Energies of .sigma.* orbitals - The Journal of Physical Chemistry (ACS

J. Phys. Chem. 1991,95, 3923-3941 fluorophorp in cell biology and medical applications, Its exceptional Stokes shifts, producing emission wavelengths well into the visible region,greatly enhanceits potential utility - h u e other cell components can emit background light at shorter wavelengths when irradiated in the near-UV. At the same time, these Stokes shifts can foster ultrafast nonradiative relaxation‘ when a TICT state is used as the basis for the solvatochromism, reducing the fluorescence quantum yield in polar environments. In the case of indene 1, polar solvents (e& THF) diminish its quantum yield by a factor of -10 in comparison to nonpolar environments. Conversely, TICT states may serve as efficient fluorophores in hydrophobic environments, a s illustrated by 7-(diethylamino)coumarins in solutions of bovine serum albumin.3o When com-

Energies of

O*

3923

plexed with albumin, these molecules display a t least IO-fold increases in fluorescence yield over these in aqueous solution.

Acknowledgment. The Ames Laboratory is operated for the U S . Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences (W.S.S.) and by a grant from the National Institutes of Health (PHS 5R37 DKl5556, to J.A.K.). G.M.A. was supported by the Hazel I. Craig Fellowship of the Medical Scholars Program of the University College of Medicine a t Urbana-Champaign. (30) Nag, A.; Bhattacharyya, K. Chem. Phys. Le??.1990, f69, 12.

Orbitals

Einar Lindholm,f k i f Asbrink,* and Stig Ljunggren**g Department of Physical Chemistry and Department of Physics, Royal Institute of Technology, S - IO0 44 Stockholm, Sweden (Received: March 16, 1989)

In order to find the energies of u* orbitals we have parametrized a semiempirical method (CNDO) to give orbital energies for occupied and unoccupied orbitals, which can be interpreted as negative ionization energies and electron affinities, respectively. Experimental ionization energies, electron affinities, and UV excitations have been used for the parametrization. During the parametrization procedure, an intermediate version, based on a small number of electron affinities with reliable interpretations, was used to calculate UV spectra. It appeared that a number of previously unassigned UV bands could be understood as valence transitions. In this way the basis for the parametrization was extended to include a number of newly assigned states. With the final optimized parameters we obtain reasonable agreement between calculated and experimental energies of several kinds of electronic states for many molecules. It is therefore probable that the energies of u* orbitals given in this paper are reasonably accurate and useful for continued work. In a small number of cases there are discrepancies which we cannot explain. Our results for electron affinities are partly unexpected. In hydrocarbons (e.g., ethane) the u* orbitals are very low, and it is unexpected that they are not observed in electron transmission spectroscopy. In other saturated hydrocarbons (e+, cyclopropane) broad bands are seen in such studies. Tentative explanations are given based on the present calculations. In order to further investigate the utility of the method it has also been used for calculation of core excitation, where valence type final states dominate. Reasonable agreement is obtained for a large number of experimental bands in these spectra, although the calculated energies for the higher energy u* orbitals are consistently underestimated. Previously, the importance of u* orbitals was not realized, and early interpretations of core spectra predominantly invoked Rydberg orbitals. Spectra for which reassignments have been made based on the present calculations are discussed in some detail. A general result of our work is that many processes which previously have been explained by use of Rydberg orbitals are now suggested to involve unoccupied valence orbitals. Another result is that the configuration interaction matrix elements may be very strongly dependent upon correlation. The findings will probably be important in the theory of chemical reactions. They will also be useful in a future development of a better semiempirical MO theory.

1. Introduction Molecular orbital (MO) theory has been remarkably successful a t explaining the static and dynamic properties of molecules. One-electron excitations within a minimal basis M O scheme are frequently used to interpret electronic spectroscopies. This work explores the degree to which a simple orbital description and relatively crude semiempirical calculations can be successful in treating higher energy states, many of which involve u u* excitations. In contrast to occupied u orbitals whose energies are usually well-known from both experiment and theory, the corresponding unoccupied orbitals of u* type are usually unknown, although x* orbitals are well-known from both experimental and theoretical work. This is unexpected since all orbitals in a molecule are in principle similar. For several reasons it has been difficult to study u* orbitals by either theoretical or experimental methods. Theoretical studies of unoccupied orbitals imply calculations of electron affinity or excitation energy as pointed out by Roothaan

-.

‘Department of Physical Chemistry and Department of Physics. Now deceased. $Department of Physics. I Department of Physical Chemistry.

0022-3654/91/2095-3923$02.50/0

in 195 1.I The calculation of electron affinity is difficult since the errors from correlation and reorganization add; only a few such studies have been published.”” In contrast, in the ionization process these errors compensate each other, and therefore reasonably accurate ionization energies can be obtained by using Roothaan’s methods (“Koopmans’ theorem”). Also the calculation ( I ) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (2) Pariser, R.; Parr, R. G. J . Chcm. Phys. 1953, 21, 767. (3) Hush, N . S.; Pople, J. A. Trans. Faraday Soc. 1955, 51, 600. (4) Younkin, J. M.; Smith, L. J.; Compton, R. N. Theor. Chim. Acta 1976, 41, 157. (5) Radom, L. In Applications of Electronic Structure Theory; Schaefer Ill, H. F., Ed.;Plenum Press: New York, 1977; p 333. (6) Simons, J. In Theoretical Chemistry, Advances and Perspectives; Eyring, H., Henderson, D., Eds.; Academic Press: New York, 1978; Vol. 3, P 1. (7) Houk, K. N.; Rondan, N . G.; Paddon-Row, M. N.; Jefford, C. W.; Huy, P. T.; Burrow, P. D.; Jordan, K. D. J . Am. Chem. Soc. 1983, IOS,5563. (8) Ng, L.; Balaji, V.; Jordan, K. D. Chem. Phys. kff. 1983, 101, 171. (9) Ciommer, B.; Nguyen, K . M.; Schwarz, H.; Frenking, G.;Kwiatkowski, G.; Illenberger, E. Chem. Phys. Lett. 1984, 104, 216. (10) Heinrich, N.; Koch, W.; Frenking, G. Chem. Phys. k t r . 1986, f24, 20. ( I 1) Baker, J.; N o h , R. H.; Radom, L. J . Compur. Chem. 1986,7,349.

0 1991 American Chemical Society

3924 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991

- -

of excitation energies is difficult due to correlation energies; u r* singlet energies appear too high in all ab initio calculations.12 u* excitations have been little studied. The u Experimental information concerning u* orbitals has been very sparse until very recently. In part this has been the result of a very strong reliance on the use of Rydberg orbitals to explain higher energy spectral features in valence and core excitation and Feschbach resonances in electron scattering. Electron affinities and thus the energies of the u* orbitals of acetylene have been determined from resonances in vibrational excitation functions.I3 The present results depend fundamentally upon these measurements. Besides acetylene very few molecules have been studied. Another way to estimate u* energies from experimental measurements is to use valence u u* excitation. Broad bands are observed in the far-ultraviolet region of many molecules, but to date, they have usually been interpreted as excitation to Rydberg 0rbita1s.I~ An important result of the present work is the realization that many of these features are in fact excitations to u* valence orbitals. In the past four or five years there has been a number of spectroscopic studies in which u* orbitals have been invoked. In the area of core excitation this includes attempts to generate relationships between u* energies and bond lengths, within a local orbital as well as a number of spectroscopic studies investigating trends in u* energies through related series of molecules.’*J9 Several recent paper^'^,^^ have discussed the growing realization of the importance of u* orbitals in electronic spectroscopy. Even so, it is fair to say that a balanced viewpoint of the relative importance of Rydberg and u* orbitals has not yet evolved. l a . A Quantum-Chemical Method, Usefulfor Our Exploratory Work. Our goal in this paper is to compare calculated ionization energies and electron affinities with experiment for many molecules. It is of value if this can be done in a fast and easy way, which means that it is desirable to be able to use Koopmans’ theorem for both occupied and unoccupied orbitals. It is not immediately obvious that such a semiempirical method can be created. Therefore, we briefly discuss the possibilities of cancellation of errors in quantum-chemical calculations. One can show from density functional theory12*21*22 that it is possible to create a semiempirical theory which accounts for all correlation energy. The reorganization energy can then be calculated exactly by use of a AESCFcalculation. In such a method there are therefore no errors which have to be cancelled. It is possible that our parametrized method to some, probably small, extent is of this type. In conventional use of Koopmans’ theorem there is a partial cancellation of the errors from correlation and reorganization but only for the occupied orbitals. For the unoccupied orbitals the reorganization energy has opposite sign, and therefore the positive eigenvalues for the unoccupied orbitals are too large. The energy gap between the occupied and the unoccupied orbitals is thus too large. One approach for a unified treatment of occupied and unoccupied orbital energies is to select parameters with the goal

-

(12) Lindholm, E.; Asbrink, L. Molecular Orbitals and rheir Energies, Srudied by the Semiempirical HAM Meihod; Lecture Notes in Chemistry, Vol. 38; Springer-Verlag: Berlin, 1985. (13) Tronc, M.; Malegat, L. In Wuuefunctions and Mechunisms from Elecrron Scarrering Processes; Lecture Notes in Chemistry, Vol. 35; Springer-Verlag: Berlin, 1984; p 24. (14) Robin, M. B. Higher Excired Stares of folyaiomic Molecules; Academic Press: Orlando, FL, 1974. Vol. I; 1975, Vol. 11, 1985, Vol. Ill. (15) Sette, F.; Stahr, J.; HItchcock. A. P. J . Chem. f h p . 1984.81.4906. (16) Bianconi, A. In EXAFS and Near Edge Struciure; Bianconi, A., Incoccia. L.. Stipcich. S.: Eds.; Springer: Berlin, 1983; p 1, 43. (17) Shechy. J . A.; GI]. T. J.; Winstead, C. L.; Farren, R. E.; Langhoff, P. W. J . Chem. fhys. 1989, 91, 1796. (18) Hitchcock, A. P. J . ElecrronSpecrrosc. 1982, 25, 245 and updated versions of this bibliography. (19) Ishii, I.; McLaren, R.; Hitchcock, A. P.; Robin, M. B. J . Chem. fhys. 1987, 87, 4344. (20) Robin, M. B. Can. J . Chem. 1985,63, 2032. (21) Lindholm, E.; Lundqvist. S.fhys. Scr. 1985, 32, 220. (22) Lindholm, E.; Lundqvist, S.In Density Matrices and Denriry Funciionals; Smith, V. H., Erdahl, R., Eds.;Reidel: Dordrecht, Netherlands, 1986.

Lindholm et al. of achieving a smaller HOMO-LUMO gap. The ob,vious way to achieve this in a heavily parametrized theory is to make the bond parameter, j3,smaller. This means that for the unoccupied orbitals the cancellation takes place partly between the chemical bonding and the reorganization error. This method for cancellation of errors could be considered to be unsatisfactory since chemical bonding and reorganization have different origins. However, the cancellation of errors between correlation and reorganization is equally unsatisfactory, since these two effects also have no common origin. Since the latter cancellation constitutes the basis for Koopmans’ theorem, which is generally considered as acceptable, our proposed method and Koopmans’ theorem are quite equivalent in this respect. Both should be accepted if they give useful results. 2. The Computer Program

For the parametrization we have used a ZDO program, Le., a program of CNDO type. In the original CNDO program23the one-center repulsion integrals were calculated from the atomic orbitals and were thus dependent on the orbital exponents. However, we have found it necessary to be able to vary the orbital exponents. Therefore, we have used a modified CNDO program, in which the one-center repulsion integral is a parameter (e.g., 11.1 eV for the carbon atom). We have found it necessary to use very large orbital exponents in our calculations. The explanation is probably the following. In a CNDO calculation the orbital exponent enters only in the resonance integral PS,,,,, which describes the interaction. Although this expression describes the angular dependence of the interaction correctly, one can question whether the overlap S,,, describes the radial dependence equally well. For 2s-2s and 2pr2p7r interaction the overlap is positive for all internuclear distances, but for 2pu-2pu interaction the overlap changes sign when going from normal internuclear distances to zero (united atom). For molecules with very short internuclear distance (N2, CO, HCCH) the result is that the 2pu-2pu interaction is slightly reduced in both the bonding and antibonding molecular orbitals. It is possible that this effect is responsible for the unexpectedly low orbital energies that we obtain in our calculations. In HAM/324 this effect was reduced by multiplication with R-dependent factors. The obvious way to correct for this difficulty is to increase the orbital exponents, i.e., to use orbitals of smaller size. It is then necessary to increase the parameter 0 to obtain the desired extent of orbital interaction. The resonance integral 3jS, is thus approximately unchanged and the anomaly in the 2po-2pu case has been moved to still shorter internuclear distances where it cannot affect our calculations. In this way the results are improved for small molecules, which we consider to be especially important in our work. Unfortunately, the improvement is not complete. The highest energy molecular orbitals in N2, CO, and acetylene are built up not only from 2pu but also from 2s atomic orbitals, and the repulsion is caused by both types of orbitals. When the size of the orbitals is diminished, the 2pu-2pu repulsion increases as desired, but the 2s-2s repulsion decreases when the overlap becomes smaller. Therefore, the higher energy unoccupied orbitals in these and similar molecules will always have too low an energy in our calculations. For larger molecules the reduction of the orbital size may cause errors. An instructive example is the 1bh orbital in benzene, for which the calculated energy is -18.9 eV instead of the experimental lbzuIP of -14.8 eV. The explanation is probably that this orbital is strongly u bonding between each pair of carbons, but the bonding is counteracted by the orbitals from the two neighbor carbons, which lie outside each pair. With smaller orbitals the counteracting effect disappears, and the bonding becomes stronger and the energy lower. It is possible that this effect will selectively influence the energies of “negligible-hydrogen” (n.h.) orbitals in this molecule (vide infra). (23) Pople, J. A.; Bcveridge, D.L. Approximate Molecular Orbital Theory; McGraw-Hill: New York. 1970. (24) QCPE 393 (1980); also QCMPOO5 (1985) for IBM-PC and QMACOO5 (1988) for Macintosh.

