- Email: [email protected]
Correlation between ionization potentials and MO energy levels
Votume 41, number 1
1 JuSy 1976
CHEMICAL PHYSiCS LEXTERS
and
C.R. BRUNDLE and N.A. KUEBLER Bell Telephone Laboratories. Mutray Chili, New &mey 07973. fJS;I Received 3 September 1975 Revised manuscript received 19 March 1976 The vertical iordzaticn potentials from 9-22 eV for ethylene, cycfoprppene, cyclobutene and methylene ~e~apropa~e are correlated with t%e ab initio 431G molecular orbital energies by -IP = 0.772 Ehfo - 2.22 with an rms error of 0.2 eV. The result is related to the reorganization and correlation energies.
The principal connection between experiment and moiecular orbital theory arises from photoelectron spectroscopy and the use of Koopmans’ theorem f t 1. Tim complements of the molecular orbital energy levels are found to roughly correspond to the observed ionization potentials [2) . The use of a scaling factor has been suggested for improving the correspondence [3], but good fits have not been achieved for polyatomic moiecuies **. We bave obtained He1 and HeI1 photoelectron spectra for a number of hydrocarbons and have carried out ab initio molecular orbital calculations for these compounds [5]. The availability of these data make it possible to re-examine the correlation. The spectra of ethylene, cyclopropene, cyclobutene and methylenecyclopropane were sufficiently well resolved so that all the ionization potentials through 22 eV could be identified.
-rP
= 0.772
Eni0
-
2.22,
wifh an rms error of 0.22 eV. Since the range of ionization potentials was 15 eV, the error is quite small. The prediction of the photoelectron spectra of larger alkenes
23.0
* Remch *
sponsoxest by the Air Force Office of Scientific Remch, Air Farce Systems Command, USAF, under Grant No. AFUSR-72-2239. B&i et al. [4] observed a linear coxreIation between the calculated STO-3G MO energies and the first four ioniwtion potentials of alIene, vinylacetylene, divinylacetylene acd bu&&iene ;(--IP = 0.634 ITMO - 4.63). They did not determine whether this cotrelaticm would fit the higher iotiation potentials.
If the vertical ionization potent&Is for these compounds are plotted against the complements of the calculated orbital energies (4-3 1G basis set) a rem~kab~y good fit is found (eg. 1). The correlation line is given by
11.0
3.0
3.0
11.0
13.0
15.0
17.0
19.0
21.0
23-O
25.0
2
4-316 MO ENERGIES
Fig. f. Comiation beiween observed vertical i05~tion potentials (ev) and calculated MO energies (-eW for afkenes.
37
Volume 41, number 1
CHEMICAL PHYSICS LETTERS
which havs overlapping bands using the above correlation is quite satisfactory f.51. An important part of the correlation is the non-zero intercept. This is not an artifact derived from the basis set used sins-e the vertical W’s of ethylene f6] are eorrelated with the near Hartree-Fock limit 6-31 G* orbital energies 171 by -fP = 0.768 E&,
- 2.47,
with an rms error of 0.06 eV. The error is close to the uncertainty in the measurement of the ionization potentials. These results show that it is possible to satisfactorily estimate ionization potentials of hydrocarbons knowing the orbital enera ievels. The major problem now is to calculate the slope and intercept. It is well recognized that Koopmans’ theorem depends on cancellation of $&hereorganization enerw (~5~) and the change in correlation energy (AEC) on going from the neutral molecule to the doublet ion [8] : -IP=E,,,
+Ex
+AEc_
The present correlation is -IP = AE,,,
t B.
Thus EMO
=
-(ER
f &‘&(1-A)
+ B/(1-A).
