Volume 67, number 2,3 CHEMICAL PHYSICS LETTERS 15 November 1979

ELECTRONIC STRUCTURE AND SPECTRUM OF CYANOGEN

Stephen BELL Department of Chemistry, University of Dundee, Dundee DD1 4HN, UK

Received 17 August 1979

Ab initio RHF calculations have been made with a double-zeta basis of contracted gaussian functions for the ground state +

of C2 N2, 40 excited states of different configurations and symmetries, and four states of C2 N2. The assignments of known UV absorption and PE spectra are considered in the light of calculated excitation energies.

1. Introduction

Although a number of electronic states o f cyanogen, ~ C2N2, have been characterized [ 1 - 5 ] , only a few ab initio electronic structure calculations have been made and these only for the ground state at the experimental geometry [6,7].

In the near ultraviolet region, four weak electronic transitions have been studied in some detail and there is clear evidence for assigning these as transitions .from the ground state to 3N+u(3000A ) [1], 3A u (2500 A.) [2], 1N u (2200 A) [3], and 1A u (2070 A) [4]. In the vacuum ultraviolet, a strong electronic transition with origin tentatively assigned at 1655 A shows considerable detail with some evidence pointing to the excited state being 1 iiu, i.e. an allowed transition from the ground state [5]. Another very strong electronic transition showing rather diffuse bands has its first band near 1320A [4] and must also correspond to a spin and symmetry allowed transition. Because of their relative ordering and intervals between them [8], the 2; u and A u states were thought to be all derived from a 7r3n electronic configuration, either lr3uTrg or 7rg3n u. As a re- sult of this, the 1320 A system of bands is tentatively assigned as transition to the 1 Z+ state of this electronic configuration, which is in agreement with being an al- lowed electric dipole transition from the ground state. A II u state must arise from a ~r 3 o or on configuration.

The photoelectron spectrum has also been studied in some detail [9,10]. The four photoelectron band systems with origins at 13.36, 14.49, 14.86 and 15.47

498

eV have been assigned to correspond with the 2 lIg, 2]~;, 2 + Z u and 2II u states of the ion, these assignments being made on qualitative grounds concerning the molecular orbitals and the appearance of progressions involving the stretching frequencies of the ion.

It is the purpose of this paper to report on ab initio SCF calculations of the ground state and several excited states of neutral C2N 2 and also four states of the C2N ~ ion. The calculated energies are used in an attempt to check on the assignment mentioned above. A subsidiary purpose of the paper is to test the procedures for cal- culating all the states of some electronic configurations of linear molecules with one and two open shells.

2. Procedure

All the calculations discussed below have been made on the Dundee University DEC system 10 computer using the Berkeley-Cal Tech-Ohio State version of POLYATOM [1 I ] , the SCF part of which includes the OCBSE method of Hay et al. [12] for the calculation o f open-shell states. Although all the results listed below were obtained as the lowest roots of particular occupa- tions and irreducible representations in the D2h point group, a useful facility of this program is that it allows the calculation o f higher roots of the same irreducible representations. This has been used in some calculations in the C2h and C2v point groups in the process of geom- etry relaxation or optimizations.

A double-zeta basis set was used for the calculations

Volume 67, number 2,3 CHEMICAL PHYSICS LETTERS 15 November 1979

where the (9s 5p) primitive set by Huzinaga [13] is contracted to [4s 2p] according to Dunning [14]. In order to study the Rydberg character of some of the high states, for some calculations a single set of Rydberg s and p functions was added at the centre of symmetry of the molecule, the s function having exponent 0.023 and the p functions exponent 0.021. Although this is not an extensive set of Rydberg functions, it is suffi- cient to indicate that some states are rather Rydberg in character and others are not.

No polarization functions have been added to the double zeta basis, since this set on its own gives good predicted geometries and excitation energies for a number of states. The method of geometry optimiza- tion and the results for the ground state, a few excited state and states of the ion will be reported in a subse- quent paper. All the results in the present report have been made at the experimental ground state r 0 geometry, rcc = 1.389A and rCN = 1.162A, as obtained by in- frared spectroscopy by Maki [15].