Thle Journal of Physical Chemistry, Vol. 95, No. 10, 1991 3925

Energies of u* Orbitals

c

orbital exponents c in Table I (parameter RHYB in HAM 3). The complete computer program is available from QCPE.

TABLE I: Panmeters Used in the CNDO Calculation

atom H

I;

B 0 -28

I, 10.0

4

18.0 30.0 43.0 55.0 67.0

9.0

TAA

12.85 11.11 12.1 13.6 15.6 18.1

3. Photoelectron Spectra and Electron Affinities The output from the CNDO program is interpreted in the 2.45 -33 14.5 following way. The eigenvalues of the occupied orbitals give the 2.6 -39 16.0 negative ionization energies. They are compared with those from 2.8 -45 20.0 photoelectron spectroscopy (PES). The eigenvalues of the 3.0 -51 25.0 unoccupied orbitals give the negative electron affinities and are compared with available experimental data, sometimes from our TABLE II: Panmeters Used in Excitation Calculations (Modified previous paper.” The calculated and experimental data are HAM/3) collected in Table 111. We observe first that there is a general atom P RO ( = 7 . 2 / P ) approximate agreement between the calculated values in Table H 17.0 0.4235 111 and those in our previous paper in which extended Hiickel C 11.0 0.6545 calculations were used.31 This indicates that the agreement in N 14.0 0.5143 ref 3 1 between experiment and calculation is not accidental since 0 17.0 0.4235 the two calculational methods are very different. F 20.0 0.3600 The experimental ionization energies from photoelectron spectroscopy are very well-known for many molecules and it is It is thus probable that it is impossible to achieve good results easy to parametrize the method from these data. However, it is with semiempirical techniques simultaneously for both small and necessary to use spectroscopic results sensitive to the properties large molecules as long as the interaction is described by j3SWv. of specific unoccupied orbitals for a complete parametrization. Although this expression has been used in all previous semiThe number of experimental electron affinities is insufficient for empirical M O methodsi in a future semiempirical M O method25 such work but, fortunately, the missing values can be obtained it would be better to replace this overlap factor by an empirical from valence and core excitation. The values derived from the R-dependent expression, different for the different symmetries CNDO calculations (Table 111) have been obtained by using of interaction, especially for 2s-2s and 2pu-2pu, as pointed out parameters chosen by inspection to optimize the agreement beabove. The theoretical basis for this has been given by Asbrink” tween calculation and experiment for those cases in which exin his deduction of a semiempirical theory from first principles. perimental assignments were considered unambiguous. Since there However, such a project would require nearly as much work as is a subjective aspect to the latter, the procedures used to derive the original HAM/3 parametrization. the parameters are not given in detail. Instead, the readers are In our work we have used a CNDO/S program2’ adapted for asked to make their own judgment on the utility of the method IBM-PC from the original CNDO/S program.28 We have and the quality of the parametrization based on the comparisons changed it into double precision and replaced the factor 0.585, with experiment presented in following sections. which is characteristic of CNDO/S, by 1.000. We should 3a. Electron Affinities: Problems in the Comparison with therefore denote our program as CNDO. Further, we have reExperiments. The most general method to study negative electron placed the Mataga form for the two-center repulsion integral TAB affinities of molecules is probably the vibrational excitation mewith an expression of Ohno-Klopman type. The parameters are t h ~ d .Within ~ ~ an independent particle, orbital approximation, given in Table I. it provides information for both T* and u* orbitals. For instance, For the calculation of excitation energies with CI we have Tronc and MalegatI3 have been able to study negative ion resoreplaced this part of the CNDO/S program27 with the correnances which are associated with three virtual orbitals in acetylene: sponding part of the HAM/3 program” after including “-J T * at -2.6 eV, C-H antibonding (4uJ at -6.4 eV, and C-C K” in the HAM program, which is absent due to the H A M antibonding ( 4 4 at -21.4 eV. A resonance associated with the treatment of self-repulsion, but which has to be calculated in 3uu orbital was not observed. Unfortunately, very few molecules CNDO (as in other Roothaan-type methods). Most parameters have been studied by this technique. The most common method in the HAM/3 program have been used. For the calculation of used to determine negative electron affinities of molecules is -J + K the parameters in HAM/3 appear to be too small. The electron transmission spectroscopy (ETS).33 A large number of new parameters are given in Table 11. Note that different pamolecules have been ~ t u d i e d . l ~ *Low-energy ~ ~ - ~ ~ resorameters for the one-center, two-electron repulsion integrals ( T ~ organic ~ nances associated with T * orbitals tend to dominate ETS. Alin CNDO and F” in HAM/3) are used in the wave function and though the number of u* orbitals is usually much larger, resoexcitation portions of the calculations. The CI calculation (i.e., nances associated with these orbitals occur at higher energy, have an approximate evaluation of the interactions among one-particle much greater width, and thus are usually not observed. Thus ETS configurations) has usually been performed using the 60 lowest is less general than vibrational energy loss spectroscopy as a means excitations with excitation energies usually up to 25 eV. The CI of mapping the unoccupied electronic structure of molecules. matrix elements are calculated in conventional ways (see ref 12, According to our calculations the values for the electron afpp 172 and 149). finities of many u* orbitals are low enough for observation in Conventional methods29have been used for the calculation of electron transmission. In ethane, for instance, the calculated intensities. Evaluation of the intensities of u u* transitions electron affinities are similar to those in benzene. Appropriate at high excitation energies is more complicated than that of T signals have been measured in b e n ~ e n e , ~but ~ Jnothing ~ is seen T * transitions. In the latter case, a ZDO expression for the in the corresponding energy region of the ETS of ethane.3s An intensity is sufficient, but for a hydrocarbon one has to consider exception to the general invisibility of u*-related signal in ETS also 2s 2p excitations within the carbon atoms. These conis cyclopropane and similar cyclic hydrocarbons, where u* orbitals tributions are negative. The resulting transition moment is thus which are carbon-carbon antibonding and carbon-hydrogen the difference between two large terms. For the atomic transition moment we have used the formula 0.76/{29 together with the C N 0 F Ne

1.2

2.3

+

-

-

-

(25) Lindholm, E. Tetrahedron 1988.447461. (26) Asbrink, L.; Fridh, C.; Lindholm, E.; de Bruijn, S.;Chong, D. P. Phys. scr. 1980, 22, 475. (27) QCPE QCMP034. (28) QCPE 174. (29) Ellis, R. L.; Kuehnlenz, G.; Jaffe, H. H. Theor. Chfm.Acta IW2.26, 131.

(30) Lindholm, E.; Asbrink, L. QCPE 586 (1990). (31) Lindholm, E.; Li, J. J . Phys. Chem. 1988, 92, 1731. (32) Boness, M. J. W.; Schulz, G. J. Phys. Rcu. A 1974. 9, 1969. (33) Sanche, L.; Schulz, G. J. Phys. Rev. A 1972, 5, 1672. (34) Jordan, K. D.; Burrow, P. D. Ace. Chem. Res. 1978, 1 1 , 341. (35) Jordan, K. D.; Burrow, P. D. Chem. Reo. 1987,87, 557. (36) Allan, M. J . Electron Spectrosc. 1989, 48, 219. (37) Burrow, P. D.; Michejda, J. A.; Jordan, K. D. J. Chem. Phys. 1987, 86, 9.

Lindholm et al.

3926 The Journal of Physical Chemistry, Vol. 95, No. 10, I991

TABLE III: Comparison of Calculated and Experimental Electron Affinities, Ionization Potentials, and Core Excitation Energies and Intensities i CNDO tYPe -EA ref i CNDO int type ref -T A.1. Methane (CHI) NH4' +8.4 3a1 +7.8 91-93 8 -0.4 8 5 -3.7 strong 87 -3.1 +5.1 2t2 +5.0 94 5

9 8 6

-PES I t2 -1 4.0 -22.9 2a I A.2. Acetylene (C2H2) 40, n.h. +21.4 +15.1 4% +6.4 +6.5 +5.5 3@, T8 +2.6 +4.0

4 3 2 I

-12.0 -1 6.7 -18.2 -27.6

12

-1 1.5

11

9 8 7

+7.2 +6.8 +6.2 +4.6 +2.4

6 5 4 3 2 I

-10.9 -12.6 -1 5.8 -16.7 -1 8.7 -26.5

22 21 20 19

+ I 1.9 +11.4

2 I

IO

IO

18

17 16 15

14 13 12

-14.4 -22.7

+8.8

+7.4 +6.7 +6.5 +5.9 +5.3 +5.1 +3.6 +1.5

-PES -11.5 -16.7 3% -18.7 2% 2% -23.5 A.3. Ethylene (C2H4) 4blu n.h. +11.0 2b3, 4% +6 3b1, 2b2u 1 b28 n.h. +1.8 -PES 1 b3u -10.7 b38 -12.8 -14.8 3% -16.0 1b2u 2blu -19.1 2a8 -23.6

NCH,' 13 13.95

IO

13, 34

9 . 8 6

40

12

+5.3 -1.9 -3.1 -5.8

0.59 0.26 0.1 1 0.58

+2.3 -0.7 -1.4 -1.7 -2.9 -6.3

0.61 0.16 0.49 0.14 0.39 0.48

+3.6 +2.2 +1.6 +0.9 -0.1 -0.3 -0.9 -1.5 -2.5 -5.7

0.53 0.33

11

IO 98, 99 34

A.4. Butadiene 1 la, n.h. 1 Ib, n.h. lobu n.h. 1Oa, 9b" 9% 8b,,

9 8 7

9

Ib, la, 7%

I

-27.3

3%

7~

T

-9.2 -1 1.4 -12.1

+6.2 +3.3 +1.9 +1.9 +0.7 -0.1 -0.4

-1.5 -1.8 -2.7 -5.8 16 I5 14 13 II 9 7 5 4 3 2 I

+14.1 +9.7 +6.8 +6.7 +6.4 +2.2 -10.3 -1 5.7 -16.8 -17.5 -25.5 -26.5

96, 97 86 86 86

+5.0, b.7 -1.9, b.3 -2.8, b.2 -5.2. b.1

A.5. Allene (C,H,) 5b2 n.h. 6a1 n.h. 4b2 5a I 4e 3e 3e le 3b2 4a I 2b2

NCH4' n.h. CH2a CH2* CH~S CH~T

96, 100

+2.5, b.7 -1.3, b.5 -2.8, b.3 -5.9, b.1

T*

+5.9

34 34

-9.1 -21.1 -12.2

IO

n.h.

1T U

0.16 0.16 0.16 0.3 1 0.49 0.15 0.41

-PES II

u*

+8

+1.9 -PES -10.3 -14.7 -15.5 -17.5

13

16

+6.4

15

+1.7

14 13 12

+0.5 -0.1 -0.8 -1.1 0.10 -5.5

13

11

IO

-4.6 9

n.h. n.h.

101

+5.5, b.9

CH~U

101 101, 17 101,77

-I .9, b.6 -2.5, b.5 -5.6, b.2

101

+5.5, b.9

101

-1.9, b.6 -2.8, b.4 -6.1, b.1

2b28

2%

H2C= IHCH=CH2 n.h. 0.62 n.h. 0.12 C 0.25 C 0.38 C 0.29 0.12 CH 0.18 0.27 CH 0.19 2b2, 0.47 2% H2NCCH2' 0.34 a* n.h. 0.52 a* n.h. 0.13 0.16 0.62

CH2a CH2r

0.42

T*

101,77 101,77 101

+5.0, b.11 +2.8, b.9

-2.0, b.4 -4.4, b.2 -5.1, b.1

H2CNCH2' 16 15 14 13

+5.9 +0.7 -0.3 -0.5

0.69

u*

n.h.

101

+5.0, b.11

The Journal of Physical Chemistry, Vol. 95, NO. 10, 1991 3927


TABLE 111 (Continued) i

CNDO

type

-EA

ref

i

IO

a

+7.2 f6.9 +5.5 +4.5 2e,

type

9

14 13 II 10 8

+1.4 -0.7 -1.2 -1.4 -3.2

0.06 0.49 0.12 0.31 0.60

18 17 13 12

-0.3

0.55 u* n.h. 0.40 CH,a 0.38 CH,a 0.13 CH~S 0.60 CH2pi CH3CH2NH2CHZCH3’ 0.50 u* 0.52 CH2a 0.60 CH~A

10

+a.o

int 0.21 0.2 1 0.49 0.49

11

14 13 12

CNDO -1.1 -1.1 -5.6 -5.6

12

ref

-T -5.1, b.1 -5.1, b.1

A* A*

NCH6+

A.6. Ethane (c&) 4a1, 4a2, n.h. 3% 2%

a2

u* a2,

+0.2,b.4

CH2a a2, CH~A

-1.1, b.3 -2.1, b.2

-PES 6 5 3 2 1

-12.9 -14.3 -1 5.5 -19.9 -25.0

1% 3a1, 1 e, 2a2, 2a1,

-12.0 -1 2.7 -I 5.0 -20.4 -23.9

CH,NH~CH,+~

A.7. Propane (C,H,) 12 11

+5.0 +4.6

IO

-1 2.5

9

-1 2.7

-PES -1 1.5 -12.1

11

-0.5 -1.1

-1.5 -2.8

A.8. n-Pentane (C5Hl2) 17

+4.3 -PES

16

-1 2.0

22 20 17

-0.4

ia 17 16 15 15 12 12

+1.6 +0.6 +0.1

-0.8

-2.6

a2

+ 1 .O, b.4 -1.2, b.3 -1.2, b.3 -2.8, b.2

a2

+ 1 .O, b.4 -1.3, b.3 -2.8. b.2

A.9. Neopentane (C(CH3)J 32 29 26 25 23 20 17

+7.8 +7.6 +7.1 +7.0 +5.0 +4.9 +4.3

14 II

-12.7 -13.7

6a, 7t2 n.h. 6t2 Sa, n.h. 2e 2tl 5t2

+6. I

84

+6.1

a4

36 32 20 19

-PES -1 1.0 4t2 It, -1 2.6 A.10. Cyclopropane (C,H,) +a.7 5e’ n.h. +8.2 +7.4 4al’ +6.4 4e’ 1e” +6.1 +4.6 2aT +5.3 +4.6 la; t n.h. -PES - 10.9 -12.0 3e‘ -1 3.2 1e” -13.0 -16.5 3a,’ -15.7 - 1 7.2 1a? -16.7 -19.4 2e’ -19.7 -29.6 2al’ -26 A.l I . Cyclohexane, (C6Hl2) +a.a t* n.h. +a.5 +7.3 s* n.h. +7.0 A* +4.9 +4.7 A*

la

-I 1.9

30 29 27 25 23

+11.8

17 16 14 I2 II

IO 8 6 5 4 2 1

38

38

+10.9

16

+ 10.4 +9.6 +6.3 +6.0 +5.9 +5.a +4.7 + I .6

14 12 II

-9.7 -1 3.0 -I 3.3

21

20 19 18

NCzH6’ n.h.

