereby is 1243 cm-- I, which can be compared with the corresponding experimental value of 1239.799 cm- ’ [ 71. In general there is quite good agreement

J. Gu et al. / Chemical Physics 185 (I 994) 39-45 Table 4 The first five vibrational energy levels (cm-‘)

state

43

of the six lowest-lying electronic states of CP ’

Vibrational energy levels u=o

v=l

v=2

v=3

u=4

X3+

0 0

1%’ 1% 14A B%’

0 0 0 0

2437 (2438.6) 2079 (2088.8) 1739 1306 1721 1627

3630 (3637.3) 3095 (3115.1) 2585 1934 2560 2421

4805 (4822.4)

A%

1227 (1226.1) 1047 (1050.4) 877 661 868 820

(zz.3) 3416 2544 3385 3201

’ The experimental data from ref. [ 71 are given in parentheses.

between the measured and computed vibrational spacings for the X ‘I%’ and A 211 states. The electronic dipole transition moments RerE between the three lowest doublet states and those between the three lowest quartet states have been calculated as a function of the CP internuclear distance as well. Using these data, the Einstein spontaneous emission coefficients A,.,. (s -‘) between various vibrational levels u ’ of the upper electronic state and u” of the lower electronic state are obtained as (with m in au) A “sow=getd 2.1419x

10+‘“(bE)3S,,,.

,

(1)

where SU~Um = I (x”N(r)R,,/(r)x,,(r))

I’

(2)

is obtained by using a polynomial fit to the discrete data for the electronic transition moment R,.,. and the vibrational wavefunctions x,(r) generated for respective pairs of electronic states [ 30-321. The factor gefE is derived from the fact that the transition moment used in the calculation is only for one component of a given degenerate system. Thus g,,,” equals one for the and A ‘II --) X ‘2 + transitions, but B 2~++X2~+ two for the B 2x’ + A 211transition. The radiative lifetime rU, of the vibrational level of the upper electronic state is obtained as .I 9

(3)

where the sum runs over all vibrational levels which can be reached among lower-lying electronic states.

The oscillator strength cfvalue) tion process is obtained as

fur,- = $g’,,,-

hE S,.,. ,

for a given absorp-

(4)

where the degeneracy factor g:,,” is introduced for the same reason as in the calculation ofA,,,. . In this present case, g:,,” equals one for B ‘Z+ +X ‘I;+ and two for the A 211+ X ‘c + transition. The computed f values for various pairs of vibrational levels in different electronic transitions are given in Table 5, while the corresponding data for Einstein coefficients and radiative lifetimes are shown in Table 6. There are no experimentally reported vibrational intensities for the CP spectrum. It is possible to compare the present results with theoretical data obtained in ref. [ lo], specifically for the lifetime of the first vibrational levels of the A ‘Il and B 21: + states and for foe values between these two states and the X 2Z’ ground state. In general, there is a reasonably good correlation between the two sets of results, especially for the lifetimes. Since a constant value of 1.O debye for the transition moments is employed throughout in ref. [ 101, however, it is not surprising that the two sets of results are not completely consistent with one another. If we compare the Einstein coefficients for different pairs of states in Table 6, it can be seen that the intensitiesoftheB2~++X2C+andB2~++A211transitions are larger than those of A 2II-X ‘2 + . And, generally speaking, the intensities between doublet states are larger than those between quartet states. The present results are certainly consistent with the fact that the B 21;‘-X 2Z’ and B 2Z’-A ‘II transitions were already observed in the 1930s [ 1,21, whereas the

44

J. Gu et al. /Chemical

Table 5 Calculated oscillator strengths&

A %--X *8 +

0

0.110x 0.944x 0.338X 0.640~ 0.634~

lo-* 1o-3 1o-3 1O-4 lo--’

0.126~ 0.104x 0.488~ 0.479x 0.152~

lo-* 1o-5 1O-3 lo-) 1O-3

0.814~ 0.478x 0.292x 0.924X 0.412~

1O-3 lo-’ 1O-3 1O-4 1O-3

0.395x 0.856~ 0.269 x 0.449x 0.179x

1o-3 1O-3 lo-+ lo-? 1o-5

0.160~ lo-’ 0.711 x lo-’ 0.463X 1O-3 0611~10-~ 0.338~ 1O-3

0.770 x 0.133 x 0.117x 0.663 x 0.265 x

10-3 10-Z 10-Z lo-’ 1O-3

0.182~ 0.927X 0.177x 0.257 x 0.554x

lo-’ 10-j 1o-4 1O-3 1o-9

0.227~ 0.412X 0.552X 0 504x 0203x

lo-* lo-.’ 10-j 10-j 1O-4

0.199x 0.355x 0.735x 0.202x 0.384~

1o-z 10-J 1o-3 10-h 1O-3

0.139x 1o-2 0.127 X lo-* 0 122x 10-3 0.468~ lo-’ 0253x10-’