3. Electronic c o n f i g u r a t i o n s

In the ab initio study by Clementi and McLean [6], the electronic configuration of the ground state was found to be

1 2 2 2 2 2 2 2 2 2 4 4 Og lou2Og2Ou3Og 3Ou4Og4Ou5Og lrr u Drg ,

with the orbital energies of 4Ou, 5Og and lrr u being approximately the same and Drg a little higher. Table 1 contains the orbital energies obtained from calcula- tion of the ground state of C2N 2 (with the double zeta basis set). Since 21r u and 5o u are low lying virtuals, it is easy to assume that all the observed u states arise from excitation from the In orbital to those orbitals g There are, however, a large number of states arising from configurations that result from exciting an elec- tron from one of the highest four occupied orbitals to one of the lowest four virtuals but these all belong to the types 7r3~r, 7r3a, o~r and oo.

In order to calculate the states of these open-shell configurations with the proper equivalence and sym- metry restrictions, it is necessary to find the coefficients that allow the total energy to be written in terms of one-electron, hi, Coulomb Jii, and exchange Ki/integrals thus:

E = ~. 2fih i + .~. (2aiJii - bi/Kii). t l ,]

For the n37r configuration, Rose and McKoy [16] have shown how this can be done by working with real 7r x and 7rp functions rather than imaginary 7r+ and 7r_ functions and have derived the f, a, and b coefficients for the six states 3,1~+, 3,1]~-, and 3,1A of this con- figuration.

For the two states of a n3o configuration, the coef- ficients are given by the following matrices, where the row and column subscripts are i, j = 1 for the inner closed shell part of the function (o 2 say), L/" = 2 for the n 3 open shell and i, f = 3 for the o open shell.

311

O,

1II

l a n d a as for 3II , b =

, b ~-" 3

.

oo/

Notice that both 7r x and Try have the same coefficients and are thus in the same shell, whereas in the 17r32n case, 17rx, lny, 27rx, and 2Try are in separate shells. The energy expression used here is slightly different from that of Rose and McKoy where the f coefficient appears as a common factor. As well as employing imaginary rather than real functions, the coefficients given by Huzinaga [17] for 7r3a are incomplete due to n,rr- interactions being omitted.

For the two states of a on configuration, the coeffi- cients are given by the following:

3I/

f = ( 1 7 ~ ) , a = ~ , b : ' •

1II

1 g -

fandaasfor311, b= ½ ¼1 , 1

499

Volume 67, number 2,3 CHEMICAL PHYSICS LETTERS 15 November 1979

where subscripts i, j = 2 corresponds with the o shell and i, j = 3 with the n shell.

The states of the cyanogen positive ion o f interest to us arise from o or 7r 3 configurations only, and for the latter the coefficients are given by the following:

211 f = (1 ~), a = b = .

4. Results

For the ground state of cyanogen at the experimental r 0 geometry by Maki [15], the RHF energy obtained with the double-zeta basis is - 184.516153 hartree, which is better than the minimal STO result of Clementi and McLean [6] but a little higher (0.140 h) than the extended STO energy by McLean and Yoshimine [7]. The orbital energies from this calculation are given in table 1 in order to consider which excited configura- tions to calculate. The bonding character of some MO's are given as an indication of what kind of geometry change to expect on excitation.

The RHF energies of all the states arising from 12 different excited configurations have been calculated at the ground state geometry and are listed in tables

Table 1 Orbital energies for C2N2 in the ground state

Orbital Orbitalenergy Bonding character a) (hartree)

C-C C-N

log -15.68481 lo u -15.68481 2Og -11.38208 2o u - 11.38105 3ag -1.33201 3o u -1.31298 4Og -0.97888 4o u -0.63360 nb nb 5Og -0.61733 nb nb In u -0.61223 b b lng -0.50463 ab b 2n u 0.05684 b ab 5a u 0.22933 ab ab 2rig 0.31214 ab ab 6Og 0.36910 b ab

total -184.51615

a) b = bonding, nb = nonbonding, ab = antibonding.

2 and 3. The advantage of the particular SCF program used is that all of these excited states can be calculated variationally and with proper restrictions in D2h sym- metry, since although some states have the same overall symmetry they have different occupations. This study of several excited states of cyanogen is similar to the study by Dykstra and Schaefer [18] on glyoxal, with which it is isoelectronic, except that many of the states reported for glyoxal are not t ruly variational. As a test, however, some states were calculated as second roots

in C2v or C2h point groups and were found to give the same energy as the truly variational calculations in D2h.