0.66

CH2a

0.28

CH2r

0.56 0.45

CHZr t * n.h.

11 10

-0.4 -1.1 -1.6 -2.4 -3.0

34 27 24 21 20 19

+2.6 +1.1 -0.2 -0.7 -1.2 -2.1

0.15 0.18 0.55 0.50 0.23 0.62

30 29

+5.7 +4.a +4.4 +4.0 +3.0 +2.2 +0.9

0.19 0.14

a3 +2.6. b.3

-1.6, b.2 -2.9, b. 1

NCSH,,+ 38 38

-PES -I 1.8 A. 12. Benzene (C6H6) lals t * n.h. ? 4bl, n.h. ? 5e,, n.h. ? 5e2, n.h. ? 4e2, +a 4e1, 3b1, 4a1, 1 bls r*n.h. +4.8 le,, r*n.h. +1.1 -PES le,, = -9.3 3e2, -11.6 la2u -1 2.4

+o.o

0.20

37, 50 31, 50 37, 50 37, 50 31 37 37

28

27 26 25 24 23 22 21 20 19

ia 17

+o.a

a3

+ 1.6, b.3

t* n.h. CH,a CH2s n.h. CHZA NCsH6’

n.h.

-I . I , b.2 -2.6, b. 1 102

n.h. n.h. n.h. n.h. n.h.

+3.5, b.c. +3.5, b.c. +3.5, b.c.

0.21 0.31

CH CH b,,

-1.2, b.B

0.18

A*

-1.2, b.B

0.25 0.55 0.46 0.19 0.13

+0.7 +0.2

+o. 1

-I .o -1.3 -4.0

A*


Lindholm et al.

TABLE 111 (Continued)

24 23 22 21 17

CNDO type -EA -15.0 2blu -1 5.4 -15.2 3% -14.0 -18.2 3a1, -16.9 -18.9 1b2" -14.8 -21.4 2e2, -19.2 -24.9 2% -22.6 -28.9 -25.9 A.13. Naphthalene (C,,H,) + 12.2 n.h. ? these n.h. ? +8.5 n.h. ? +5.3 =10 +4.72 +3.7 =9 +3.38 +2.6 =a +1.67 +1.3 *7 +0.90 +0.8 *6 +O. 19 -PES -8.8 7 5 -8.1 -9.2 774 -8.9 -10.7 "3 -10.1 -12.1 =2 -11.0 -14.1 TI -1 2.7

8 6

+14.8 +2.3

3au I=,

5 3 2

3%

1

-15.7 -16.8 -1 8.7 -37.0

7 5

+8.8 +5.6

i

IO 8 7 6 4 2 I 48 all 38 29 28 27 26 25

ref

16

CNDO -5.4

42 41 40 39 38 31 30 29 28 27 26 25

+4.7 +4.4 +4.2 +3.3 +2.5 +0.4 +0.4 -0.4 -1.3 -2.5 -3.6 -5.1

103 104

8 6

+3.5 -8.9

0.57 0.63

106 45-47

7 5

-0.9 -3.8

0.27 0.58

107 107

9 8 6

+4.2 -4.4 -7.5

0.61 0.25 0.65

9 8 6

+4.7 -3.8 -6.8

0.57 0.12 0.56

35, 27 35-37 35-37

i

4 2 I 9 8 6 4 3 2 I 13 12 II

IO 9 8

7 6 5 4 3 2 I 25 24 23 21 20 19 18 16

14

1T

U

-PES - I 1.4 -9.6 -1 3.2 -13.5 -14.8 -14.4 -1 5.8 -1 5.5 -1 7.0 -16.3 -21.2 -28.6 B.5. Trimethylamine (N(CH,),) +8.4 x(N) n.h. +6 +6 +8.4 y(N) n.h.

-5.4, b. 1

u*

105

+8 -9.0

88

-1.4, b.6 -3.2. b.3

108

+IO, b.10 -4.3, b.3 -7.0, b. 1

108

+IO, b.10 -4.3, b.3 -7.1. b.1

T*

OH,'

H"+

T*

a*

CH A*

NH3NH2' 13 12

+l.5 -0.9

11

-1

IO

-I .9 -3.3 -3.4

9 8

.o

88 0.42 0.46 0.60 0.60

CH,a

-1 .O, -1.4, -2.8, -2.8,

a*

CHjn CHI*

b.5 b.4 b.2 b.2

CH30H2+ 13 12 II

IO 9 8

+1.1

-0.7 -1.6 -I .6 -1.9 -2.9

88 0.53

NH2a

-0.3, b.4

0.14 0.35 0.59

NH~s NH2n

-1.6, b.3 -3.1, b.2

O(CHi),' 85 85

+2.0 +1.4 +0.8 +0.8

+6

a*

CH

HCOC

+8.0

e e

+3.2, b.6 +3.2, b.6 +3.2, b.6 +3.2, b.6 +3.2, b.6 -0.I , b.5 -0. I , b.5 -0.1, b.5 -2.0, b.4 -3.2, b.3

-PES -15.6 -16.9 -1 8.8 -37.3

B.2. Ammonia (NH,) 4a I +7.3 2e +5.6

e 2s(N) n.h.

100

=7 ~g

0.46

-T -5.1, b.A

NOt +22 +2

-PES -12.3 3a1 -10.9 le -1 5.8 -16.1 -27.0 2a, -28.0 B.3. Hydrogen Cyanide (HCN) +14.9 7a +4.8 6a +6.7 2n +2.3 +3.2 -PES In -1 3.6 -14.3 5U -14.0 -15.3 -18.9 4a -19.1 -32.1 3a B.4. Methylamine (CH3NH2) +8.3 a* n.h. +7.3 +7.1 +5.9 +5.3 +5.0

+7.4 +7.3 +5.3 +5. I +5.0 +4.9

ref

A*

NC9HBt (C, excited)" 0.11 n.h. n.h. 0.16 0.45 n.h. 0.30 n.h. 0.35 n.h. 0.10 *IO 0.15 CH 0.33 CH 0.12 "9 0.16 "8

B.1. Nitrogen (N2)

2 UU 2%

type

int 0.42

85

-0.6 -1.0 -1.1 -1.3 - I .5

88 e 0.60 0.60 0.25 0.13 0.24

x(N) n.h. y(N) n.h.

+ I .7, b.3 +1.7. b.3

e e 2s ( N ) n.h.

-1.8, b.2

Energies of

u*

Orbitals

The Journal of Physical Chemistry, Vol. 95, No. 10, 1991 3929

TABLE I11 (Continued) i

CNDO

13 II

-10.7 -13.4

6

+8.5

5

+6.4

4 3 2 I

-13.1 -14.6 -17.6 -32.3

8 6 5 3 2 1

12 II 9 7 5 4 3 2 I

IO 9 8 7 6 5 4 3 2 1

12 I1

IO 9 8 7 6 5 4 3 2 1 18 17 16

15 14 13 12 II

type nN

-EA

e C.1. Water ( H 2 0 ) 4a I +7 +8.5 2b2 +6.5 -PES 1 bl -12.6 -1 4.7 3a1 1b2 -18.5 -32.2 2a I

C.2. Carbon Monoxide (CO) 6a +19.5 27r +1.8 -PES 5a -14.0 -12.5 -16.3 lu -1 6.9 -20.2 40 -19.7 -37.8 3a C.3. Carbon Dioxide (CO,) + 15.8 4% +30 10.4 5% +10 +3.1 2*U +3.8

+

1I 8

1AU 3uu 45 2% 3%

i

CNDO

int

109 42-44 42-44

6

-2.5

0.34

5

-4.9

0.53

103 103

8 6

+2.7 -9.3

0.62 0.78

7r*

8 6

+3.3 -7.8

CFC 0.53 0.38

u* u*

12 11 9

+5.1 -1.5

0.70

NO2+ u*

-8.5

0.71

r*

12

+6.1 -0.0 -6.5

0.32 0.47 0.27

+2.3 -3.4 -4.0 -8.3

0.63 0.21 0.62 0.65

+1.9 -2.9 -3.7 -8.0

0.56

1 IO

110 95, 110

-PES -1 3.8 -17.6 -18.1 -19.4 -38.0 -38.0

C.4. Formaldehyde (H2CO) 7al u* n.h. +5.5 6a1 C H ~ S +6.9 +5.1 3b2 CH2n +2.1 2b1 A* n.h. +0.9

-8. I +7.5 +6.8 +5.1 +5.0

2b2 1 bl 5a1 1 b2 4a I 3a1

ref

-T

87

-2.6, b.3

11

9

u*

COF' u* u*

105

+7.5, b.6 -8.0, b. 1

105

+7.5, b.6 -8.5, b.1

111

+I4 -6.8, b.1

111

+I7 -2. I , b.3 -5.4, b. 1

113

+6, b.6

T*

H2NO'

IO 112 34

-PES -1 0.9 -14.5 -16.1 -17.0 -21.4 -34.2

9 8 7

IO 9 8 7

C.5. Methanol (CH,OH) OH u* n.h. CHSS CH3n CH,*

-PES -I 1.9 10.9 -1 3.0 -1 2.7 -I 5.7 -15.2 -1 5.8 -1 5.7 -17.2 -17.5 -22.0 -22.7 -33.0 -32.2 C.6. Dimethyl Ether ((CH,),O) +8.8 7b1 (I* n.h. +6 +7.6 9al CH, +7.4 8al u* n.h. +6 +7.1 6bl CH, +5.2 3bzCH3 +5.0 7alCH, +4.9 SblCH, +4.7 2alCH3 -PES

-5.7, b.1

NO'

+ 12.8

- I 1.0 -14.4 -17.3 -18.1 -20.7 -35.4

type

-PES -8.4 -1 2.7

+15.1 +3.3

-12.7 -18.5 -1 9.0 -20.4 -36.7 -37.2

ref

12 11

IO 9 8

+0.7 -1.2 -2.2 -3.7 -3.8

u* CH~S CHIT

-3.3, b.3 -8.5, b.1

7r*

H2CFS u*

0.13 0.38

7r*

0.51 0.40 0.60 0.61

NHIOH' OH CH~S u* CHIT CH~T

113

+4.6, b.5 -3.3, b.3 -8.6, b. 1

81 -1 .O, b.4

-2.0, b.3 -2.9, b.2 -2.9, b.2

CH,FHt 12 11

IO 9 8

+0.3 -1.9 -2.3 -2.4 -3.0

87

0.55

us

-1.8, b.2

0.40

OH

-4.8, b.1

(CHAzF' 85 85

18 17 16 15

14 13 12 11

+0.9

87

+0.5 -0.4

- I .6 -1.7 -1.9 -2.0 -2.1

0.53 0.25

lb, n.h.

-0.0, b.2

8a, n.h.

-3.1, b.1

0.12 0.33


Lindholm et al.

