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Configuration interaction intensity borrowing in photoelectron spectroscopy
Volume.6,
number 3
CHEMICAL PWsl&
CONFIGURATION IN
Institut
INTERACTION PHOTOELECTRON
+: .. ,*
LETTERS
INTENSITY
1 August 1970
BORROWING
SPECTROSCOPY
J. C. LORQUET and C. CADET de Chimie de Z’Unixrsit& de iX?ge, Sa?f Ttintan: 84000,
Li2ge.
Belgium
Received 26 May 1970
The purpose of this work is to examine the range of validity of the selection ruIe which, in photoion-
ization experiments and photoelectron spectroscopy. forbids transitions to ionic states whose electronic configuration differs from that of the ground state of the neutral molecule by more than one molecular
-orbital. This rule is shown to constitute a convenient first approximation only. If configuration interaction is taken into account, other transitions may becomo allowed. Calculations have been performed in the case of the N20+ ion: the agreement with experiment is very satisfactory.
Sincq the interaction behveen a molecule and a photon is described by a one-electron operator, only states wEch, in the simple molecular orbital description, are characterized by an electronic configuration differing from that of the neutral molecule by one molecular orbital, will normally be observed in photoelectron spectroscopy or in photoionization experiments. This situation has given rise to the usual language, according to which photoelectron spectroscopy measures ionization potentiaIs which correspond to the removal of electrons from different orbftals. However, many of the electronic states of a molecular ion have to be described by a configuration which differs from that of the ground state of the neutral molecule by two molecular orbital6 or more (i. e., ionization of one electron and simuItaneous excitati3n of another electron into an unoccupied orbital). These states are norma.!ly undetectable in photoelectron spectroscopy and in photoionization experiments, because photons cannot induce two-electron transitions. However, states of this kind, wkch we propose to call “douare by far the most numerous bly-orthogonal”, especially at high energies, and they will play a role in the determination tii the subsequent evolution of the ion. If, instead of the simple molecular orbital description of electronic states, configuration interaction is taken into account, transitions to doubly excited states of the molecular ion become allowed, although usually with a smaller ‘intensiQ. An example of this situation was found by, .198
.
._
.--
Dixon and Hull in the case of oxygen [l]. They predicted the existence of a higher 211u state of 05 at approximately 22 eV and with an intensity of approximately one-third that of the a%$, state at 16S eV. This was in agreement with experiment. In connection with a study of the electronic St&es of the N20’ ion, we performed a configuzation interaction calculation including four 2Il states. Three of them derived from the configuration (~1)~ @~)2 (~72)~(?r#, and the fourth derived from configuration (771)s (cr,)2 (~2)~. Since the electronic configuration of the neutral molecule is (7r1)4 (0~)~ (7~2)~, we see that intensity will derive from the fourth configuration. Ths matrix elements were calculated in three approximations: a) an ab initio calculation using a minimal basis set of STO’s. b) an NDDO-Qpe calculation [2] with semiempirical parametrization of tbe integrals. The variation with the internuclear distance of the bicentric integrals was approximated by a fourthdegree polynomial. c) Same a.&(b), but with a Mataga-Nishimoto [3] relation for the bicentric integrals. Table 1 gives the calculated energies afterconfiguration interaction. Method (a) is known to exaggerate the energy intervals, as noted by Diton‘and Hull and others [5]. The correspon$ing intensities (cakulat$d by taking the square of the coefficient of the fourth configu-
ratLou) are given in table 2. After the caIculation was made, Price
and
Volume 6, number 3
CHEMICALPHYSICS LETTERS
Exp. intens.
tensity borrowing from the A 22;+ state at 16.4 eV might also explain the appearance of some of them, but we did not make calculations for this case. Intensity borrowing by configuration interaction is expected to be important in the high energy region of photoelectron spectra. The more complex and unsymmetrical +he molecule is, the more likely this effect. More specifically, we think that effects of this kind mig’.S provide an explanation for the appearance of broad and diffuse bands, sometimes reported as doubtful, in the high-energy region photoelectron spectra, such as those reported, e.g., in H2S around 18.21 eV. These bands might arise from a redistribution of intensities among a great number of electronic states. A report on the electronic states of N20f will be published elsewhere.