0.186X 0.403x 0.623 x 0.516~ 0.503x

1o-2 1o-3 1O-4 lo-’ 1o-6

0.573x 0.938~ 0.547 x 0.151 x 0.189~

1o-3 1O-3 lo-? lo-’ 1O-4

0 660X 0.883x 0 394x 0.540x 0.237X

1o-4 1O--3 1o-3 10-Y lo-”

0.210x 1o-5 0.199x 1o-1 0.964X 10-j 0.111 x10-j 0.449x lo-’

0.247 X 0.138 x 0.362~ 0.878 x 0.772 x

lo-’ 1O-4 1O-3 lo-’ 1o-5

0.936X 0 214x 0.215 x 0.124x 0.452 x

1O-4 10-j 10-3 lo-’ lo-”

0.227 x 0.191 x 0.123~ 0.427x 0.110x

1O-3 1o-3 lo-“ lo-“ 1o-3

0.304x 0.444x 0.592~ 0.106X 0.583 x

lo--’ 1o-4 lo-“ lo-’ lo-’

0.300x 0.330x 0.133x 0.754x 0.606X

0.242 x 0.737 x 0.764 x 0.350x 0.700 x

lo-? 1o-4 1o-4 1o-4 lo+

0

0 2 3 4

1 ‘Q-1 ‘% +

v’=l

v’=O

2 3 4 B%+-A%

for transitions between different low-lying electronic states of CP

0”

2 3 4 B %+-X22+

Physics 185 (1994) 39-45

0 2 3 4

Table 6 Calculated Einstein coefficients A,,,,,

(in s -

v’=2

v’=4

v’=3

1o-3 1o-5 10-j 1o-5 1o-4

I ) for transitionsbetween different low-lying states of CP and corresponding lifetimes T,, (in s)

(jII

cl’=0

v’= 1

A ‘l-I-X % +

0 1 2 3 4 T( A *l-I)

0.188X 10fS 0.111x10+~ 0.252 X 10f4 0.267~ 1O+3 0.118~ lo+* 0.306X lo+“

0.283 x 0.170x 0.542~ 0.334x 0.588 x 0 265 x

lo+’ lo+* 1O+4 1o+4 lo+’ lo+“

0.232 X 0.102 x 0.450x 0.968 x 0.270 X 0.236 X

1O+5 lot5 10f4 1O+3 1O+4 1O+4

0.138 x 0.232 x 0.548 x 0.656X 0.177x 0.214~

10’” 1O+5 1O+3 1o+4 lo+* 1O+J

0.675 x 0.238 x 0.120x 0.118~ 0.467X 0.197x

lo+“ lo+’ 1O’j 10f4 lot4 1o+4

B *Z+-X28+

0 1 2 3 4

0.418X 0.665x 0.532X 0.275 X 0.997 x

0.105 x lo+’ 0.490x 1o+6 0.858x 1O+4 o.114x1o+6 0.223 x 10f6

0.138 x 0.230~ 0.283 x 0.237 x 0.871 X

lo+’ lo+’ 1O+6 10+h 1O+4

0.127 X 0.209~ 0.399 x 0.101 x 0.175 x

lo+’ 1O+6 lot6 lo+’ lot6

0.932X 0.787~ 0.699x 0247X 0.123X

10” lo+” 1O+5 10+h lOi’

B%+-A%

0 1 2 3 4 T(B%+)

0.114x lo+’ 0.223 x 1O+6 0311x10”~ 0:231x 1O+4 0.201 x 10+3 0.292x lo+’

0.378 X 0.562~ 0.296x 0.740x 0.831 x 0.290x

1O+6 1O+6 1O+6 1o+5 1O+4 10f6

0.466~ 0.569 x 0.231 x 0.286~ 0.113x 0.284~

lo+’ 1O+6 IO+” 10c6 lo+6 lo+”

0.158X 0.137 x 0.607 x 0.638X 0.233 X 0.279~

10f4 lot6 1O+6 10” 1O+6 lo+’

0.200x 0.102x 0244x 0.541 x 0.433 x 0.277~

1o+2 10’ 5 1o+6 1o+6 1oc4 10c6

1%-l

0 1 2 3 4 7(1%)

0.186X 0.336x 0.258 x 0.110x 0.281 x 0.108x

0.534x 0.360~ 0.182X 0.481 X 0.909x 0.901 x

1o+4 1O+4 lo+? lo+’ 1o+3 1o-4

0.830X 0.986X 0.105x 0.147x 0.615 X 0.787 X

lot4 1O+3 1o+4 1o+4 lo+’ 1O-4

0.933 x 10f4 0.849X lo+* 0.279 X 1O+4 0.126~ lo+’ 0.789x lo+’ 0721x10-“

%’

10+h 1O+6 1O+6 1O+6 1o+5

1o+4 lot4 1O+4 1o+4 1O+3 1O-3

v/=2

u’=3

v’=4

0.851 x 1O+4 0.217X 1O+4 0.186X 1o+4 0.691 x 1O+3 0.110x 1o+4 0.667 X 1O-4

J. Gu et al. /Chemical

A%-X*1:+ transition was not reported until 1987 [ 61, and also that transitions between the low-lying quartet states 1 411 and 1 4);+ have not yet been reported.