TABLE 111 [Continued) i

CNDO

IO

-1 1.2

-1 0.0

9 8 7 6 5 4 3 2 1

-12.9 -13.7 -14.3 -16.8 -16.9 -1 7.0 -20.3 -24. I -33.8

-12.8 -1 3.4 -14.2 -16.0 -1 6.0 -16.5

12 11

9 7 6 4 3 2 I

type

-EA

C.7. Dinitrogen Oxide ( N 2 0 ) +14.7 9a +8.4 80 +8.4 +1.2 3lr +2.3 -PES -12.1 2* -12.9 -17.3 7a -16.4 -1 9.8 Iif -18.2 -20.7 60 -20.1 50 -36.0 -38.8 4a

ref

i

18 17 16 15 14 13 12 I1

8

+1.5

loa' (no') 2a" 9a' 1 a" 8a' 7a' 6a' D. I . Fluorine (F2) 30"

0.50 0.35 0.60 0.6 1

+5.2 -1.3 -8.5

0.48 0.45 0.52

+4.9 -2.9 -9.3

0.67 0.12 0.58

9

+5.4 -2.1 -7.8

0.29 0.57 0.20

14 13 12 II IO

+2.6 -0.6 -0.8 -4.2 -8.0

0.66 0.44 0.35 0.36 0.67

8

-12.3

115

5

-5.8

54

15 14

-5.8 -6.5

0.70 0.53

16 15 14

-3.8 -4. I -7.1

NFZNE' 74 6e 0.45 6e

18 17

-3.5 -4.9

12 13 13

11

9

12 11

9

3 2

-PES -16.0 -20.0

1

16 14 13

II

IO 8 7 5 4 2 I 18

17

-1.1, b.3

CHla CHIS CHIT CHIT ONO+ a* a*

-2.8, b.2 -2.8, b.2

111

if*

NNFC a* a*

111

Ill

-2.4. b.4 -6.6, b.1

if*

HNOOH+ n.h. OH OH CH

+IO -2.5, b.6 -7.8, b.2

if*

NOO+ a* a*

+IO -0.9, b.4 -7.4, b.1

78

b.5 b. 5 b.5 -3.8, b.2 -7.6, b. 1

1 I4

14.5, b.l

114

-6.7, b.1

1 I6

-7.3, b.1 -1.3, b.1

**

FNe'

d

5

1

-T

-PES -11.5 -12.6 -14.8 -1 5.8 -17.1 -17.8 -22.0

-PES - 1 5.9 -16.3 1 *a -18.8 -19.3 I *" -19.7 3% -21.1 -32.7 2% -39.7 2% D.2. Hydrogen Fluoride (HF) +7.1 4a +6.7

6 4 3 2

ref 87

0.20

C.8. Formic Acid (HCOOH) 14a' n.h. +9.4 13a' n.h. +6.4 12a' OH +4.8 I la' C H +2.5 3a" P* -1 1.3 - 1 2.3 -14.6 -16.3 -1 8.5 -18.6 -22.0

+2.3 +2.1

+o. 1

+ 12.9

9 8 7 6 5 4 3

type

-0.3 -0.9 -I .7 -3.4 -3.5

11

IO

int

(NHi)(CHi)O+

12

14 13 12 II

CNDO

-16.0 I* -18.5 3a -36.7 20 D.3. Nitrogen Trifluoride (NF,) +4.7 7a I +4.5 6e +1.7 -PES -14.1 6a I -1 3.8 -16.5 5e -1 6.4 1a2 -1 5.9 -16.9 -1 7.5 4e -17.5 -19.9 5a I -19.8 -21.4 3e -21.2 -25.2 4a I -36.6 2e 3a1 -41 .O D.4. Carbon Tetrafluoride (CF,) +7.3 5tl +7.0 +6.9 5a I -PES

HNe+

OF," 6e 7a1

I16 -5.8

m 4 +

54

strong

5t2 5%

1 I7

-3.5



TABLE 111 (Continued) i 14

II 9 6 5 2 1

11

IO 8 6 5 3 2 1 24 23 22 21 20 19 18

17 16 15 14

CNDO -16.7 -17.2 -17.9 -22.6 -24.5 -37.9 -42.3

type 4tz It1 le 3t2 4a I 2tZ 3a1

-EA

D.5. Methyl Fluoride (CH3F) 7al u* n.h. +6.5 +6.9 6al C H ~ S +4.6 3e CHI* -PES -13.5 2e -13.1 -17.5 5a1 -17.0 -17.6 le -17.0 -23.4 -22.8 4a I -36.7 3a1 -38.4 D.6. Tetrafluoroethylene (CzF4) +10.8 bl" u* +I2 +9.7 b3, +I 1 +7.7 a8 bl" +6.2 +6.8 +6.7 bZ" bzg =* +3.0 +1.6 -PES -10.5 2b3" = -10.5 -16.6 -16.0 6% -17.6 16.8 4b3g -1 6.9 4bzU -1 8.5 -17.1 1a, -19.4 +7.1

ref

i

CNDO

int

type

ref

-T

CF3Ne+

-17.4 -16.2 -18.5 -22.1 -25.1 -40.3 -43.8 86

20 19 18 17

-0.9 -0.9 -0.9 -4.1

0.35

t2 a , + t2 t2 + a l

11

-1.9 -3.2 -4.4

0.41 0.55 0.60

iVH3F+ CH3a u* n.h. CH3r

0.40

CH3Ne+ CH~S CHjx u* n.h.

IO 8

11

9 8

-0.7 -3.3 -3.9

t2

117 -2.3

89

-2.2, b.6 -3.2, b.4 -4.6, b. 1

1 I8

-3.5

121,122

+5.5 +2.0 -2.0 -4.6 -4.0 -6.4

NCF4+ 48

119, 120

24 23 22 21 20 19

+1.6 +0.9 -1

.o

-1.8 -3.1 -7.5

0.61 0.49 0.33 0.55 0.13 0.43

u*

CFZr CF2a CF~T CF~S r*

a Description: The first column gives the molecular orbital number. For a degenerate orbital only the lowest number is given. The second column gives the eigenvalues from the CNDO calculation. The fourth column gives the negative of experimental electron affinities (-EA) and the negative experimental ionization energies (-IP). In the right-hand portion of the table the corresponding Is-ionized molecule is studied in terms of the equivalent ionic core virtual orbital model (EICVOM). The core exicted atom is indicated by the 2 + 1 symbol, - e.g., HNOZHt is C Is ionized formic acid. In the second column of this part the eigenvalues of the unoccupied orbitals are listed. The sixth column lists the experimental negative core-excitation term values (-T = E - IP), together with the number of the band in the published spectrum. In the third column a measure of the calculated intensity of the core excited band is listed. For the MO indicated, this is the coefficient of the 2p A 0 at the core excited atom. The square of this value should be proportional to the transition intensity. In the case of a degenerate orbital the coefficient of only one component is listed. The fourth column gives an indication of the spatial character of the MO. C H 2 r means an orbital in which the contributions of the two hydrogen 1s AOs have opposite sign. CH2a is an orbital in which they have the same signs. C here indicates the Is-ionized carbon atom for which the nitrogen is used during the EICVOM calculation. bNH3CH2CH3+is very similar. 'The results with C2 or C9 excited are similar. dSee ref 51.

nonbonding have been ob~erved.'~In these molecules, higher energy features are seen in the transmission spectra which can be correlated with negative ion species involving occupation of high-energy u* virtual orbitals, which are carbon-hydrogen nonbonding. From these observations we have formulated the following hypothetical rule: features are not observed in the ETS of hydrocarbons when the orbital is antibonding between hydrogen and a heavier atom, but features may be observed when the orbital is nonbonding and has little density on hydrogen atoms. In Table 11 orbitals of the latter type are denoted n.h., which means negligible hydrogens. We believe that several published electron transmission spectra may be explained in this way, e.g., those of dimethyl ether, trimethylamine, and methyl fluoride. It is also possible that the high-energy bands in the ETS of benzene and naphthalene have this explanation, although the uncertainties of our calculations make this at most a provisional suggestion. The number of n.h. orbitals among the unoccupied orbitals in hydrocarbons can be understood by considering benzene as an example. There are six C-H bonds in benzene and thus there must be at least six virtual orbitals of C-H antibonding character. Since there are 15 virtual orbitals in a minimal basis set description of benzene, there are at most 9 n.h. orbitals. Since three of these are r* orbitals, there can be at most 6 n.h. orbitals of u* type. All six of these n.h. orbitals can be identified in our calculations. Similarly in other molecules all n.h. orbitals expected from the minimal basis description are found. For the occupied orbitals (38) Howard, A. E.;Staley, S.W. ACS Symp. Ser. 1984, 263, 183.

INTERNUCLEAR SEPARATION

Figure 1. Schematic potential energy curves3' for a molecule and its anion, when the electron enters a nonbonding or nearly nonbonding molecular orbital (MO), such as r*.

we should expect the same picture but here mixing takes place to such a n extent that the occupied orbitals cannot be divided into sets of n.h. and non-n.h. orbitals. The reader is referred to the excellent book by Jorgensen and Salem39which presents orbital density maps for most of the molecules studied in this work. These electron densities were derived from semiempirical minimal basis set calculations similar to the present ones. The distinction between (39) Jorgensen, W. L.;Salem, L. The Organic Chemist's Book oforblr~ls; Academic: New York, 1973.

Lindholm et al.


I ?*

co

Ir

..

!I

I 1

i :

i

\

.*e *’

x10

Awibm.

.-.*

,; +. e+ *e -*&” I1

5

...

I . . .

10

I .

15

e . .-. . I .

20

Electron energy (eV)

25

Figure 2. Electron attachment spectrum of CO exhibiting

?r*

and u*

resonances.lo3

n.h. and hydrogen-dominated orbitals made in this work is amply illustrated in their plots. 3b. Line Widths and Visibility of States in ETS. In experimental studies of vibrational excitation by inelastic scattering, two types of spectra are recorded: the energy loss spectrum which shows the molecular vibrations and the excitation function which shows the formation of anions, Le., the electron affinities. The visibility of the temporary negative ion states is strongly dependent on the width of the resonances. In the a* case the potential energy curve for the anion ABlies nearly exactly above the curve for the molecule AB (Figure 1). In a Franck-Condon transition, only a small number of vibrational levels are reached (for N 2 about 4) and the breadth of the excitation function is therefore only about 1.0 eV. In transmission experiments a narrow band is observed, which exhibits resolved vibrational structure.M In contrast, u* orbitals are usually strongly antibonding. This means that, within the Franck-Condon approximation (which may not be valid for short-lived resonances) u* resonances will be broad in the vibrational excitation and the transmission spectra. As an example the u* resonance in the vibrational excitation spectrum gf CO (Figure 2) is a featureless band nearly 10 eV wide. It cannot be seen in transmission experiments. A second factor affecting line width and thus visibility of u* resonances is the very large broadening due to the finite lifetime of high-energy anion states. Thus it is not surprising that u* resonances have rarely been identified. In addition to the two extreme cases of narrow a* and extremely broad u* negative ion resonances, there will also be intermediate cases. Many of the n.h. type of u* orbitals discussed in this paper are weakly antibonding since the strong interaction with hydrogens is missing. Thus in many cases resonances associated with these orbitals will be observable in transmission experiments as broad features. When a virtual orbital contains contributions from hydrogens it often becomes so strongly antibonding that it cannot be observed simply since it is too broad. In transmission experiments many structureless features have been seen in the 3-5-eV energy range, for example, the band at 4.82 eV in ben~ene.’~J’ Their breadth has usually been ascribed to short lifetime due to high energy. We suggest that another factor may also be important. The higher energy implies that the associated virtual orbital is antibonding and, thus, that the resonance may be dissociative. Therefore, there will be band broadening related to the slope of the resonance potential curve within the ground-state Franck-Condon zone. 3c. Electron Affinities: Dissociative Attachment (DA). In the dissociative attachment (DA) process a negative ion is formed, which afterwards dissociates. This technique has been used to study the virtual orbitals in a few molecule^,^*^' but since secondary processes (notably excited electronic states) also play an important role in DA, it is not certain that these studies result in reliable electron affinities. Since there are many molecules for which DA studies are the only existing source of electron affinity estimates, we will discuss some cases here (see also ref 31). (40) Electron-Molecule Interactions and their Applications; Christophorou, L. G., Ed.; Academic, Orlando, FL, 1984; Vol. I , Vol. 2. (41) Heni. M.; Kwiatkowski, G.; Illenberger, E. Ber. Bunsen-Ges. fhys. Chem. 1984.88, 670.

The DA spectrum of water shows three bands.”Those at 6.5 and 8.5 eV are in good agreement with our calculated EA’S (6.4 and 8.5 eV) and with other measurements. In ammonia the calculated EA’S (5.6 and 8.7 eV) are close to the energies of the two DA bands (5.6 and 7.3 eV).4s47 In the case of fluorine compounds most electron affinities are from DA studies (cf. the data for F,, CF,, NF,, and C2F4 in Table 111). In C2F4,* there are resonances in the CF,- and F yields at 3 eV corresponding to population of the a* orbital. Since the A* orbital is strongly C-C antibonding, it is likely that the CF2ion is first formed. This then dissociates giving F. At higher energies there are several orbitals which are also strongly C-C antibonding with comparatively small contributions from F atoms. Only F is observed at these energies in the DA spectrum. It is reasonable to believe that this is the result of a stepwise dissociation similar to that believed to occur at 3 eV. It may take place more completely due to the higher energy. The u* orbital in CzH4 (of n.h. type and C-C antibonding), calculated at 11.5, eV is in good agreement with DA features at 10 eV in the CHI- and CH- yields.49 All other virtual orbitals in this molecule contain large hydrogen Is contributions and thus are not likely involved in DA processes. In benzene dissociative attachment giving C,Hy is observed between 8 and 11 eV.% The explanation is possibly the n.h. orbitals. 3d. Accuracy of the CNDO Calculations. The agreement for the occupied orbitals between photoelectron spectroscopy and CNDO calculations is comparatively good for hydrocarbons (see Table 111). The reason is partly because the rather primitive CNDO procedure seems to work well for hydrocarbons, but also because there is lots of experimental data suitable for the parametrization. In the case of fluorocarbons, our calculations are less successful. It is possible that some of the experimental data are unsuitable for the parametrization. This is certainly the case for F2 for which the calculated vertical EA differs by 3 or 4 eV from the measured adiabatic EA of 3.1 eV5‘ (seeTable 111). This could also be the case for other fluorine compounds. 4.

UV Spectra

The electron affinity results indicated above and in Table I11 are rather unexpected in that they suggest that u* orbitals play a more important role than previously believed. Thus it is of value to have an independent check on the accuracy of our calculations of the energies of unoccupied orbitals. Valence excitation offers this possibility. According to Roothaanl singlet excitation energies (AJ?)in a closed-shell molecule may be calculated as

It is evident that if a semiempirical calculation gives reasonable orbital energies tgand ti, then the calculated excitation energies should be reasonable. This could give a valuable check of the validity of our results. However, there are complications. The first complication is that, in our Koopmans’ theorem parametrization of CNDO, we have included the reorganization energy (42) Compton, R. N.;Christophorou, L. G. fhys. Reo. 1967, 154. 110. (43) Melton, C. E. J . Chem. Phys. 1972, 57, 4218. (44) Bclic, D. S.;Landau, M.; Hall, R. 1. J . f h p . B 1981, 14, 175. (45) Stricklett, K. L.; Burrow, P. D. J . fhys. E 1986, 19, 4241. (46) Tronc. M.;Azria, R.; Ben Arfa, M. J . Phys. B 1988, 21, 2497. (47) Sharp, T. E.;Dowell, J. T. J . Chem. fhys. 1%9,50, 3024. (48) Illenberger, E.; Baumgartel. H.; S u m , S.J . Electron Spectrosc. 1984, 33, 123. (49) Heni, M.; Illenberger, E. J . Electron Spectrosc. 1986, 41, 453. (50) Fenzlaff, H.P.;Illenberger, E. Int. J . Mass Spectrom. Ion Processes 1984, 59, 185. (5 I) The potential energy curve for F2 is anomaloussz since 3a, is strongly antibonding. The adiabatic EA is therefore +3.08 eV,s3-J4although the vertical EA is small.Js We give the calculated vertical EA in Table 111. (52) Rescigno, T. N.;Bender, C. F. J . fhys. B 1976, 9, L329. (53) Chupka, W. A.; Berkowitz, J.; Gutman, D.J. Chem. fhys. 1971,55, 2724. (54) Harland, P. W.; Franklin, J. L. J . Chem. fhys. 1974, 61, 1621. ( 5 5 ) Chutjian, A.; Alajajian, S. H. Phys. Reo. A 1987, 35, 4512.