The B/( 1-A) term is the energ-- at which Ehro = -fP (x 9 eV for the 4-3 1G or larger basis sets) and E, + LSC = 0. The sum of ER and &SC appears to be pro. portiond to E&to and appears not to be markedly dependent on either the structure of the molecule or the type of AO’s which form a given MO. It is likely that the correlation will change if one or more carbons are
38
1 July 1976
repiaced by anothar atom such as oxygen. This will be investigated. The reorganization effects have been calculated for the lowest energy cations derived from ethylene, acetyiene and formaldehyde f9] ) and the correlation effects have been calculated for the ion derived from acetylene [IO]. For the iatter, I& is -1.3 eV, 5EC is 1.5 eV and the sum is relatively small. The ionization potential, 11.4 eV, lies close to the point in our correlation at which E, -f-AEC should be small. Unfortunately, no similar calculations appear to have been made for the cations formed at higher ionization potentials for which the above sum should be considerabiy larger.
References [l] T. Koopmans, Physica 111934) 104. [2] D.W- Turner, C. Bakar. A.D. Baker and CR. Brundle, Molecuhu photoelectron spectroscopy (Wiley, New York, 1970). f3] H. Basch, M.B. Robin, N.A. Kuebler, C. Baker and D.W_ Turner, J. Chem. Phys. 5 1 (1969) 52. [4] F. Brogli, E. Heilbronner, E. Kloster-Jensen, A. Schmelzer, A.S. Manocha, J.A. Pople and L. Radom, Chem. Phys. 4 (1974) 107. [51 K. B. Wiberg, G.B. Ellison, C.R. Brundle and N.A. Kuebler, to be published. Ifa G.R. Branton, D.C. Frost, T. Makita, CA. McDowell and LA. Stenhouse, J. Chem. Phys. 52 (1970) 802. 171 W-A. Lathan, L. Radom, P.C. Hariharan, W-J. Hehre and J.A. Pople, Fortschr. Chem. Forsch. 40 (1973) 1. tS1 W-G. Richards, Intern. J. Mass Spectrom. Ion Phys. 2 (1969) 419. r9] S-Y. Chu, I. Ozkan and L. Goodman, J. Chem. Phys. 60 (1974) 126% El01 A.J. Duben, L. Goodman, H.& Pamuk and 0. Sinano$$x, Theoret. Chim. Acta 30 (1973) 177.
1 JuSy 1976
CHEMICAL PHYSiCS LEXTERS
and
C.R. BRUNDLE and N.A. KUEBLER Bell Telephone Laboratories. Mutray Chili, New &mey 07973. fJS;I Received 3 September 1975 Revised manuscript received 19 March 1976 The vertical iordzaticn potentials from 9-22 eV for ethylene, cycfoprppene, cyclobutene and methylene ~e~apropa~e are correlated with t%e ab initio 431G molecular orbital energies by -IP = 0.772 Ehfo - 2.22 with an rms error of 0.2 eV. The result is related to the reorganization and correlation energies.
The principal connection between experiment and moiecular orbital theory arises from photoelectron spectroscopy and the use of Koopmans’ theorem f t 1. Tim complements of the molecular orbital energy levels are found to roughly correspond to the observed ionization potentials [2) . The use of a scaling factor has been suggested for improving the correspondence [3], but good fits have not been achieved for polyatomic moiecuies **. We bave obtained He1 and HeI1 photoelectron spectra for a number of hydrocarbons and have carried out ab initio molecular orbital calculations for these compounds [5]. The availability of these data make it possible to re-examine the correlation. The spectra of ethylene, cyclopropene, cyclobutene and methylenecyclopropane were sufficiently well resolved so that all the ionization potentials through 22 eV could be identified.
-rP
= 0.772
Eni0
-
2.22,
wifh an rms error of 0.22 eV. Since the range of ionization potentials was 15 eV, the error is quite small. The prediction of the photoelectron spectra of larger alkenes
23.0
* Remch *
sponsoxest by the Air Force Office of Scientific Remch, Air Farce Systems Command, USAF, under Grant No. AFUSR-72-2239. B&i et al. [4] observed a linear coxreIation between the calculated STO-3G MO energies and the first four ioniwtion potentials of alIene, vinylacetylene, divinylacetylene acd bu&&iene ;(--IP = 0.634 ITMO - 4.63). They did not determine whether this cotrelaticm would fit the higher iotiation potentials.