0.70 0.08 0.06 0.16
The authors are very much indebted to Professor Price and Dr. Potts for exxunining the photoelectron spectrum at their request.
Table 1
Energies of four zil states of N O+, calculated in three different approximations (a. b, c7 , and experimental (in eV)
Calc. a
Calc.
16.7 19.0 20.4 32.3
b
CaLc. c
Exp.
t;.;)
‘:9”.Z)
zo:2 23.6
21:6 25.8
18.2 19.5 22.5 24.3
Table 2 Relative intensities of the photoelectron bands of the four 2lI states of N,O+, calculated in three different approximations (a, b, c), and experimental Exp. en. !ev) 18.2 19.5 22.5 24.3
Calculated intensities Appr. a Appr. b Appr. c 0.66 0.12 0.06 0.15
0.62 0.08 0.01 0.29
0.82 0.00 0.01 0.17
1 August 1970
Potts provided us with a peotoelectron spectrum of N20 obtained using 304 A radiation in advance of publication [4]. Besides the intense bands at 18.2 and 20.1 eV, one detects three additional weak and broad bands at energies given in the last column of tabIe 1, and with relative intensities given in table 2. The agreement is very satisfactory, and demonstrates the effect of intensity borrowing by configuration interaction. However, this assignment of the additional weak bands is not the only one possible. A similar mechanism invoiving in-
REFERENCES [I] R.N. Dixon and S. E. Hull. Chum. Phys. Letters 3 (1969) 367. [2] J.A.Pople. D.P.Santry and G. A.Segal. J. Chem. Phys. 43 (1965) S129. [3] M. Mataga and K. Nishimoto.
Z. Physik. Chem. (Frankfurt} 13 11957) 140. [4] W. C. Price and A. W. Potts. private communication. (51 M. I. Al Joboury and D. W. Turner. J. Chem. Sot. (l964) 4434; P. Natalis and J. E. Collin, J. Chim. Phys. 67 (19X) 69: J. DeIwiche and P. Natatis. to be pltbiished.
199 :
:
number 3
CHEMICAL PWsl&
CONFIGURATION IN
Institut
INTERACTION PHOTOELECTRON
+: .. ,*
LETTERS
INTENSITY
1 August 1970
BORROWING
SPECTROSCOPY
J. C. LORQUET and C. CADET de Chimie de Z’Unixrsit& de iX?ge, Sa?f Ttintan: 84000,
Li2ge.
Belgium
Received 26 May 1970
The purpose of this work is to examine the range of validity of the selection ruIe which, in photoion-
ization experiments and photoelectron spectroscopy. forbids transitions to ionic states whose electronic configuration differs from that of the ground state of the neutral molecule by more than one molecular
-orbital. This rule is shown to constitute a convenient first approximation only. If configuration interaction is taken into account, other transitions may becomo allowed. Calculations have been performed in the case of the N20+ ion: the agreement with experiment is very satisfactory.
Sincq the interaction behveen a molecule and a photon is described by a one-electron operator, only states wEch, in the simple molecular orbital description, are characterized by an electronic configuration differing from that of the neutral molecule by one molecular orbital, will normally be observed in photoelectron spectroscopy or in photoionization experiments. This situation has given rise to the usual language, according to which photoelectron spectroscopy measures ionization potentiaIs which correspond to the removal of electrons from different orbftals. However, many of the electronic states of a molecular ion have to be described by a configuration which differs from that of the ground state of the neutral molecule by two molecular orbital6 or more (i. e., ionization of one electron and simuItaneous excitati3n of another electron into an unoccupied orbital). These states are norma.!ly undetectable in photoelectron spectroscopy and in photoionization experiments, because photons cannot induce two-electron transitions. However, states of this kind, wkch we propose to call “douare by far the most numerous bly-orthogonal”, especially at high energies, and they will play a role in the determination tii the subsequent evolution of the ion. If, instead of the simple molecular orbital description of electronic states, configuration interaction is taken into account, transitions to doubly excited states of the molecular ion become allowed, although usually with a smaller ‘intensiQ. An example of this situation was found by, .198
.