The Journal of Physical Chemistry, Vol. 95, NO. 10, 1991 3933

Energies of u* Orbitals in the calculation of both the occupied and the unoccupied orbitals. The unknown difference of the two reorganization energies should therefore be added to the formula above. The second complication is the large size of the Coulomb repulsion term J (of the order of 7 eV). The accuracy of our calculation of this term is therefore important. In the case of interaction between A and A* orbitals, especially in hydrocarbons, the important parameters were found already in the PPP method, but for the interaction between u and u* there is less experience. We have found agreement with experimental UV spectra only by use of larger values for the onecenter electron-electron repulsion energies than those used in HAM/3 (parameters for the excitation part of the program are given in Table 11). We observe that the large value for fluorine corresponds well to its higher ionization energy (as pointed out by Pariser in 195356). Since some of our electron affinity results must be characterized as unexpected, the check from UV spectra is of great importance. In one respect this check is especially reliable since it is based on a spectroscopy in which the ground-state electronic structure is minimally perturbed. Core excitation can also be used, as discussed below, but one must be concerned about the influence of the strong core hole relaxation and its distortions of virtual orbital shapes and energies relative to their character in the ground state. Core excitation is therefore less informative with regard to the electron affinity of the original molecule. In our calculation of the valence excited states we have tried the C1 feature of the program. In some cases we have found that this seems to impair the calculated results. Previously1*the CI aspect of the calculation had been studied in detail and found to give good results for two cases: that between two (A,**) terms in planar hydrocarbons, and that between two (A,**) terms where the excitations are mutually perpendicular. In this work we observe in planar molecules such as ethylene, butadiene, and formic acid that the real interaction between ( A , A * ) and (u,u*) terms is less than that estimated by the conventional formulas. This is discussed further in section 4d. In the remainder of this section we briefly describe the results for the UV spectra of a few molecules. Only transitions of high intensity are discussed. The results and comparison with experiment are summarized in Table IV. The general result is that there is good agreement between calculated and observed UV spectra in both energies and relative intensities for a fair number of molecules. This indicates that the CNDO parameters and the calculated electron affinities are reasonable. Although our assignments of the strong A ---L A* transitions are in agreement with previous work, the remaining spectral features, which have usually been ascribed to Rydberg states,I4 are now suggested to have very strong connections to valence states involving u* orbitals. Thus our results suggest in many cases that there should be changes in previously published spectral assignments. 4a. UV Spectra of Three Small Molecules: A Check on C-H Parameters and on CI. The UV spectrum of butadiene (Figure 3) exhibits bands at 5.9 and 9.5 eV, which were interpreted as A A* transitions in 1953 by Pariser and Parr? The strong band at 1 1.2 eV has not previously been interpreted, since it is obvious from its energy that it cannot be a Rydberg transition.12 Ab initio calculations have only been carried out for states below 8 eV.57do The agreement between experiment and our calculations is seen to be good for all major transitions, and we conclude therefore that the C-H parameters in the CNDO program are reasonable. It appears that the 1 1.2-eV band is a u(CH) u*(CH) transition. With C l included at the end of the calculation of the excitations we find that there is considerable mixing of the second and the third states. These two excitations have the same symmetry, since orbitals IO and 13 are A and A * , perpendicular to the plane of the molecule, while orbitals 9 and 14 are in the plane of the

-

-

(56) Pariser, R.J . Chcm. Phys. 1953, 21, 568. (57) Buenker, R. J.; Shih, S. K.; Peycrimhoff, S.D. Chem. Phys. Lett. 1976, 44, 385. (58) Aoyagi, M.;Osamura, Y.;Iwata, S.J . Chcm. Phys. 1985,83, 1140. (59) Cave. R. J.; Davidson. E. R. J . Phys. Chrm. 1987. 91, 4481. (60) Kitao, 0.;Nakatsuji, H.Chcm. Phys. Lori. 1988, 143, 528.

0 I

5

.

.

.

.

I

.

.

.

10 Energy (eV)

.

I

.

.

.

.

15

Figure 3. The valence shell electron energy loss spectrum of butadiene, observed by Fridh.IZ3 The valence transitions calculated by CNDO (without C1) are shown as arrows whose heights are proportional to the calculated intensity. The orbital numbering, energies, intensities, and symmetry labels are given in Table 111. The influence of C I is discussed in the text.

0 1 . . . . 1 . . . . 1 . . . .

5

10 Energy (OW

15

Figure 4. The valence shell electron energy loss spectrum of ethylene observed by Lassettre et a1.6' The results of the CNDO calculations (no CI)are indicated. The transitions at 7.0 and 9.0 eV are of Rydberg type. The 14.4- and 16.9-eV transitions have been observed by Brion et al.Iu

molecule. (The last two orbitals have been denoted as u and u* orbitals in the above.) According to the CI calculation, state interaction shifts intensity to the higher energy transition, such that thefvalue of the 9.5-eV transition is predicted to change to 0.05 and that of the 11.2-eV transition to 0.82. This is in complete disagreement with the spectrum. We conclude that the CI matrix element is too large, and it is better to neglect the CI completely. The UV spectrum of ethyleneb1 is shown in Figure 4. The generally accepted interpretation" is that the A A* transition occurs at 7.6 eV and that the features around 7,9, and IO eV are 3s, 4s, and (5s ...) Rydbergs. Our calculation (before CI) reproduces the accepted position of the T A* transition but it also suggests that there is a u(CH) u*(CH) transition making strong contributions around 10 eV. After CI the agreement with experiment is less good. The interaction pushes down the first band to 6.64 eV and reduces its intensity tof = 0.22. The intensity goes to the second band which becomes much too intense (f 0.73) when compared to experiment. It is clear that the CI matrix element is also far too large for this molecule. In the U V spectrum of formic acid there is a strong T T * band at 8.3 eV (Figure 562) and several weak bands at higher

- -

-

-

(61) Lassettre, E. N.;Skerbcle. A.; Dillon, M.A,; Ross. K. J. J . Chcm. Phys. 1968, 48, 5066.

Lindholm et al.


I

0 I , . . . l . . . . l . .

5

10

15

. .

0

1 . . . . 1 . . . .

10

Energy (eV)

Figure 5. The valence shell electron energy loss spectrum of formic acid.62 The band at 9.0 eV is assumed to be Rydberg.12

20 Energy (eV)

30

Figure 7. The valence shell electron energy loss spectrum of acetylenes'

0

10

I . . . . I . . . . I . . . .

5

10 Energy (PV)

15

Figure 6. The valence shell electron energy loss spectrum of cyclo-

propane63compared to the CNDO calculations.

energy. Without CI the calculation is in good agreement with the observed spectrum. If CI is included there is strong interaction between the A --c A* transition and several transitions of u us type (e.g., the transitions 9 1 1 , calculated a t 9.40 eV, and 9 13, calculated at 13.24 eV). The intensity will then move to the higher energy transitions, and the f value of the A A* transition will be reduced to 0.19. The disagreement with experiment shows that the calculated matrix element for configuration interaction between a A A* transition and a u u* transition is so incorrectly large that it is better to perform the calculation completely without CI. The C1 effect in CNDO can be studied most easily in molecules where only a small number of intense transitions are observed in the experimental spectrum. We have found that butadiene, ethylene, and formic acid are particularly useful in this regard. In molecules that have more congested spectra, the calculation without CI indicates a corresponding high density of moderately intense transitions. In these cases the changes produced by the CI are small and it is difficult to evaluate whether the agreement with experiment is better before or after CI. However, the butadiene, ethylene, and formic acid results indicate that the CI does not necessarily produce better results than the calculation without CI. 46. Other Hydrocarbons. The UV spectrum of cyclopropane (Figure 663)has two very intense bands at 10.0 and 13.0 eV. The calculation reproduces these and in addition suggests there is a third transition in between which may not be observed due to

-

-

-

(62) Fridh, C. J. Chem. Soc., Foradoy Trans. 2 1978, 74, 190. (63) Fridh, C. J. Chem. Soc.. Foradoy Trans.2 1979, 75,993.

-

20 Energy (eV)

30

Figure 8. (a) The valence shell electron energy loss spectrum of bcnzene.6' The bands at 6.2 and 6.9 eV are a=-** states; all other features seem to be transitions to Rydbcrg states. (b) The vacuum-UV absorption spectrum of benzene." The intense, broad peak at 18 eV may be due to valence-type transitions (see text).

overlap. This assignment would attribute the 7.8-eV band to a Rydberg. CI impairs these results. CI must be used to treat the low-energy region of acetylene. The A A* transitions give three bands of which only the 'A, seems to have been recognized." In the high-energy region the calculation gives three bands, which are little influenced by the CI. They agree well with the observed spectrum (Figure 76s). These results (see Table IV) are an important confirmation of the electron affinity work, from which the original parameter estimation was begun. The identification of a high-energy valence excitation involving the 4u8 orbital supports Tronc's interpretation of a high-energy resonance as being associated with this orbital." CI is also necessary to treat the A A* transitions in the low-energy region of the UV spctrum of benzene. The calculated result is reasonable with the singlet transitions a t 4.9 eV (IB2"), 6.2 eV (IBlU),and 6.9 eV (lEIu)calculated at 4.90, 5.10, and 7.29 eV. (The inaccuracy for the second singlet is caused by the use of the Ohno-Klopman interaction, which for aromatics should be replaced by the Mataga interaction.) The calculation gives energies of 3.93, 4.41, and 4.89 eV for the triplets, in good agreement with the experimental values of 3.9,4.8, and 5.5 eV.% In the energy region between 7 and 14 eV (Figure 8a6'), all transitions have a negligible intensity, and all features here should be due to Rydbergs. Between 14 and 17 eV, the calculation predicts several strong a(CH) u*(CH) transitions. At higher energy, up to 22 eV, there are strong transitions to n.h. orbitals.

-

-

-

(64) Asbrink, L.; Fridh, C.; Lindholm, E. Chem. Phys. 1978, 27, 159. (65) de Souza, A. C.; de Souza, G. G. E. Phys. Reu. A 1988, 38,4488.



J

1

1

1

14

10

,

1

18

1

1

22

I

I

26

Energy (eV)

0

I

I! I

2

5

”-

Figure 11. Vacuum-UV spectra of linear alkanes.l*’

I . . . . I . . . . I . . . .

10 15 Energy (eV)

20

Figure 9. The valence shell electron energy loss spectrum of allene observed by Brion et a’!t

UV spectra of a number of linear alkanes are shown in Figure 11 and are consistent with this. The reasonable agreement between the ethane calculation and the experimental UV spectra for the other hydrocarbons indicates that the UV absorption is due mainly to u U* excitations with very little contribution from Rydberg excitation or direct ionization. Finally, we discuss methane whose spectrum is one of those plotted in Figure 11. There are only a small number of u u* transitions but the broad nature of the experimental spectrum is probably associated with a dissociative character of states involving excitation (or ionization) from the Itz orbital. 4c. Other Molecules. It has been claimedI4 that the spectra of water and ammonia only involve Rydberg states and that valence final states are not involved. However, our results (Table 1V) indicate that most of the UV spectral features of these molecules are in fact the result of valence transitions. Surprisingly, the UV spectra of many small linear molecules are not very well understood. The present results for N2and CO, calculated with CI, suggest that many of the higher energy features involve u u* excitations. All features in the UV spectra of fluoromethanes have previously been attributed to Rydberg tran~iti0ns.I~ Our calculations indicate that only the lowest energy band is of Rydberg type. and that most of the intensity arises from valence transitions. Although the results are uncertain because of the questionable reliability of the CI calculation, this has little influence on the results for the fluoromethanes. In tetrafluoromethane (Table IV) one finds good agreement between the calculated and observed energies with only the band a t 13.5 eV not being reproduced. The agreement concerning the 4t2 5tz transition lends strong support to the assignment of the corresponding 5tz EA which had been only observed in DA. The agreement for trifluoromethane and difluoromethane is also good (see Table IV). In each case there is a strong band at low energy which must be attributed to a Rydberg transition since it lies significantly below the lowest energy calculated valence transition. Since the electron affinity of CH3F is of importance for the theory of SN2reactions,’O we will look in detail at its UV spectrum. ’ At high energies our calculation predicts a very strong Sal 7al transition at 18.0 eV. This may correspond to a band at 20.0 eV (620 A), observed by Wu et aI.’l If so, this demonstrates that the calculated electron affinity of -7.1 eV for 7al is reasonable and that a smaller value is not probable. At lower energies the UV spectrum has been studied by Lassettre et al.14*72We present in Table IV the calculated spectrum without CI. The agreement is reasonable and assumes that the band observed at 11.2 eV is Rydberg 3p. This is reasonable since the shape of the 2e orbital is similar to that of a T * orbital. The reasonable agreement between calculation and experiment for the UV spectra of all these molecules indicates that this CNDO method gives a reliable description of unoccupied orbitals. In the context of our use of the UV spectra as a check on the quality of the CNDO results, it is important to note that most of the

-

-

-

I

Figure 10. Vacuum-UV spectrum of ethane.@ The broad maximum may be due to valence not Rydberg transitions.