The excited states are more or less in the order ex- pected, i.e. the median of each manifold of states is approximately in the order indicated by the orbital energies of the ground state, except for example, that 17r35Ouo states are lower than 5Og27r u states. The lowest excited states derive from a n3rr manifold of u symmetry,

17rg321ru, but these are part ly overlapped by namely states o f a 7r3~r manifold o f g symmetry, most of which

Table 2 RHF energies for the ground state of C2 N2 and excited states from 7ra~r occupations at the ground state r o geometry

Configu- State Energy Calc. AE Obs. To ration (hartree) (cm-1) (cm-l)

ln~ 1~;~ -184.516153

17r~ 2n u 3 ~ -184.316309 aA u -184.295381 aZ u -184.274684 1 Xu -184.274684 1A u -184.262789 1 y.~ -184.047233

Dr3u27ru aZ~ -184.204600 ~ ,~_ -184.185805

-184.167167 "16~ g -184.156300 1 ~ -183.995207

17r~2~rg 3 ~ -184.061955 aA --184.043320 3,Xgg --184.024930 IAg -184.015502 l ~ -183.859139

Drau2~rg 3 ~ -183.967686 3A u --183.946464 a,I~U --183.925394 1Au --!83.915533 x ~ -183.762672

0 0

43861 33289.9 48454 39868.9 52996 - 52996 45399.9 55607 48309

102916 75760

68378 -

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Volume 67, number 2,3 CHEMICAL PHYSICS LETTERS 15 November 1979

Table 3 RHF energies of the ground state, excited states from ~ratr and on occupations and ionic states at the ground state r 0 geometry

Configu- State Energy Calc. AE Obs. To ration (hartree) (cm -x) (cm-l)

lng l r ~ -184.516153 ln~5o u 311u -184.089683

IrIu -184.053398 5Og2rr u 3IIu -184.036202

111 u -183.995510 4Ou27r u 3II -184.019548

1 g Hg -183.973872 Drau5ou 311 -184.000207

1Hgg -183.959790 5Og5a u 31~ u -183.975850

1z u -183.962031 4Uu5O u 31~g -183.955807

1 ~ -183.948621 ln~6Og 3rI~ -183.909066

1 II -183.894654 3 g lnau6ag 11u -183.813263 lIIu -183.787374

0 0 93600 -

101563 60393

Ion (eV) (eV)

ln~ 2Hg -184.035367 13.08 13.36 5o~ 2 ~ -183.936950 15.76 14.49 ln~ 2Hu -183.930934 15.92 15.47 4u~ 2 ~ -183.920471 16.21 14.86

states are lower than the lowest II states, i.e. those from 1 lr 3 5 arising o u •

The RHF energies of the lowest four states of the ion, C2N~2 are also given in table 3. These states are in the order expected from the orbital energies of the ground state neutral species except that the middle two are reversed, but very close together in either case.

Vertical excitation energies have been calculated from the RHF energies for a number of states and these are listed in tables 2 and 3 with the observed wavenumbers of the origins, T O ("adiabatic" excitation energies) of the various band systems analysed. The assignment of the 3 + 3 2;u, A u, lY~ u and 1A u states ob- served by spectroscopy in the near UV as components of the llr321ru manifold appears adequately justified, although the calculated vertical excitation energies are consistently higher than the observed T O . However, from the intensity distribution in the band systems, observed vertical excitation energies should be about 3000 cm -1 higher than T 0. Geometry optimization

does, in fact, bring calculated and observed adiabatic energies into very good agreement. It should be noted that in the single configuration RHF approximation, the 3 y~- and 1 N- states of a 7r 3 rr manifold are dege- nerate because of having the same energy expression [16]. Although not expected to be degenerate in ob- servation, it is unlikely that bands due to transition to 31~ u will be observed among those to 1 Y'u since tran- sition to the former is likely to be weaker due to being spin forbidden.

It is noticeable that the lowest 1 ~+ and 1 l-Iu states have calculated excitation energies rather different from those tentatively assigned in the vacuum UV spectrum of cyanogen. The energies of these two states have been calculated to be quite close to the ground state of ion, as have quite a number of the other energies listed, and therefore they lie in the region expected for Rydberg transitions. To be calculated more correctly, the basis set should contain diffuse Rydberg functions and, even more correctly, configuration interaction between valence states and Rydberg states should be included.