If the vertical ionization potent&Is for these compounds are plotted against the complements of the calculated orbital energies (4-3 1G basis set) a rem~kab~y good fit is found (eg. 1). The correlation line is given by
11.0
3.0
3.0
11.0
13.0
15.0
17.0
19.0
21.0
23-O
25.0
2
4-316 MO ENERGIES
Fig. f. Comiation beiween observed vertical i05~tion potentials (ev) and calculated MO energies (-eW for afkenes.
37
Volume 41, number 1
CHEMICAL PHYSICS LETTERS
which havs overlapping bands using the above correlation is quite satisfactory f.51. An important part of the correlation is the non-zero intercept. This is not an artifact derived from the basis set used sins-e the vertical W’s of ethylene f6] are eorrelated with the near Hartree-Fock limit 6-31 G* orbital energies 171 by -fP = 0.768 E&,
- 2.47,
with an rms error of 0.06 eV. The error is close to the uncertainty in the measurement of the ionization potentials. These results show that it is possible to satisfactorily estimate ionization potentials of hydrocarbons knowing the orbital enera ievels. The major problem now is to calculate the slope and intercept. It is well recognized that Koopmans’ theorem depends on cancellation of $&hereorganization enerw (~5~) and the change in correlation energy (AEC) on going from the neutral molecule to the doublet ion [8] : -IP=E,,,
+Ex
+AEc_
The present correlation is -IP = AE,,,
t B.
Thus EMO
=
-(ER
f &‘&(1-A)
+ B/(1-A).
The B/( 1-A) term is the energ-- at which Ehro = -fP (x 9 eV for the 4-3 1G or larger basis sets) and E, + LSC = 0. The sum of ER and &SC appears to be pro. portiond to E&to and appears not to be markedly dependent on either the structure of the molecule or the type of AO’s which form a given MO. It is likely that the correlation will change if one or more carbons are
38
1 July 1976
repiaced by anothar atom such as oxygen. This will be investigated. The reorganization effects have been calculated for the lowest energy cations derived from ethylene, acetyiene and formaldehyde f9] ) and the correlation effects have been calculated for the ion derived from acetylene [IO]. For the iatter, I& is -1.3 eV, 5EC is 1.5 eV and the sum is relatively small. The ionization potential, 11.4 eV, lies close to the point in our correlation at which E, -f-AEC should be small. Unfortunately, no similar calculations appear to have been made for the cations formed at higher ionization potentials for which the above sum should be considerabiy larger.
References [l] T. Koopmans, Physica 111934) 104. [2] D.W- Turner, C. Bakar. A.D. Baker and CR. Brundle, Molecuhu photoelectron spectroscopy (Wiley, New York, 1970). f3] H. Basch, M.B. Robin, N.A. Kuebler, C. Baker and D.W_ Turner, J. Chem. Phys. 5 1 (1969) 52. [4] F. Brogli, E. Heilbronner, E. Kloster-Jensen, A. Schmelzer, A.S. Manocha, J.A. Pople and L. Radom, Chem. Phys. 4 (1974) 107. [51 K. B. Wiberg, G.B. Ellison, C.R. Brundle and N.A. Kuebler, to be published. Ifa G.R. Branton, D.C. Frost, T. Makita, CA. McDowell and LA. Stenhouse, J. Chem. Phys. 52 (1970) 802. 171 W-A. Lathan, L. Radom, P.C. Hariharan, W-J. Hehre and J.A. Pople, Fortschr. Chem. Forsch. 40 (1973) 1. tS1 W-G. Richards, Intern. J. Mass Spectrom. Ion Phys. 2 (1969) 419. r9] S-Y. Chu, I. Ozkan and L. Goodman, J. Chem. Phys. 60 (1974) 126% El01 A.J. Duben, L. Goodman, H.& Pamuk and 0. Sinano$$x, Theoret. Chim. Acta 30 (1973) 177.