Acknowledgement The authors wish to thank Dr. Yan Li for helpful discussions and Mr. P. Liebermann and Mr. P. Funke for their technical support which was essential to this work. This work was supported in part by the Deutsche Forschungsgemeinschaft in the form of a Forschergruppe grant. The financial support of the Fonds der Chemischen Industrie is also hereby gratefully acknowledged.

References [ 1] M. Guelin, J. Cemicharo, G. Paubert and B.E. Turner, A&on. Astrophys. 230 (1990) L9. [2] G. Herzberg, Nature 126 (1930) 131. [3] H. Baenvald, G. Her&erg and L. Her&erg, Ann. Phys. 20 (1934) 569. [4] A.K. Chaudhry and K.N. Upadhya, Indian J. Phys. 43 (1969) 83. [5] R. Tripathi, S.B. Rai and K.N. Upadhya, Pramana 17 (1981) 249. [6] R.S. Ram and P.F. Bemath, J. Mol. Spectry. 122 (1987) 282. [7] R.S. Ram, S. Tam and P.F. Bemath, J. Mol. Spectry. 152 (1992) 89. [8] R.F. Borkman, G. Simons and R.G. Parr, J. Chem. Phys. 50 (1969) 58. [9] P.D. Singh and A.N. Pathak, Indian J. Pure Appl. Phys. 7 (1969) 132. [lo] T. Wentink and R.J. Spindler, J. Quantum Spectry. Radiat. Transfer 10 (1970) 609. [ll] N.S.MurthyandB.N.Murthy,J.Phys.B3 (197O)L15.

Physics 185 (1994) 39-45

45

[ 121 N.S. Murthy, L.S. G0wdaandB.N. Mm-thy, Pmmana6 (1976) 25. [ 131 L.S. Gowda and N.S. Murthy, Indian J. Pure Appl. Phys. 14 (1976) 238. [ 141 S. Wilson, Astrophys. J. 224 (1978) 1077. [ 151 C.M. Rohhing and J. Almlof. Chem. Phys. Letters 147 (1988) 258. [ 161 L.B. Knight Jr., J.T. Petty, S.T. Cobranchi, D. Feller and E.R. Davidson, J. Chem. Phys. 88 (1988) 3441. [ 171 K.W. Richman, Z.G. Shi and E.A. McCullough, Chem. Phys. Letters 141 (1987) 186. [ 181 A.D. McLean, B. Liu and G.S. Chandler, J. Chem. Phys. 97 (1992) 8459. [ 191 T.H. Dunning Jr., J. Chem. Phys. 53 ( 1970) 2823. [20] B. Roos and P. Siegbahn, Theoret. Chim. Acta 17 ( 1970) 199. [21] T.H. Dunning Jr. and P.J. Hay, in: Methods of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 1. [22] A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [23] R.J. Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33; 39 (1975) 217. [24] R.J. Buenker, S.D. Peyerimhoff and W. Butscher, Mol. Phys. 35 (1978) 771. [25] R.J. Buenker, in: Proceedings of the Workshop on Quantum Chemistry and Molecular Physics, Wollongong, Australia, ed. P. Burton (University Press, Wollongong, 1980). [26] R.J. Buenker, in: Studies in physical and theoretical chemistry, Vol. 21. Current aspects of quantum chemistry, ed. R. Garbo (Elsevier, Amsterdam, 1981) p. 17. 1271 R.J. Buenker and R.A. Phillips, J. Mol. Struct. THEGCHEM 123 (1985) 291. [ 281 K.P. Huber and G. Her&erg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, Princeton, 1979). [29] L.F. Patios and P.A. Christiansen, J. Chem. Phys. 82 (1985) 2664. [ 301 S.D. Peyerimhoff and R.J. Buenker, Theoret. Chim. Acta 27 (1972) 243. [31] R.J. Buenker, S.D. Peyerimhoff and M. Per% Chem. Phys. Letters 42 (1976) 383. [32] M. PeriC, R. Runau, J. Remelt and S.D. Peyerimhoff, J. Mol. Spectry. 78 (1979) 309.