This probably explains the maximum around 18 eV (Figure 8b‘). The valence shell electron energy loss spectrum of allene has recently been studied by Brion and co-workers (Figure gat). The calculation without C1 agrees well with the spectrum. After CI the first band is displaced to 8.36 eV, but the other bands are not influenced. The UV spectrum of ethane (Figure loa8) consists of a large number of broad overlapping bands. The calculations (Table IV) predict a number of strong transitions to closely spaced valence-type states. These transitions prabably explain the main intensity in the UV spectrum and imply that it is not necessary to invoke Rydberg transitions in order to explain the main intensity of the UV spectrum of ethane. Since nearly all orbitals are C H bonding or antibonding, the situation is similar to that in benzene in that the broad maximum appearing in the spectra of both species may originate from a band of u u* transitions. Many other hydrocarbons have similar broad spectral maxima (see Figure 1 I ) which are probably also of u u* origin. This can be understood qualitatively as follows. It is well-knowna9that the 2s level in methane broadens to a band around this energy in larger hydrocarbons. We assume that this is also true for the u(CH) and u*(CH) levels. This gives two bands which give rise to transitions which are approximately equally broad in all hydrocarbons. It follows that the spectra of all hydrocarbons will be more or less the same with a broad maximum near 16 eV. The

-

-

(66) Koch, E. E.;Otto, A. Chem. Phys. L i t . 1972, 12, 476. (67) Sodhi, R. N. S.; Brion, C. E. 1. Electron Spectrosc. 1985, 37, 1. (68) Koch, E. E.: Skibowski, M. Chem. Phys. L t r . 1971, 9, 429. (69) Pireaux, J. J.; Svensson, S.; Basilier, E.;Malmqvist, P.-A,; Gelius, U.; Caudano, R.;Siegbahn, K. Phys. Reo. A 1976, / I , 2133.

-

-

(70) Sand, P.;Bergman, J.; Lindholm, E.J . Phys. Chem. 1988,92,2139. (71) Wu, C. Y.R.;Lee,L. C.; Judge, D. L. J . Chem. Phys. 1979, 71,5221. (72) Harshbarger, W. R.; Robin, M. B.; Lassettre, E. N. J . Electron Spectrosc. 1973, I , 319.

3936 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991 TABLE I V Commrison of Calculated and Exmimental UV Swctra" calculation molecule E f exvt E butadiene 6.14 0.93 5.9 9.47 0.32 9.5 0.47 11.2 11.60 0.29 12.38 13.0 ethylene 7.29 0.57 7.6 10.0 0.42 10.47 12.0 0.45 12.96 14.4 0.26 13.38 17.42 16.9 0.32 formic acid 5.6 4.30 0.00 0.57 8.3 8.69 0.2 1 10.1 9.40 1 1.29 0.12 11.3 12.05 0.17 11.3 13.24 0.17 11.3 10.28 1.03 cyclopropane 10.0 11.33 0.50 ? 13.0 13.88 0.87 14.8 14.57 0.29 7.42 acetylene 0.00 ? 7.99 0.00 7.2 ? 9.81 0.56 14.72 13.3 0.22 15.88 15.7 0.50 17.81 18.7 0.31 benzene 3.93 3.9 4.41 4.8 4.89 5.5 4.9 4.90 0.00 0.00 6.2 5.10 7.29 2.17 6.9 14-17 large 17-22 large allene 7.06 7.2 1.61 10.89 11.3 0.2 1 0.31 13.16 14.0 ? 0.60 16.7 ethane 10.55 1.01 9.2 0.48 11.6 13.29 0.52 13.5 13.70 0.1 I 13.5 13.84 14.6 0.54 15.92 16.99 16.0 0.35 24.95 20.2 0.13 methane 0.82 11.88 10.5 13.5 0.52 15.52 19 0.34 20.92 water 9.49 0.10 9.5 (0.06) 14.50 0.21 13.0 17.04 0.30 17.7 7.46 ammonia ? 0.04 12.50 11.2 0.60 16.65 15.0 0.32 24.28 0.1 1 nitrogen 6.52 7.6 6.88 7.6 1.72 8.6 8.44 9.5 9.78 10.4 8.38 8.9 0.00 8.43 9.9 0.00 10.2 0.00 9.15 12.17 12.5 0.28 14.2 1.18 13.82 22.94 ? 0.46 co 8.1 1 0.1 1 8.3 9.32 0.00 9.6 9.89 0.00 9.8 14.02 0.98 13.7 14.06 0.16 13.2 20.77 0.21 ? 27.41 ? 0.39 16.00 0.77 15.9 16.50 0.26 21.70 21 0.77

Lindholm et al. interpretation

-

----- **

MO's 11 12 IO- 13 9 - 14 9 - 16 6-7 5-8 5-9 4-8 3-11 9 - IO 8-10 9 - 11 6-10 7 - 11 9 - 13 8,9 IO

tYPe u u* u A* u(CH) u*(CH) 2s" "2p

6.7

le"

---

14,15

4,5 6,7 4,5 6,7 6,7 4,5 6,7 2 3-8 2-9

7r

u*

u(CH) u*(CH) n2p 2s" 1.p.

A*

u* 1.p. u*(CH) 7r

7r

3e'

-

-

la; 4e' (with CI)

Ix; (with CI)

)A, (with CI) Ix: (with CI) 2u, I*, 3u, 3u, 40, 20, 'Blu (with CI) 'El, (with CI) 'B2, (with CI) 'B2, (with CI) l B l u (with CI) IEiu (with CI) u a*(CH) u u*(CC) 3e 2e 50, 2e 3e 40, 50, and 40, le le, 2e, 3a2, le, 2e, le, 3a2, 34, 3a1, 4a2, le, 4a1, h, 3% 1t2 2t2 It2 3al 2t2 3al 2b2 3a, 1b2 2b2 1b2 4al 2e 3ai le 2e 4al le 2e 2al (with CI)

---

-------

-----

--'x:

'n, 3Au (with CI) 'C;(with CI) 'nu

:2;

(with CI)

lAU (with C1)

In,

5-8

'xi (with CI) u-u* In

Ix- (with CI)

] A (with CI) (with CI)

5-8 2-8

----

In 7 I

s

4t2 le 3t2

u* u*

512

5t2

5tz



TABLE IV (Continued) ~

~~

~~

calculation

f

22.06

0.32

molecule CF3H

10.95

CFZH2

17.2 21.5 9.62 1 1.79

15.97 10.23 13.15

CH3F

18.33 a

interpretation

E

MOs

expt E 21

0.27 0.56

-----

11.8 17.5

12.4

15.5 9.3 13.2 20.0

2e 3e 2e 6al 5a1 7a1

22.1 9.4

0.8 1

0.17 0.26 0.43 0.34 0.32 0.62

7al 6e 6e 3b, 7a1

6sl 5e 3e 2bl 2bl

3t2

-

type Sal

('D")

(with CI) (with CI) (in CH2; "B") (in CH2) (1.p. on F with CI) (in CH3; "B") (in CH3) (I

-

' 6

For most molecules no C1 has been used. since we have found that CI in many cases may impair the calculated results.

excitations considered are isolated and not overlapped by other states. The reason for this is that the energies of the lower orbitals in these molecules are well distributed. The occupied orbital involved in each excitation can therefore be identified. 4d. CI in Molecular Excitation Studies. Several matrix elements, especially Ji,, Kh,and the CI matrix elements, are critical to the evaluation of the excitation spectra of molecules. In the LCAO formalism they are calculated from the one-center and twecenter electron+ectron repulsion energies. Both are strongly influenced by correlation. In 1953 Pariser and Parr studied the UV spectra of planar hydrocarbons and were able to take into account the correlation difficulties by rules for calculation of both the one-center and the two-center energies. These rules are therefore valid primarily for A x* transitions in planar hydrocarbons, including possible interactions with other A A* transitions. As an example of such calculations the UV spectrum of benzene can be mentioned, which has been discussed above. Since these rules are truly empirical, one cannot feel sure that they are applicable in other situations, where the correlation energies may be different. The first observation of such a difficulty concerned the calculation of UV spectra of aromatic molecules by semiempirical methods. It was observed that if one keeps the one-center energies unchanged, one has to change the two-center energies into the Mataga repulsion f o r m ~ l a . ~This ~ ? improves ~~ the calculated UV spectrum of benzene as mentioned above. We are not aware of any theoretical basis for this rule. The second observation seems to be our finding for butadiene, ethylene, and formic acid that the interaction between one A A* transition and one u u* transition cannot be handled by the Pariser-Parr rules, which give too strong an interaction. The correlation is thus different from that in Pariser and Parr's study. These two observations make it of interest to look for other cases in which CI studies have given unexpected results. A third observation of similar type concerns the study of shake-up bands in photoelectron spectroscopy. Such bands are common a t energies around 30 eV in hydrocarbons and are due to two-electron transitions with zero intensity. They can acquire intensity by CI, but it has been observed that the calculated CI matrix element is too large (ref 12, p 252). It was suggested that the reason is interaction with the vibrations, but a more probable reason seems now to be a special correlation situation, which requires special parameters. The shake-up studies have been carried out on acetylene and C02. A fourth observation of similar type concerns the role of shake-up bands in the formation of negative ions, especially studied by ETS (see ref 12, p 268). The shake-up configurations interact with the primarily formed negative ion and displace its energy. It has been found by comparison with experiment (ref 36, p 283) that the displacements and thus the CI matrix elements are too large. Thus we have also in this case a special correlation situation which requires special parameters. It is therefore probably better

to omit the CI procedure completely in studies of negative ion resonances. A fifth observation concerns the commonly expressed ~ p i n i o n ' ~ . ' ~ that u* orbitals may be lost due to mixing with and dissolution in the Rydberg sea. These ideas disagree with our results for butadiene, ethylene, and formic acid for which the u u* excitations are observed as well defined, not very broad bands with intensities which apparently can be calculated by use of conventional methods. We suggest that at least part of the underestimation of the importance of higher energy u* orbitals in UV spectroscopy has been the use of CI matrix elements which are far too large. With more reasonable matrix elements there should be less Rydberg-valence mixing. In summary, we stress that in quantum-chemical calculations CI should always be added. However, if the CI matrix element calculated by conventional semiempirical methods is too large, it may be better to omit the CI procedure completely. Our finding that the CI matrix elements are very strongly influenced by correlation might be of interest in ab initio calculations of CI type. Here, one tries to calculate the correlation by use of CI, but of course, it is then not possible to include the dependence of the matrix elements themselves on the correlation. Therefore, such a method could perhaps be described as a circulus vitiosus.

(73) Ellis, R. L.; Jaffe, H.H.In Semiempirical Merhods of Elecrronic Structure Calculation; Parr B Applicarions;Segal, G . A., Ed.; Plenum Press: New York, 1977; p 49. (74) Lindholm, E. J . Mol. Specfrosc. 1983, 101, 444.

(75) Brion, C. E.; Daviel, S.; Sodhi, R.N. S.; Hitchcock, A. P. Inr. Conf. X-ray Atomic Inner-Shell Phys. AIP Conf. Proc. 1982, 94, 429. ( 7 6 ) Hitchcock, A. P. Ulframicroscopy 1989, 28, 165. Hitchcock, A. P. Phys. Scr. 1990, T31, 159.

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5. Core-Excitation Spectra Core-excitation spectra are dominated by one-electron excitations to virtual valence orbitals, typically of x* or u* character in simple molecules. Only K-shell (1s) spectra are considered in this work, with most emphasis placed on carbon 1s excitation which occurs around 300 eV. The excitation energy can be supplied by electron impact (inner-shell electron energy loss spectroscopy, ISEELS)75or photoabsorption. To date most carbon Is spectra have been obtained by ISEELS.i8*76 In early core-excitation studies (those prior to 1984) the importance of core u* excitations was not realized and thus many early interpretations invoked core Rydberg transitions or multielectron processes to explain many of the spectral features. More recently it has been generally recognized that the spatially localized core orbital has greatest overlap with compact virtual valence orbitals. In many cases, particularly larger molecules or those with numerous electronegative atoms, there is little or no evidence for core Rydberg transitions. The evolution of the spectral interpretation from Rydberg-dominated to valence-dominated has been associated in part with the development of a simple local-bond model of core excitation which has been expressed in terms of semiquantitative relationships between bond lengths and core u* energies.lS-I7 Our use of the CNDO method offers an additional means to test the hypothesis that core excitation spectra are dominated by transitions to unoccupied valence orbitals. To calculate the core excitation energies we first calculate the core ion state; i.e., we remove one electron from the Is orbital of atom A and let it go to infinity. The corresponding experimental

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3938 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991 binding energy is obtained from X-ray photoelectron spectroscopy; for a hydrocarbon the C 1s IP is about 291 eV. We now have a molecule in which the core charge of atom A has increased by one unit. Instead of acetylene HCCH we have HNCH+ (Umethod of equivalent cores"). We now let the electron go from infinity to A* or u*. The released energy is the electron affinity EA of, e.g., HNCH+, and the total core-excitation energy is then (core IP - EA). This equivalent ionic core virtual orbital (EICVOM) method of calculating core excitation has been used extensively in both ~ e m i e m p i r i c a l ' ~and . ~ ~a.b~initio ~ ~ o r k . ' ~ JIf~our theoretical method is able to give good EA'S of, e.g., HCCH, it will probably give equally good EA'S of HNCH+, since the reorganization energies can be expected to be equal. The CNDO calculation is performed in the following way. We calculate, e.g., HNCH and use in the input the same number of occupied orbitals as in HCCH. This means that our calculation concerns the positive ion HNCH+. In the output the eigenvalues of the occupied orbitals lack meaning. In the experimental work the energy difference between the XPS IP and the excitation energy is usually denoted "term value" T instead of EA. The calculated core-excitation energies and intensities are given in Table 111 in comparison with the experimental term values. In this table the specific core excitation is indicated by identifying the Z 1 ionic species, e.g., H2NO+ indicates C 1s excitation in formaldehyde. The transition probability of a 1s M O transition is large if the virtual valence molecular orbital (MO) (T* or a*) has a large contribution from a 2p atomic orbital (AO) on the core excited atom. The relative intensity of a Is MO transition can then be approximated as the sum of the squared 2p A 0 coefficients in that Moa7* It is possible that neigboring atoms should also be considered in the calculation which would reduce the calculated intensity due to destructive orbital overlap. We note that, although this approach to determining core excitation intensities is an essentially atomic one, it does not imply that transitions to orbitals containing, e.g., large 2s character have negligible intensity. In fact the intensity can be estimated from the dipole allowed (e.g., Is 2p) intensity at the core-excited atom, but the general question of allowed or forbidden character for any given transition is best treated by group theory with consideration of the full molecular symmetry. 5a. Core Excitation: Evaluation of the CNDO Results. It is important to determine whether these CNDO calculations give meaningful core excitation energies and intensities. As with the EA and UV energies, the answer to this question depends not only on the quality of the calculation but also on the reliability of the spectral assignments. The Is T* excitations in molecules like ethylene, butadiene, N2, and benzene are observed as intense narrow bands at low energy and their interpretation is unequivocal. The calculated values in Table 111 agree reasonably well with the measurements. Thus our method of calculation appears to be satisfactory for Is A* excitations. The situation regarding Is u* excitations is less clear. In part the present work may help to clarify spectral assignments by identifying features previously un- or misassigned. Thus, in certain cases, the energies of various experimental features indicated in Table 111 correspond to features for which different assignments were given in the original presentations of the spectra. The experimental term values of Is u* excitations in a number of simple molecules, where the spectral assignments are well-documented (CH4, C2H2,C2H4,C,H6, N2, NH3, HCN, CO, and C02),are plotted against the calculated energies in Figure 12. I t is clear from this plot that, although there is reasonable

+

15-

Core Excitation kea*

I

/

-10 :z/

/ /

/

,

I

I

I

I

I

I

-1 (eV) Figure 12. Plot of core-excitationterm values (for 1s -.u* transitions only) versus CNDO calculated virtual orbital energies for the equivalent ionic core virtual orbital species [(Z+ 1)+]. The atom underlined is core excited. See Table 111 for numerical values. The dashed line is a guide to the eye while the dotted line indicates unit slope.

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NEXUS

Po-

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-

(77) Lindholm, E . J . Chem. Phys. 1986,85, 1484. It must be mentioned that in a semiempirical theory the 'method of equivalent cores" can be implemented in two ways, which are slightly different. One can remove one Is electron,12which means that in, e.g., acetylene, carbon parameters are used, or one can change C into N and thus use nitrogen parameters. (78) Ishii, I.; Hitchcock, A. P. J . Chem. Phys. 1987, 87, 830. (79) Schwarz, W.H. E.;Chang, T. C.; Seeger, U.; Hwang, K. H. Chem. Phys. 1981, 117, 73. (80) Schwarz, W.H. E.;Seeger, U.; Seeger, R. Chem. Phys., submitted

for publication.

LAi, , 280

290

300

, , , 310

j

320

Photon En*W (.v)

Figure 13. Near-edge X-ray absorption fine structure spectra (NEXA B ) of highly oriented polyethylene.*' In the top spectrum the ex-

perimental geometry is such that the X-ray electric vector is parallel to the film and thus to the polyethylene chains. Orbitals populated by electric dipole transitions lie along the chain direction (e.g., u * ( C C ) ) . In the bottom spectrum the electric vector is orientated perpendicular to the chains. In this direction transitions to u*(C-H) are emphasized. In the context of the present calculations, polyethylene may be compared to the central CH2 group in propane or n-pentane. match between experiment and calculation for bound and lowenergy (Is,u*) states, the energies of the high-energy u* resonances embedded in the 1s ionization continua are systematically underestimated. Thus the present results are perhaps of use in identifying low-lying 1s u* states but are not reliable for interpreting the continuum structure. A tentative explanation for these difficulties has been given above in section 2. Since n.h. orbitals are localized on the heavy atoms in the molecule, the 2p A 0 coefficients are often large, giving rise to intense Is excitations to such orbitals. Several examples are presented in Table I11 or discussed below, e.g., in acetylene, ethylene, benzene, naphthalene, trimethylamine. In general, while the agreement with experiment (taking into account some reassignments) is reasonable for Is u* energies below 5 eV, the agreement is poor for those at higher energy. These are invariably excitations to u*(n.h.) orbitals in unsaturated molecules with short bond lengths. One question which has received considerable attention recently is the origin of sharp structures generally observed around 288 eV, 2-4 eV below the core ionization thresholds of molecules containing C-H bonds. In the case of species with CH, groups

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I

0 I

I

I

I

I

T'

2

I

1

I

6

I

8

TI

I

1

0

Electron energy (eV) 0

Figure 14. Electron transmission spectra of some cyclic hydrocarbon^.^^

a strong band appears in the experiments with a term value of about 3 eV. In, for example, ethane, this was originally assigned to Is 3p Rydberg transitions but more recently it has been described as a Is u*(CH) excitation?'J2 Our calculated results for saturated hydrocarbons (Table 111) predict a reasonably intense 1s u*(CH) transition around this term value. This supports assignment of this band to a valence rather than a Rydberg core-excited state. This interpretation is supported by X-ray absorption studies of oriented polyethylene,s' which are in reasonable agreement with our calculated results for the CH2group in propane and n-pentane. In these studies the angular dependence (Figure 13) unambiguously identifies the first peak as due to u*(H-C-H) and the second peak as due to u*(C-C). The calculated separation of the u*(C-H) and u*(C-C) orbitals for propane is 2.5 eV, in reasonable agreement with the measured energy difference of 5 eV. Similarly the u*(C-H)/u*(C-C) separation for core excitation a t the central CHI group in npentane is calculated to be 2.2 eV.

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6. Orbitals of n.h. Type in Cyclic Hydrocarbons: Comparison of CNDO, ETS, and Core Excitation Although electron transmission studies of saturated hydrocarbons have usually been unsuccessful, Howard and stale^^^ have succeeded in determining electron affinities of four cyclic hydrocarbons (Figure 14) as mentioned above. We have calculated cyclopropane and planar cyclobutane, cyclopentane, and cyclohexane in order to find the n.h. orbitals. The planar conformations are useful, since this minimizes orbital mixing, although calculations with nonplanar conformations give nearly identical results. We list here the calculated energies of the n.h. orbitals. The negative ion resonance energies from ETS experiments are given in parentheses. With regard to the labeling, t* orbital is built up from carbon 2p orbitals in the tangential direction. The s and ss orbitals are formed from carbon 2s, and are nondegenerate and degenerate, respectively. Cyclopropane: 4.6 eV (5.3 eV) and 8.7 eV (8.2 eV). The first, la;, is o f t * type and the second, 5e', is of ss type. Cyclobutane: 6.2 and 6.4 eV (5.8 eV) and 8.9 eV (9.3 eV). The first, 4e,, is of ss type, the second, la2*, o f t * type and the third, 4b2,, of s type. Cyclohexane: 7.3 and 8.8 eV (experimental band from 7.0 to 8.5 eV). The first is of ss type and the second o f t * type. The experimental band at 4.1 eV cannot be explained. Thus we find that the energy of the t* orbital changes considerably from 4.6 eV in cyclopropane to 8.8 eV in cyclohexane and that the calculated values reproduce the trend in the observed negative ion resonance energies. In the experimental electron affinity spectra these bands are very broad. In core ex~itarion,8~ cyclobutane and cyclohexane have a spectrum with one band at (81)

StBhr, J.; Outka, D. A.; Baberschke, K.;Arvanitis, D.; Horsley, J. A.

Phys. Rev. 1987, 836. 2916. (82) Hitchcock. A. P.; Ishii, 1. J . Elecrron Specrrosc. Relaf. Phemm. 1987, 42, 11.

2

4

6

8

1

0

ELectron energy (eV)

Figure 15. Electron transmission spectra of neopentane,8' trimethylamine, and dimethyl ethers5and methyl fluoride*6*w

about 3 eV and a broad maximum which starts a t about 1 eV. Cyclopropane differs, having two bands, the first wpker than the second. This difference can be explained in the following way. According to the CNDO calculations of all four molecules, the first band in the core-excitation spectrums3 is associated with a C-H antibonding ?r orbital at the CH2group. The calculated term value is about 2 eV in all four molecules. The t* orbital is also given by the calculations but its term value changes from 3.0 eV in cyclopropane to 0.2 eV in cyclohexane. This corresponds to the changes in the electron affinity spectrum. Therefore, we conclude that both orbitals appear in the core-excitation spectrum of cyclopropane, but the t* orbital is hidden in the broad u*(C-C) maximum and only the CH2band can be seen in cyclobutane and cyclohexane. This is in agreement with the original assignments which were supported by measurements of the polarization dependence of the spectra of oriented monolayers and by MS-Xa

calculation^.^^ 7. Orbitals of n.h. Type in Some Saturated Compounds We have looked for other molecules in which experimental evidence for n.h. orbitals may be present. Giordan et al.84*8shave studied the ETS of neopentane, trimethylamine, and dimethyl ether in order to understand the ETS of substituted benzenes. They found very broad features with midpoint around 6 or 7 eV (Figure 15). Our calculations (Table 111) show that in all three molecules the highest virtual orbitals are of n.h. type. In neopentane, C(CH3)4,orbital 25 with calculated EA = -7.0 eV is localized on 2s in the central carbon and orbitals 29, 30, and 3 1 with calculated EA = -7.6 eV on 2p,, 2py, and 2p, in the same atom. The experimental EA is about -6.0eV. In trimethylamine the calculated EA'S are -7.3 eV (2s on nitrogen) and -8.4 eV (2p, and 2py on nitrogen). The experimental value is about -5.0 eV. In dimethyl ether the calculated EA'S are -7.4 and -8.8 eV and the experimental value is about -6.0 eV. Methyl fluoride is a similar case. It has four virtual orbitals, one of which is of n.h. type, for which our calculation gives EA = -7.1 eV. In methyl fluoride OlthofP observed a broad feature from 5 to 9 eV (Figure 15) which we attribute to the u* orbital. Our calculations for methyl fluoride are also in agreement with the UV spectrum, as discussed earlier, and with the experimental core-excitation spectra (Table 111). In the carbon K-shell spectrum, band 4 at -3.25 eV (Figure 16) and the band at -3.5 eV in the fluorine K-shell spectrum are interpreted as due to Is u* excitations. This is in good agreement with the CNDO core-excitation calculation, which indicates that the orbital or-

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(83) Hitchcock, A. P.; Newbury, D. C.; Ishii, 1.; StBhr, J.; Horsley, J. A,; Redwing. R. D.; Johnson, A. L.; Sette, F. J . Chem. Phys. 1986, 85, 4849. (84) Giordan, J. C.; Moore, J. H. J . Am. Chem. SOC.1983, 105, 6541. (85) Giordan, J. C.; Moore, J. H.; Tossell, J. A.; Kaim, W. J . Am. Chem.

Soc. 1985.107, 5600. ( 8 6 ) Olthoff, J. K. Ph.D. Thesis, University of

Maryland, 1985.

3940 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991 CHp

1

1

1

288

1

a*

l

290

Energy (eV)

1

CH3a

I

l

I

292

Figure 16. Core-excitation electron energy loss spectrum of methyl fluoridesg The CNDO EICVOM transitions are shown as arrows whose height is proportional to the calculated intensity (square of c2pcoefficient from Table 111).

dering is strongly affected by the core hole relaxation. In the isoelectronic molecules CH3F, CH30H, CH3NH2,and CH3CH3, the CH3 groups are similar. The C 1s excitation calculations for all molecules predict a strong CH3 a band and a weaker CH3 a band (see Table 111). The difference in energy of these orbitals is 1.8 eV for ethane and about 2.4 eV for the other three molecules. These orbital energies seem to be independent of the substituent in R-CH3 molecules, as is expected from the similarity of their carbon 1s ~ p e c t r a . ~ ~ *Thus ~ ~ - these * ~ results suggest an alternate interpretation of the C 1s spectrum of CH3F, namely, to assign band 1 and band 6 as due to CH3 group orbitals and band 2 or 4 to the a*(C-F) n.h. orbital. Previ0usly,8~bands 1,4, and 6 have been given a Rydberg assignment while band 2 has been attributed to a*(C-F), although this assignment has been debated.1s.80*89*90 The CH3F results are of importance for the (87) Wight, G. R.; Brion, C. E. J. Electron Specrrosc. Relar. Phenom. 1974, 4, 25. (88) Sodhi, R. N. S.; Brion, C. E. J . Electron Spectrosc. Relar. Phenom. 1985. 36. 187. -- . (89) Hitchcock, A. P.; Brion, C. E. J . Elecfron Specrrosc. Relat. Phenom. 1979, 17, 139. (90) Benitez, A.; Moore, J. H.; Tossell, J. A. J . Chem. Phys. 1988, 88, 6691. (91) Mathur, D. J . Phys. B 1980, 13, 4703. (92) Barbarito, E.; Basta, M.; Callicchig, M.; Tessari, G. J . Chem. Phys. 1979. 71, 54. (93) Tanaka, H.; Kubo, M.; Onodura, N.; Suzuki, A. J . Phys. B 1983,16, 2861. (94) Rohr, K. J . Phys. B 1980, 13,4897. (95) Dressler, R. A. Dissertation, Freiburg, Switzerland, 1985. (96) Hitchcock, A. P.; Brion, C. E.J . Electron Specrrosc. Relar. Phenom. 1977, IO, 317. (97) Hitchcock, A. P.; Brion, C. E. J . Electron Specrrosc. Relar. Phenom. 1981, 22, 283. (98) Sanche, L.; Schulz, G.J. J . Chem. Phys. 1973, 58,479. (99) Van Veen, E. H. Chem. Phys. Lerr. 1976, 41, 535. (100) Robin, M. B.; Ishii, I.; McLaren, R.; Hitchcock, A. P. J . Electron Specrrosc. 1988, 47, 53. (101) Sodhi, R. N. S.; Brion, C. E. J . ElecfronSpecrrosc.Relat. Phenom. 1985, 37, 1. (102) Horsley, J. A.; StBhr, J.; Hitchcock, A. P.; Newbury, D. C.; Johnson, A. L.; Sctte, F. J . Chem. Phys. 1985, 83, 6099. (103) Trone, M.; Azria, R.; LeCoat, Y . J . Phys. E 1980, 13, 2327. (104) Mathur, D.; Hasted, J. B. Chem. Phys. 1976, 16, 347. (105) Hitchcock, A. P.; Brion, C. E. J. Electron Specrrosc. Relat. Phenom. 1980, 18. I . (106) Ben Arfa, M.; Tronc, M. J . Phys. B 1985, 18, L629. (107) Tronc, M.;Malegat, L. In Phorophysics and Phorochemisrry above 6 eK Lahmani, F., Ed.;Elsevier: Amsterdam, Netherlands, 1985; p 203. (108) Hitchcock, A. P.; Brion, C. E. Chem. Phys. 1979, 37, 319. (109) Seng, G.; Linder, F. J . Phys. E 1976, 9, 2539. ( I 10) Tronc, M.; Azria, R.; Paineau, R. J . Phys. Leu. 1979, 40, L323. ( I 1 I ) Wight, G.R.; Brion, C. E. J . Electron Specrrosc. Relat. Phenom. 1974, 3, 191. ( 1 12) Van Veen, E. H. Chem. Phys. Lerr. 1976, 41, 540. ( I 13) Hitchcock, A. P.; Brion, C. E. J . Electron Specrrosc. Relar. Phenom. 1980. 19, 231.