Calculations have been made using the double zeta basis augmented by one set of 3s and 3p Rydberg functions centred between the C atoms for the ground state and for states of relevant excited configurations. The results are given in table 4. The states most affected by this addition involve the 6Og orbital which becomes almost pure 3s, while the energies are lowered by about 0.25 hartree. The states of interest to us for making as- signments are also significantly affected, the 11~+u state being lowered by 0.071 hartree which brings the excita- tion energy to within 12000 cm -1 of the observed T 0. The 2g u orbital becomes almost a pure 3p orbital in the 1 N+ state but all the other states involving 2~ u are lowered by 0.0015 hartree or less and have very small Rydberg coefficients in all MO's. The lowest 1 I] u state is lowered by 0.055 hartree which reduces the excita- tion energy considerably and brings some credibility to this excitation being responsible for the 1655 A band system. There are however three sets of 17 u states cal- culated in the one-configuration approximation to be close together, so that configuration interaction should bring the lowest 1 iI u state down further and hence into better agreement with the observed T O .

The first ionization energy calculated (removal of a ~g electron) is in good agreement with the photoelec- tron spectrum, and if the previous assignments of other PE band systems are accepted [9] the third ionization

501

Volume 67, number 2,3 CHEMICAL PHYSICS LETTERS 15 November 1979

Table 4

RHF energies of C2N 2 at the ground state r o geometry with a double zeta plus Rydberg basis

Configu- State Energy Calc. AE Obs. To ration (hartree) (cm-1) (cm-1)

ln~ 1 ~ -184.517369 0

llr~ 2n u 3X~ -184.317676 43828 3zau -184.296766 48417 3X u -184.276091 52955 1 ~u -184.276091 52955 IA u -184.264223 55559 1 ~ -184.118675 87503

17rau21ru 3Z~ -184.206164 ~,~1 gg -184.187345

-184.168679 1 A --184.157764 1Z~ --183.996458

l~r~6Og 3H --184.157008 1H g -184.154163

lzr~Sa u 3 g rl u -184.116871 87899 1flu -184.108525 89731

lnau6Og 3H u -184.055850 1H u -184.050291

50g27r u 3IIu -184.037086 1F lu -183.998435

l~rau5Ou 3rlg -184.015916 1Hg -184.005546

33289.9 39868.9

45399.9 48309 75760

60393

energy is also in reasonable agreement. However, these assignments are at variance not only with the ordering of orbital energies in the ground state but also the order of ionic states obtained by RHF calculations. The previous assignment is based on rather indirect evidence and certainly does not justify reordering the ground state orbital occupation [10]. Since the double zeta basis seems adequate to give the correct ordering of low lying states of the neutral molecule, it is disappoint- ing that it is not adequate for the positive ion.

Further work involving geometry optimization of a number states of cyanogen is being done. Further cal- culations with a better basis set need to be done for states shown to be Rydberg in character. Of particular interest for spectroscopic assignments is the potential function o f the lowest 11-1u for which calculations with more than one configuration may be necessary. We

may conclude at this point that where clear experiment- al evidence points to the spin and symmetry of an ex- cited state, the assignment has been corroborated by the above RHF calculations.

Acknowledgement

I would like to thank Professor H.F. Schaefer III for a copy of the version of POLYATOM employed and Dr. P.A. Warsop for provoking this study.

References

[1 ] J.H. Callomon and A.B. Davey, Proc. Phys. Soc. (London) 82 (1963) 335.

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[3] G.B. Fish, G.J. Cartwright, A.D. Walsh and P.A. Warsop, J. Mol. Spectry. 41 (1972) 20.

[4] S. Bell, G.J. Cartwright, G.B. Fish, D.O. O'Hare, R.K. Ritchie, A.D. Walsh and P.A. Warsop, J. Mol. Spectry. 30 (1969) 162.

[5] P.A. Warsop, unpublished work. [6] E. Clementi and A.D. McLean, J. Chem. Phys. 36 (1962)

563. [7] A.D. McLean and M. Yoshimine, IBM J. Res. Develop.

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(1973) 881. [9] D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle,

Molecular photoelectron spectroscopy (Wiley, New York, 1970).

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[11 ] D. Neumann, H. Basch, R. Kornegay, L.C. Snyder, J.W. Moskowitz, C. Hornback and P. Liebmann, QCPE 11 (1971) 199.

[12] W.J. Hunt, P.J. Hay and W.A. Goddard, J. Chem. Phys. 57 (1972) 738.

[13] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [14] T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [15] A.G. Maki, J. Chem. Phys. 43 (1965) 3193. [16] J.B. Rose and V. McKoy, J. Chem. Phys. 55 (1971) 5435. [17] S. Huzinaga, Phys. Rev. 120 (1960) 866. [18] C.E. Dykstra and H.F. Schaefer, J. Am. Chem. Soc. 98

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