3

International JOU~M~ of ilhss Spectrometry 0 Elsevier Scientific Publishing Company,

and Ion Physics,

Amsterdam -

ENERGIES OF DOURLY-CHARGED USING HAM/3

L. &BRINK, Department

32 (1979)

93

93-96

Printed in The Netherlands

MOLECULAR

IONS CALCULATED

C. FRIDH and E. LINDHOLM of Physics,

(Received 21 December

Royal

Institute

of Technology,

S-100

44 Stockholm

(Sweden)

1978)

ABSTRACT The energies of some doubly-charged molecular ions are cakulated using the new semiempirical MO method HAM/3. The calculated energies are compared with the corresponding mass-spectrometric appearance potentials and energies from Auger spectra Both small molecules (Nz, CO, HzO, NH 3, CO*, N20 and CsO2) and large molecules (benzene, toluene and naphthalene) have been considered.

INTRODUCPION

Doublycharged positive molecular ions have not received a great deal of attention in the literature. The recent “Energetics of Gaseous Ions” [l] tabulates only 34 such ions composed of the atoms H, C, N, 0 or F. Half of these are large hydrocarbon ions. One reason for the lack of interest in these ions is that it is often difficult to discriminate between these and fragment ions in the mass spectrometer. Another reason may be that the experimentalist cannot usually derive aid from theoretical studies, since very few calculations of the appearance potentials of such ions have been performed. A theoretical method for the rapid and cheap estimation of such appearance potentials would therefore be of great value. It will be shown below that the new semiempirical method HAM/3 goes a considerable way to fulfilling these criteria. Another field of research in which doublycharged ions play an important role is Auger spectroscopy [2]. The minimum energy required to produce doublycharged ions has been tabulated for a number of molecules [ 33. THE HAM/3

METHOD

One reason why calculation of the energies of doublycharged molecular ions has appeared so difficult is that the correlation energy change is large, and Roopmans’ theorem cannot be used for two-electron transitions-It is

therefore desirable to use a semi-empirical method in which the correlation energy error has been compensated. This is done in HAM/3 in a unique way, i.e. before the ;nolecular quantum-chemical method is developed. The method could therefore prove useful in the extreme case of double ionization. The HAM/3 method [4-81 is based upon a study of the atoms comprising the molecule. The atoms are treated according to a concept introduced by Slater in 1930 [9,10]. He calculated the total energy of the atom from the effective nuclear charge for each of its electrons by the use of shielding constants. In HAM/3 this idea has been extended by replacing the shielding constants ovP by functions 0 v/J =0 VP-

(b”,

+ c,,-Ws,

where cP is the orbital exponent of the shielded electron, 2 is the nuclear charge and a, 6 and c are constants, different for the ten shielding situations (between Is and 2s, between Is and 2p,, and so on)_ In this way very good agreement can be obtained with the total energies from atomic spectroscopy, not only for ground state atoms but also for a large number of ionized and excited atoms. The average error over 311 atomic states from H to Ne is only 0.16 eV. The good agreement shown for multiply-charged atoms is the basis of the success of the HAM/3 method for doubly-charged molecular ions. A molecular theory has been built up from this atomic study. Molecular parameters for the different bonds (CC, CN, CH, Nl? and so on) have been introduced in addition to the atomic parameters. These molecular parameters have been determined mainly from molecular ionization energies measured by photoelectron spectroscopy. Since the calculated atomic total energies are in good agreement with experiment, it is reasonable to expect that the calculated molecular total energies wilI display a similar agreement with experiment due to the use of the same parameters a, b and c. Ionization energies cannot be obtained by use of Koopmans’ theorem, but can be found by subtracting the total energies calculated for the ionized and the neutral molecule. For details see previous papers. The computer program is available at several laboratories. APPEARANCE

POTENTIALS

OF DOUBLY-CHARGED

MOLECULAR

IONS

The total energies have been calculated for several molecules and their doublycharged ions using the HAM/3 program. The difference gives the appearance potential (AP) directly. The results for a number of molecules are presented in Table 1, together with experimental data from mass spectrometry and Auger spectroscopy. The agreement is reasonable, especially for the larger molecules. The com-

95 TABLE

1

Energies (eV) of doublycharged positive molecular ions, calculated using the semiempiricai method HAM/3 and compared with results obtained by mass spectrometry (MS) and

Auger spectroscopy

Moiecuie

Calculated AP

Tabulated MS value

Recent MS value

111 N2 co H2O NH3 co2 N20 c302 CZHB

Benzene Toluene Naphthalene

42.04 39.48 40.84 32.84 37.83 34.86 29.12 30.85 25.12 24.37 22.15

43.5; 41.5; 33.7 38.0; 36.4 33.0 26.0 23.5 22.7;

42.7 41.8

36.4;

36.3

42.9 41.8

1111 [12]

34.4 37.2

[13] 1141

Auger electron value 42.9 39.9; 39.2

[S] 40.2 [33

[3]

37.8;

37.4

[3]

29.5; ~34.8 ~26.1

29.9 [IS] [16]

[ 151

22.8

puter times are also reasonable: 1.8 s for N2 and 62 s for naphthalene. A few computational details can be added. Since the lowest unoccupied orbital and the highest occupied orbital in the doublycharged ion often differ very little in energy, it is necessary to consider the interaction with the doubly-excited state. The configuration interaction matrix element Ria is small for all molecules in Table 1 and has therefore been neglected. It can further be noted that the doubly-charged state is probably a triplet in. the case of NZ and benzene. In this case the energy change is small and can again be neglected. ACKNOWLEDGEMENT

The authors cil for support.

are indebted

to the Swedish

Natural Science

Research

Coun-

REFERENCE9 1 2 3 4 5 6

HM. Rosenstock, K. Draxl, B.W. Steiner and J.T. Herron, Energetics of Gaseous Ions, J. Phys. Chem. Ref. Data, Suppl. 1, 6 (1977). T.A. Carlson, Photoelectron and Auger Spectroscopy, Plenum Press, New York, 1975. W.E. Moddeman, T.A. Carison, M.O. Krause and B.P. Pullen, J. Chem. Phys., 55 (1971) 2317. L. &brink, C..Fridh and E. Lindholm, Chem. Phys. Lett., 52 (1977) 63, 69, 72. L. &brink, C. Fridh and E. Lindholm, Z. Naturforsch.. Teil A. 33 (1978) 172. L. &brink. C. Fridh and E. Lindhoim, Int. J. Quantum Chem., 13 (1978) 331. .

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Magnusson,

L.O.

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Relat.

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