--.--.

Lindholm et al.

0

5

10

15 20 25 30 -EA (eV) Figure 17. Plot of experimental electron affinities versus CNDO-calculated virtual orbital energies (see Table 111 for numerical values). The dashed line is a guide to the eye while the dotted line indicates unit slope.

theory of chemical reactions of SN2 type.'O In a recent paper Benitez, Moore, and TossellWestimated the electron affinity of the a* orbital in methyl fluoride as -1 eV from an empirical correlation of core-excitation and EA energies in the methyl halides. On the basis of this they attributed the broad feature around 6-7 eV in the ETS spectrum (Figure 15) as an experimental artifact. It is interesting to note that their observation of a strong correlation between ETS and core-excitation energies (consisting of an average shift of 6.3 eV in the haloethenes) is supported by the present calculations in which the curves correlating CNDO-EA and CNDO-core excitation are of a similar shape and shifted relative to each other by about 8-9 eV (compare Figures 12 and 17). It is important to point out that the contribution of the hydrogen 1s A O s to the CH3 group orbitals in methyl fluoride depends considerably upon the choice of the CNDO parameters. With some parameters we have found that mixing takes place between the two virtual orbitals in CH3F of a l symmetry, since they have very similar energies (see Table 111). The n.h. characteristic is thus masked. The reverse procedure, demixing, may possibly take place when the negative ion is formed. It is therefore possible that n.h. orbitals for several molecules are more easily observed in transmission experiments than otherwise expected. 8. Summary Although A* orbitals in many molecules are well-known from experimental and theoretical studies of electron affinities and UV spectra, the a* orbitals, especially their energies, have been largely unknown. We have therefore tried to create a semiempiricalSCF method, which can be used to estimate electron affinities, UV transitions, and core-excitation energies. It has been possible to (114) Hitchcock, A. P.; Brion, C. E. J . Phys. E 1981, 14, 4399. ( 1 15) Deleted in proof. ( I 16) Sodhi, R. N. S.; Brion, C. E.; Cavell, R. G. J . Electron Specrrosc. 1984, 34, 373. ( I 17) Wight, G. R.; Brion, C. E. J. Electron Spectrosc. Relat. Phenom. 1974, 4, 327. ( I 18) Hitchcock, A. P. Private communication. ( 1 19) Chiu, N. S.; Burrow, P. D.; Jordan, K . D. Chem. Phys. Leu. 1979, 68, 121. (120) Paddon-Row, M. N.; Rondan, N. G.; Houk, K.N.; Jordan, K. D. J . Am. Chem. Soc. 1982, 104, 1143. (121) McLaren. R.; Clark, S. A. C.; Ishii, I.; Hitchcock, A. P. Phys. Reo. A 1987, 36, 1683. ( I 22) Robin, M. B.; Ishii, 1.; McLaren, R.; Hltchcock, A. P. J . Electron Spectrosc. Relat. Phenom. 1988, 47, 53. (123) Asbrink, L.; Fridh, C.; Lindholm, E. Chem. Phys. Len. 1977, 52, 72. (124) Ibuki, T.; Cooper, G.; Brion, C. E. Chem. Phys. 1989, 129, 295. ( I 25) Schoen, R. I. J . Chem. Phys. 1962, 37, 2032.

J. Phys. Chem. 1991,95, 3941-3946 obtain a parametrization which seems capable of giving both occupied and unoccupied orbital energies which can be related to several spectroscopies. We have used the new CNDO method to study the spectra of many molecules and thus in this way extended the basis for the parametrization. Since the method is heavily parametrized on experimental data it is probably best considered as a systematic procedure for correlating the properties of different molecules. For example, we have obtained approximate values for the electron affinities of ethane mainly by use of an electron affinity of acetylene and UV bands in the spectra of ethylene and butadiene. Previously, u* orbitals have been discussed very little, probably since the experimental studies are very difficult and since ab initio calculations seem to be too difficult. Instead, Rydberg orbitals have been used to explain UV spectra, core-excitation spectra, and details in attachment processes. On the basis of the present

3941

results we suggest that some of these explanations need to be revised. Our work will probably be useful as part of the foundation of a future semiempirical MO method.25 As discussed in ref 25 the parametrization should be performed in two steps. The first step concerns the orbital energies of occupied and unoccupied orbitals and the second step, the total energy (heat of formation). Until now it has been impossible to carry out the first step in a reliable way due to lack of data for the u* orbitals. This work should be considered as a pilot study directed toward a unified treatment of states involving high-energy u* orbitals.

Acknowledgment. We are grateful to Prof. Peter Stilbs for valuable help and to Prof. Delano P. Chong and Prof. Adam P. Hitchcock for stimulating discussions and assistance with revisions to the manuscript.

Hydrides of Alo- and Borogallane(4), AlGaH, and BGaH, Jerzy Leszczyiiski and Koop Lammertsma* Department of Chemistry, University of Alabama at Birmingham, UAB Station 21 9 PBS, Birmingham, Alabama 35294 (Received: August IS. 1990)

The potential energy surfaces of the mixed gallium hydrides AIGaH, and BGaH, have been studied by ab initio molecular orbital theory at the correlated MP2 level by using a Huzinaga valence triple{basis set augmented with d-polarization functions. The salt-like tridentate forms are the global minima. Their endothermic dissociation energies with respect to the neutral MH and M'H3 monomers are estimated. Hydrogenations of BGaH, and AIGaH, to the corresponding hexahydrides are calculated to be endothermic by only 2.5 and 10.8 kcal/mol. The Ga+[AlH,]- tridentate form is ca. IO kcal/mol more stable than ionic AI+[GaH4]-. The structural and bonding similarities and differences between the aluminum- and gallium-containing systems are discussed. The ionic and covalent nature of bonding in the HF/3-21G* geometries is examined with Bader's electron density theory of atoms in molecules.

Introduction The recent syntheses and IR characterizations by Downs and co-workers of digallane(6), Ga2H6,1 its ( N - C ~derivative,2 )~ and the mixed borogallane(6) BGaH63 have demonstrated the accessibility of simple gallium hydrides. Their observations have spurred a theoretical interest in these gallanes and the corresponding alanes. Ab initio studies have been reported on the structures, binding energies, and electronic properties of the diborane-like species Ga2H6,) Ga2H2C12,SA12H6,) AIBH6,6.7 AlGaH6,' and BGaH6.6 The objectives of this study are ( I ) to evaluate the even smaller and still elusive mixed hydrides of alogallane(4), AIGaH,, and borogallane(rl), BGaH,, (2) to make comparisons with the previously theoretically studied B2H4,* AI2H4: and Ga2H4,10and (3) ( I ) Downs, A. J.; Goode, M. J.; Pulham, C. R. J . Am. Chem. SOC.1989, I l l , 1936. (2) Goode. M. J.; Downs, A. J.; Pulham, C. R.; Rankin, D. W. H.; Robertson, H. E. J . Chem. SOC.,Chem. Commun. 1988, 768. (3) Pulham, C. R.; Brain, T. M.; Downs, A. J.; Rankin, D. W. H.; Robertson, H. E. J . Chem. Soc., Chem. Commun. 1990, 177. (4) (a) Lammertsma, K.;Lcszczydski, J. J. Phys. Chem. 1990. 94, 2807. (b) Liang, C.; Davy, R. D.; Schaefer, H. F., 111. Chem. fhys. Lett. 1989,159, 393. (c) Duke, 8. J. THEOCHEM, to be published. (5) (a) Lammertsma, K.;Leszczyfiski, J. J . Chem. Soc., Chem. Commun. 1989, 1005. Instead of the reported 458 cm-', the 33-cm-' frequency is IR active. (b) Duke, 8. J.; Hamilton, T. P.; Schaefer, H. F., 111. Private communication. (6) Van,der Wocrd, M. J.; Lammertsma, K.; Duke, B. J.; Schaefer, H. F., 111. Submitted for publication. (7) (a) Barone, V.; Minichino, C. Theor. Chim. Acta 1989, 76, 53. (b) Barone, V.; Minichino, C.; Lelj, F.; RUM, N. J . Comput. Chem. 1988, 9, 518. (c) Barone, V.; Dolcctti, G.; Lelj, F.; RUM, N. Inorg. Chem. 1981, 20, 1687.

to estimate the dehydrogenation energies of the recently studied mixed h e ~ a h y d r i d e s . ~Experimental ,~,~ studies have reported on the tetrahalides B2X4,11 Al2X4,I2Ga2X!,13 In2X4114 and the mixed AlInX, (X = Br, CI, I).', Spectroscopic data suggest the halides (8) (a) Mohr, R. R.; Lipscomb, W. N.Inorg. Chem. 1986,25, 1053. (b) Vincent, M. A.; Schaefer, H. F., 111. J . Am. Chem. Soc. 1981, 103, 5677. (c) McKee, M. L.; Lipscomb, W. N. Ibid. 1981, 103, 4673. (d) Dill, J. D.; Schleyer, P. v. R.; Pople, J. A. Ibid. 1975, 97, 3402. (9) (a) Lammertsma, K.; Giiner, 0. F.; Drewes, R. M.; Reed, A. E.; Schleyer, P. v. R. Inorg. Chem. 1989, 28, 313. (b) Zakzhevskii, V. G.; Charkin, 0. P. Chem. fhys. Lett. 1982, 90, 117. (c) Charkin. 0. P. The Stability and Structure of the Gaseous Inorganic Molecules, Radicals, and Ions; Nauka: Moscow, 1980. (IO) Lammertsma, K.; Lcszczybski, J. J . fhys. Chem., 1990, 94, 5543. (11) (a) Danielson, D. D.; Hedberg, K. J . Am. Chem. Soc. 1979, 101, 3199. (b) Danielson, D. D.; Patton, J. V.; Hedberg, K. Ibid. 1977,99,6484. (c) Durig, J. R.; Thompson, J. W.; Witt, J. D.; Odom. J. D. J . Chem. fhys. 1973, 58, 5339. (d) m o m , J. D.; Saunders, J. E.;Durig, J. R. Ibid. 1972, 56, 1643. (e) Ryan, R. R.; Hedberg, K. Ibid. 1%9,50,4986. (f) Atoji, M.; Wheatley, P. J.; Lipscomb, W. N. Ibid. 1957, 27, 196. (g) Trafanos, L.; Lipscomb, W. N. Ibid. 1958, 28, 54. (12) Olah, G. A.; Farooq, 0.;Farnia, S.M. F.; Bruce. M. R.; Clouet, F. L.; Morton, P. R.; Prakash, 0. K.S.;Stevens, R. C.; Bau, R.;Lammertsma, K.;Suzer, S.;Andrews, L. J. Am. Chem. Soc. 1988, 110, 3231. (13) (a) HBnle, W.; Simon, A.; Gerlach, G . Z . Naturforsch. 1987,428, 546. (b) Gerlach, G.; Henle, W.; Simon, A. Z . Anorg. Allg. Chem. 1!W2,486, 7. (c) For thermodynamics of Ga,CI, (x = 1, 2; y = 1-6) systems, see: Bernard, C.; Chatillion, C.; Ait-Hou, A.; Hillel, R.; Monteil, Y.;Bouix, J. J . Chem. Thermodyn. 1988, 20, 129. (d) Beamish, J. C.; Wilkinson, M.; Worrall, 1. J. Inorg. Chem. 1978, 17, 2026. (e) Beamish, J. C.; Boardman, A.; Small, R. W. H.; Worrall, I. J. Polyhedron 1985, 4, 983. ( f ) Hillel, R.; Ait-Hou, A.; Berthet, M. P.; Bouix, J. J . Raman Specrrosc. 1987, 18, 265. (g) Garton, 0.;Powel, H. M. J . Inorg. Nucl. Chem. 1957, 4, 84. (14) Randloff, P. L.; Papatheodorou, G . N. J . Chem. Phys. 1980, 72,992.

0022-3654/91/2095-394l%02.50/0 0 1991 American Chemical Society

Energies of .sigma.* orbitals - The Journal of Physical Chemistry (ACS

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