._
.--
Dixon and Hull in the case of oxygen [l]. They predicted the existence of a higher 211u state of 05 at approximately 22 eV and with an intensity of approximately one-third that of the a%$, state at 16S eV. This was in agreement with experiment. In connection with a study of the electronic St&es of the N20’ ion, we performed a configuzation interaction calculation including four 2Il states. Three of them derived from the configuration (~1)~ @~)2 (~72)~(?r#, and the fourth derived from configuration (771)s (cr,)2 (~2)~. Since the electronic configuration of the neutral molecule is (7r1)4 (0~)~ (7~2)~, we see that intensity will derive from the fourth configuration. Ths matrix elements were calculated in three approximations: a) an ab initio calculation using a minimal basis set of STO’s. b) an NDDO-Qpe calculation [2] with semiempirical parametrization of tbe integrals. The variation with the internuclear distance of the bicentric integrals was approximated by a fourthdegree polynomial. c) Same a.&(b), but with a Mataga-Nishimoto [3] relation for the bicentric integrals. Table 1 gives the calculated energies afterconfiguration interaction. Method (a) is known to exaggerate the energy intervals, as noted by Diton‘and Hull and others [5]. The correspon$ing intensities (cakulat$d by taking the square of the coefficient of the fourth configu-
ratLou) are given in table 2. After the caIculation was made, Price
and
Volume 6, number 3
CHEMICALPHYSICS LETTERS
Exp. intens.
tensity borrowing from the A 22;+ state at 16.4 eV might also explain the appearance of some of them, but we did not make calculations for this case. Intensity borrowing by configuration interaction is expected to be important in the high energy region of photoelectron spectra. The more complex and unsymmetrical +he molecule is, the more likely this effect. More specifically, we think that effects of this kind mig’.S provide an explanation for the appearance of broad and diffuse bands, sometimes reported as doubtful, in the high-energy region photoelectron spectra, such as those reported, e.g., in H2S around 18.21 eV. These bands might arise from a redistribution of intensities among a great number of electronic states. A report on the electronic states of N20f will be published elsewhere.
0.70 0.08 0.06 0.16
The authors are very much indebted to Professor Price and Dr. Potts for exxunining the photoelectron spectrum at their request.
Table 1
Energies of four zil states of N O+, calculated in three different approximations (a. b, c7 , and experimental (in eV)
Calc. a
Calc.
16.7 19.0 20.4 32.3
b
CaLc. c
Exp.
t;.;)
‘:9”.Z)
zo:2 23.6
21:6 25.8
18.2 19.5 22.5 24.3
Table 2 Relative intensities of the photoelectron bands of the four 2lI states of N,O+, calculated in three different approximations (a, b, c), and experimental Exp. en. !ev) 18.2 19.5 22.5 24.3
Calculated intensities Appr. a Appr. b Appr. c 0.66 0.12 0.06 0.15
0.62 0.08 0.01 0.29
0.82 0.00 0.01 0.17
1 August 1970
Potts provided us with a peotoelectron spectrum of N20 obtained using 304 A radiation in advance of publication [4]. Besides the intense bands at 18.2 and 20.1 eV, one detects three additional weak and broad bands at energies given in the last column of tabIe 1, and with relative intensities given in table 2. The agreement is very satisfactory, and demonstrates the effect of intensity borrowing by configuration interaction. However, this assignment of the additional weak bands is not the only one possible. A similar mechanism invoiving in-
REFERENCES [I] R.N. Dixon and S. E. Hull. Chum. Phys. Letters 3 (1969) 367. [2] J.A.Pople. D.P.Santry and G. A.Segal. J. Chem. Phys. 43 (1965) S129. [3] M. Mataga and K. Nishimoto.
Z. Physik. Chem. (Frankfurt} 13 11957) 140. [4] W. C. Price and A. W. Potts. private communication. (51 M. I. Al Joboury and D. W. Turner. J. Chem. Sot. (l964) 4434; P. Natalis and J. E. Collin, J. Chim. Phys. 67 (19X) 69: J. DeIwiche and P. Natatis. to be pltbiished.
199 :
: